The Extragalactic Distance Scalepeople.physics.tamu.edu/lmacri/thesis.pdf · The Extragalactic Distance Scale The Cepheid Distance Scale and its Application to the Absolute Calibration

The Extragalactic Distance Scale

The Cepheid Distance Scale and its Application to the Absolute

Calibration of the Luminosity – Linewidth Relation

A thesis presented

by

Lucas Matıas Macri

to

The Department of Astronomy

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the subject of

Astronomy

Harvard University

Cambridge, Massachusetts

September 2001

©c 2001, by Lucas Matıas Macri

All Rights Reserved

ii

The Extragalactic Distance Scale

The Cepheid Distance Scale and its Application to the Absolute

Calibration of the Luminosity – Linewidth Relation

Advisor: John P. Huchra Lucas Matıas Macri

Abstract

This Thesis presents research into several topics related to the Extragalactic

Distance Scale; in particular, the Cepheid Period – Luminosity Relation and the

Luminosity – Linewidth relation for spiral galaxies.

The primary distance indicator of choice in the Local Supercluster is the

Cepheid Period – Luminosity Relation. While its absolute calibration is still

uncertain at the 10% level, it can yield precise relative distances. I present the

discovery of Cepheids in, and the determination of distances to, two galaxies in

the Local Supercluster: M33 and NGC 2841. I also present a test of the standard

extinction law in other galaxies using near-infrared observations of Cepheids.

One of the most-widely used secondary distance indicators for extragalactic

work is the luminosity – linewidth relation of spiral galaxies, commonly referred

to as the Tully – Fisher relation. I present a complete and consistent database of

optical and infrared magnitudes of spiral galaxies that are suitable for the absolute

calibration of that relation, and I perform that calibration in the RIHK bands.

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iv

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Citations to Previously Published Work . . . . . . . . . . . . . . . . . . . xvii

1 Introduction and Summary 1

1.1 Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Cepheid Distance Scale . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 A historical introduction to Cepheid variables . . . . . . . . . 2

1.2.2 A modern introduction to Cepheid variables . . . . . . . . . . 8

1.3 The Tully-Fisher relation . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 A Cepheid distance to M33 21

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 Observations and data reduction . . . . . . . . . . . . . . . . . . . . . 23

2.3 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.1 Initial Processing . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.2 Photometry of template images . . . . . . . . . . . . . . . . . 27

2.3.3 Photometry of individual frames . . . . . . . . . . . . . . . . . 28

2.3.4 Determination of aperture correction coefficients . . . . . . . . 28

v

2.3.5 Standard star observations and photometric solutions . . . . . 30

2.3.6 Photometric comparisons . . . . . . . . . . . . . . . . . . . . . 32

2.3.7 Artificial star tests . . . . . . . . . . . . . . . . . . . . . . . . 35

2.4 The star catalog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.5 Variable search and classification . . . . . . . . . . . . . . . . . . . . 42

2.5.1 Previously-known variables in M33 . . . . . . . . . . . . . . . 74

2.6 A Cepheid Distance to M33 . . . . . . . . . . . . . . . . . . . . . . . 75

2.6.1 The P-L relation of LMC Cepheids . . . . . . . . . . . . . . . 79

2.6.2 Extinction corrections . . . . . . . . . . . . . . . . . . . . . . 81

2.6.3 Blending bias . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

2.6.4 The metallicity dependence of the P-L relation . . . . . . . . . 94

2.6.5 The distance to the LMC . . . . . . . . . . . . . . . . . . . . 97

2.6.6 An absolute distance to M33 . . . . . . . . . . . . . . . . . . . 99

3 A Cepheid distance to NGC 2841 101

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.2 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . 102

3.3 Photometry and Calibration . . . . . . . . . . . . . . . . . . . . . . . 103

3.4 The Cepheids found in NGC 2841 . . . . . . . . . . . . . . . . . . . . 111

3.5 Period-Luminosity Relations and Distance Moduli . . . . . . . . . . . 113

3.5.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

3.5.2 Distance moduli . . . . . . . . . . . . . . . . . . . . . . . . . . 133

3.5.3 Metallicity correction . . . . . . . . . . . . . . . . . . . . . . . 136

3.5.4 Error Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

4 Infrared observations of extragalactic Cepheids 143

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

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4.2 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . 145

4.2.1 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

4.2.2 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 146

4.3 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

4.3.1 Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

4.3.2 Absolute photometric calibrations . . . . . . . . . . . . . . . . 149

4.3.3 Photometric recovery tests . . . . . . . . . . . . . . . . . . . . 152

4.3.4 Photometry checks . . . . . . . . . . . . . . . . . . . . . . . . 153

4.4 The Cepheid sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

4.4.1 Sample selection and identification . . . . . . . . . . . . . . . 157

4.4.2 Period-Luminosity relations . . . . . . . . . . . . . . . . . . . 174

4.4.3 Observed distance moduli . . . . . . . . . . . . . . . . . . . . 174

4.5 Blending effects in M101 Inner . . . . . . . . . . . . . . . . . . . . . . 175

4.6 Consistency of reddening determinations . . . . . . . . . . . . . . . . 191

4.6.1 Predicted relation between E(V–I) and E(V–H) . . . . . . . . 191

4.6.2 Observed relation . . . . . . . . . . . . . . . . . . . . . . . . . 192

4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

5 Optical and infrared observations of Tully-Fisher calibrators 197

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

5.2 Optical observations and data reduction . . . . . . . . . . . . . . . . 199

5.3 Infrared observations and data reduction . . . . . . . . . . . . . . . . 201

5.4 Galaxy photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

5.4.1 Surface photometry measurements . . . . . . . . . . . . . . . 204

5.4.2 Photometry results and external comparisons . . . . . . . . . 212

5.5 21-cm linewidths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

6 The absolute calibration of the luminosity–linewidth relation 219

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6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

6.2 The calibrator sample . . . . . . . . . . . . . . . . . . . . . . . . . . 221

6.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

6.4 An application to 2MASS data . . . . . . . . . . . . . . . . . . . . . 227

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

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List of Figures

1.1 Light and radial velocity curves of δ Cephei . . . . . . . . . . . . . . 4

1.2 P-L relation of SMC Cepheids . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Evolutionary track of a 7M� star . . . . . . . . . . . . . . . . . . . . 9

1.4 P-L tracks for Cepheids of different masses . . . . . . . . . . . . . . . 14

1.5 The original B- and H-band line width-luminosity relations . . . . . . 16

2.1 Location of DIRECT M33 fields . . . . . . . . . . . . . . . . . . . . . 24

2.2 Mosaic of DIRECT M33 fields . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Histogram of seeing values in our frames . . . . . . . . . . . . . . . . 29

2.4 Growth curve corrections . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.5 Test of the internal consistency of our photometry . . . . . . . . . . . 34

2.6 Test of the external consistency of our photometry . . . . . . . . . . . 36

2.7 Artificial star tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.8 Cumulative luminosity functions . . . . . . . . . . . . . . . . . . . . . 40

2.9 Color-magnitude diagram of 56950 stars in M33 . . . . . . . . . . . . 41

2.10 Phase coverage as a function of period . . . . . . . . . . . . . . . . . 43

2.11 Representative Cepheid light curves . . . . . . . . . . . . . . . . . . . 46

2.12 Representative eclipsing binary light curves . . . . . . . . . . . . . . . 47

2.13 Representative miscellaneous variable light curves . . . . . . . . . . . 48

2.14 Color-magnitude diagram of 682 variables in M33 . . . . . . . . . . . 72

2.15 Observed I-band P-L relation for all Cepheids . . . . . . . . . . . . . 73

2.16 LMC Cepheid P-L relations . . . . . . . . . . . . . . . . . . . . . . . 80

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2.17 Interstellar extinction curves . . . . . . . . . . . . . . . . . . . . . . . 83

2.18 Determination of the extinction towards a Cepheid . . . . . . . . . . 83

2.19 Effect of blends on Cepheid colors . . . . . . . . . . . . . . . . . . . . 84

2.20 Blending data for 91 Cepheids in our sample . . . . . . . . . . . . . . 87

2.21 V and I P-L relations of 61 Cepheids in M33 . . . . . . . . . . . . . . 90

2.22 Distribution of ∆µ0 vs. P for 61 Cepheids with V & I data . . . . . . 91

2.23 Distribution of ∆µ0 vs. P for 20 Cepheids with B, V & I data . . . . 93

2.24 Distribution of ∆µ0 vs. r for 20 Cepheids with B, V & I data. . . . . 96

3.1 Ground-based image of NGC 2841 . . . . . . . . . . . . . . . . . . . . 105

3.2 Mosaic of the WFPC2 field of view of NGC 2841 . . . . . . . . . . . . 106

3.3 Medianed images of the four WFPC2 chips . . . . . . . . . . . . . . . 114-117

3.4 Individual finding charts for the variables . . . . . . . . . . . . . . . . 118

3.5 V and I light curves for the variables . . . . . . . . . . . . . . . . . . 119-123

3.6 Color-magnitude diagram for the stars detected in our images . . . . 124

3.7 Observed differential luminosity functions . . . . . . . . . . . . . . . . 125

3.8 V-band P-L relation for the selected Cepheids in our sample . . . . . 134

3.9 I-band P-L relation for the selected Cepheids in our sample . . . . . . 135

3.10 Distribution of Leo Cloud & Spur galaxies . . . . . . . . . . . . . . . 141

4.1 Growth curves for the NICMOS bandpasses . . . . . . . . . . . . . . 150

4.2 Photometric recovery tests . . . . . . . . . . . . . . . . . . . . . . . . 154-155

4.3 External photometry comparison . . . . . . . . . . . . . . . . . . . . 159

4.4 Astrometric selection of candidates . . . . . . . . . . . . . . . . . . . 161

4.5 Color-color selection of candidates . . . . . . . . . . . . . . . . . . . . 162-163

4.6 Images of the fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164-169

4.7 Individual finding charts . . . . . . . . . . . . . . . . . . . . . . . . . 170-171

4.8 Near-IR P-L relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 176-181

4.9 Optical P-L relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 182-186

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4.10 Simulated M101 Inner fields . . . . . . . . . . . . . . . . . . . . . . . 188

4.11 P-L relations from simulated M101 Inner fields . . . . . . . . . . . . . 190

4.12 Correlation between color excesses in our fields . . . . . . . . . . . . . 195

5.1 BVRI surface brightness profiles . . . . . . . . . . . . . . . . . . . . . 207

5.2 HK surface brightness profiles . . . . . . . . . . . . . . . . . . . . . . 208

5.3 Disk scale lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

5.4 Extrapolation from last isophote . . . . . . . . . . . . . . . . . . . . . 210

5.5 Sky surface brightness . . . . . . . . . . . . . . . . . . . . . . . . . . 211

5.6 21-cm profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

6.1 Near-infrared luminosity–linewidth relations . . . . . . . . . . . . . . 224

6.2 Optical luminosity–linewidth relations . . . . . . . . . . . . . . . . . 225

6.3 Ursa Major RIK luminosity–linewidth relations . . . . . . . . . . . . 228

6.4 Luminosity–linewidth relations for 20 mag/ut′′ magnitudes . . . . . . 229

6.5 Luminosity–linewidth relations for the Coma and A1367 clusters . . . 231

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xii

List of Tables

2.1 Photometric solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 Photometry comparisons . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3 Artificial star test results . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.4 Cepheids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49-61

2.5 Eclipsing Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62-63

2.6 Miscellaneous variables . . . . . . . . . . . . . . . . . . . . . . . . . . 64-71

2.7 M33 Classical variables . . . . . . . . . . . . . . . . . . . . . . . . . . 76-78

3.1 HST Observations of NGC 2841 . . . . . . . . . . . . . . . . . . . . . 104

3.2 WFPC2 Zeropoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

3.3 Secondary standard stars in NGC 2841 . . . . . . . . . . . . . . . . . 109

3.3 Secondary standard stars in NGC 2841 . . . . . . . . . . . . . . . . . 110

3.4 Variables discovered in NGC 2841 . . . . . . . . . . . . . . . . . . . . 112

3.5 Individual V band photometric measurements . . . . . . . . . . . . . 126-130

3.6 Individual I band photometric measurements . . . . . . . . . . . . . . 131-132

3.7 Error Budget for the Cepheid Distance to NGC 2841 . . . . . . . . . 137

3.8 Galaxies with Cepheid Distances in the Leo Cloud & Spur . . . . . . 139

4.1 Log of observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

4.2 Photometry apertures . . . . . . . . . . . . . . . . . . . . . . . . . . 150

4.3 Results of the photometric recovery tests . . . . . . . . . . . . . . . . 156

4.4 Secondary standards in the IC 1613 field . . . . . . . . . . . . . . . . 158

4.5 Cepheid magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . 172-173

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4.6 Observed H, I and V distance moduli . . . . . . . . . . . . . . . . . 187

4.7 Observed J and K distance moduli . . . . . . . . . . . . . . . . . . . 188

4.8 Mean color excesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

5.1 Cameras used in the observations . . . . . . . . . . . . . . . . . . . . 200

5.3 Inclination data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

5.4 Photometric data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

5.5 Photometric data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

5.6 Linewidth data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

6.1 Calibrator data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

6.2 Fit results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

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Acknowledgments

I would like to acknowledge my Thesis Advisor, John Huchra, for his guidance

over the past six years, and for letting me carry out my research activities in an

independent way. That independence helped me grow and mature as a scientist,

and it is greatly appreciated.

I would also like to acknowledge many collaborators and colleagues for their

help and guidance, including Kris Stanek, Dimitar Sasselov, Guillermo Torres and

Chris Kochanek at CfA; Jeremy Mould at NOAO; Robert Kennicutt at Steward

Observatory; Shoko Sakai at UCLA; Peter Stetson at DAO; Wendy Freedman,

Barry Madore and Eric Persson at Carnegie; and Paul Schechter at MIT.

An important part of graduate school are the relationships one establishes

with other students. I am grateful to Hector Arce, for his friendship since our

first day at Harvard and to Gregory Sobczak, for being a great office mate and

putting up with me for three years. I also want to thank Pauline Barmby, David

Charbonneau, Saurabh Jha and Scott Ransom for their comaraderie.

I would also like to thank to my parents Alicia & Eduardo, for their love,

support and constant encouragement over the past three decades; to my sisters

Carolina & Constanza and my brother Mariano, for their constant love and

friendship; to my extended family, for remembering me in spite of the 9,000 km.

between us; and to my life-long friends, Santiago & Fernando.

Finally, I would like to thank my wife Gloria for her constant love and support

during the past eight years and the decades to come.

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xvi

Citations to Previously Published Work

Chapter 2 contains material from:

“The DIRECT Project: Catalogs of Stellar Objects in Nearby Galaxies.

I. The Central Part of M33”, L.M. Macri, K.Z. Stanek, D.D. Sasselov,

M. Krockenberger & J. Kaluzny, Astronomical Journal 121, 861 (2001).

“DIRECT distances to nearby galaxies using detached eclipsing

binaries and Cepheids. VI. Variables in the fields M33A and M33B”,

L.M. Macri, K.Z. Stanek, D.D. Sasselov, M. Krockenberger &

J. Kaluzny, Astronomical Journal 121, 870 (2001).


“The Discovery of Cepheids and a New Distance to NGC 2841

Using the Hubble Space Telescope”, L.M. Macri, P.B. Stetson,

G.D. Bothun, W.L. Freedman, P.M. Garnavich, S. Jha, B.F. Madore &

M.W. Richmond, Astrophysical Journal 559, 243 (2001).


“HST/NICMOS observations of extragalactic Cepheids. I. Photometry

Database and a Test of the Standard Extinction Law.”, L.M. Macri,

D. Calzetti, W.L. Freedman, B.K. Gibson, J.A. Graham, J.P. Huchra,

S.M.G. Hughes, B.F. Madore, J.R. Mould, S.E. Persson & P.B. Stetson,

Astrophysical Journal 549, 721 (2001).


“A Database of Tully-Fisher Calibrator Galaxies”, L.M. Macri,

J.P. Huchra, S. Sakai, J.R. Mould & S.M.G. Hughes”, Astrophysical

Journal Supplement Series 128, 461 (2000).

xvii

I dedicate this Thesis to my parents,

Alicia & Eduardo, and to my wife, Gloria.

xviii

Chapter 1

Introduction and Summary

1.1 Structure of this thesis

This thesis contains research into two areas of the Extragalactic Distance Scale:

• The determination of Cepheid distances to spiral galaxies in the Local

Supercluster (Chapters 2 and 3), and a test of the methodology commonly

used to correct these distances for the effects associated with the scattering

of light by dust in the interstellar medium (Chapter 4).

• Optical and near infrared observations, and the resulting surface photometry

measurements and determinations of total magnitudes for spiral galaxies with

existing Cepheid distances (Chapter 5), that are suitable for the absolute

calibration of the luminosity – linewidth relation (Chapter 6).

The two halves can be read separately from each other; however, the second

subject relies on Cepheid distances such as those derived in the first half of the

Thesis. Brief introductions to these two areas of research are presented below.

1

2 Lucas Matıas Macri

1.2 The Cepheid Distance Scale

1.2.1 A historical introduction to Cepheid variables

The knowledge that some stars exhibit changes in their brightness may date back

to humankind’s distant past. The flux of β Persei, the sixty-third brightest star in

the sky, drops to 30% of its maximum every ∼ 3 days. This star is named “Algol”,

meaning “Demon Star” in Arabic, which suggests that this civilization knew about

its peculiar behavior. The first variable star known to Western civilization was o

Ceti, whose variability was discovered in 1596 by Fabricius. β Persei’s variability

was noticed in 1669 by Motanari, and within a few years, three more variable

stars were known: η Carinae (by Halley in 1677), χ Cygni (by Kirch in 1687)

and R Hydrae (by Maraldi in 1704). After a long hiatus, R Leonis was found to

be variable by Koch in 1782. With the exception of β Persei, all other stars are

semi-regular variables with long-term periodicities.

John Goodricke was born in 1764 to an aristocratic family in Yorkshire,

England. He was found to be deaf at an early age, and sent to a school for the “deaf

and dumb” in Scotland. He was later enrolled in Warrington Academy, a progressive

Unitarian theological seminary, where he was introduced to astronomy. By 1781

he was back in Yorkshire, living with his parents, and had met a 28-year old man

named Ed Pigott, whose father had built one of three existing private observatories

in England, located near to the Goodricke home. A scientific collaboration ensued

between the two young men, and by November 1782 they started observations

of β Persei. Goodricke found it to be periodic, and presented his results to the

Royal Society in May 1783. Following confirmation of the periodicity a year later,

he was awarded the “Copley Medal” for the most significant discovery in science

of the year. He also discovered a second Algol-like system, β Lyrae, around the

same time, and proposed that Algol’s unequal minima were due to the transit of a

planet.

Starting on October 19, 1784 and continuing until June 28, 1785, Goodricke

made observations of δ Cephei on an almost daily basis. He found the star

The Extragalactic Distance Scale 3

was variable and had a period of “5 days, 8 hours, 37 1/2 minutes” (Goodricke

1786), but unlike β Persei and β Lyrae, its light curve did not exhibit narrow,

deep minima, but rather a sharp rise followed by a slow decay and a pronounced

minimum (see the top panel of Figure 1.1 for a modern version of the light curve of

δ Cephei from Moffet & Barnes 1984). Soon thereafter, Pigott discovered that η

Aquilae was variable and that it had a similar light curve. For his contributions to

astronomy, Goodricke was elected as a Fellow of the Royal Society in April of 1786,

but died later that month of pneumonia, likely contracted from prolonged exposure

to cold winter nights during the second season of observations of δ Cephei.

Other stars with photometric variations similar to δ Cephei and η Aquilae

were discovered during the nineteenth century, and by the end of that century, the

advent of photographic plates allowed the study of their radial velocity curves.

The first one to be obtained was that of δ Cephei, reported in the first issue of the

Astrophysical Journal by Belopolsky (1894) (see the bottom panel of Figure 1.1 for

modern version of this curve from Bersier et al. 1994). Fifteen years later, fourteen

Cepheids had been studied spectroscopically (Duncan 1909), and the favored

explanation for the flux and velocity variations involved a binary system, albeit of

a very peculiar nature: the size of the semi-major axis of the system was of the

order of R�, and the unseen secondary star had a very small mass function, around

2.5 × 10−3. Once the parallaxes of some Cepheids were measured, it was found

that the “primary stars” of these systems had radii of ∼ 5R� and luminosities of

∼ 103L�, making the binary star hypothesis untenable. Shapley (1914) presented

the aforementioned facts as evidence for the dismissal of the binary-star hypothesis

and stated that:

“... [t]he explanation that appears to promise the simplest solution of

most, if not all, of the Cepheid phenomena is founded on the rather

vague conception of periodic pulsations in the masses of isolated stars.

The vagueness of the hypothesis lies chiefly in our lack of knowledge

of the internal structure of stellar bodies, and not in the difficulty of

explaining the observed facts if once we assume the stars to be ideally

gaseous figures of equilibrium [...] It is to this phenomenon of pulsating


Fig. 1.1.— Modern versions of the light and radial velocity curves of δ Cephei. The

former comes from Moffet & Barnes (1984), while the latter is due to Bersier et al.

(1994).


stellar masses, however, that the writer would ascribe the light and

velocity variation of Cepheid and cluster variables, and the theoretical

work of Moulton, Jeans, Emden and others on the properties of gaseous

spheres already justifies the conclusion that such oscillations are both

possible and probable...”

A similar paradigm shift, from a binary-star hypothesis to a single pulsating

star hypothesis, was proposed a few months later by Martin & Plummer (1915) to

explain the radial velocity variations of RR Lyrae, the prototype of another class

of variables, then known as “cluster variables”.

A few years before the papers by Shapley and Martin & Plummer, Cepheids

had been discovered in the Magellanic Clouds by Leavitt (1908), who subsequently

found that the variables the Small Magellanic Cloud exhibited a clear relation

between their periods and their mean magnitudes (Leavitt 1912). A modern

version of that relation (with a much larger sample of variables) due to Udalski

et al. (1999) can be seen in Figure 1.2. This relation came to be known as

the “Cepheid Period-Luminosity Relation”, commonly abbreviated as the “P-L

relation”.

A few years after Leavitt’s discovery of the P-L relation, Eddington (1918)

strengthened the case for the pulsating-star hypothesis by developing a theory

of adiabatic oscillations of a stellar atmosphere. He noticed that for Galactic

Cepheids, Π√ρc ∼ constant, where Π is the period of a variable and ρc is its

central density; this correlation was hard to explain in terms of a binary system,

but came out naturally from pulsation theory. In a companion paper, Eddington

(1919) showed that the pulsations would not dissipate after a few cycles, but

would last for more than 103 years. Furthermore, based on the already-known

Cepheid Period-Luminosity Relation, he dismissed the hypotheses of collisions

of meteorites with the stellar surface, or the close encounter of two stars, as the

starting mechanisms for pulsations, and postulated that they were due to one of

two sources:


Fig. 1.2.— Modern version of the Period-Luminosity Relation of Cepheids in the

Small Magellanic Cloud, from Udalski et al. (1999). The first Cepheid P-L relation

was based on Cepheids present in this Milky Way satellite, and was constructed by

Leavitt (1912).


“1) During a certain stage the conditions are such that an oscillation

having the appropriate period would tend to increase; thus the pulsation

would start automatically.

2) At a certain stage there is a sudden change in the state of stable

equilibrium, and the collapse to the new state throws the star into a

pulsation, which [...] could last for a period of the order 1000 years.

In either case, it seems likely that every star of sufficient mass will

become a Cepheid for a brief part of its life [...]”

Eddington continued on to hypothesize that “the condition for Cepheid

variation may be a particular distribution of internal temperature” and that “the

specific heat may change with temperature, being abnormally high for temperatures

at which ionisation occurs rapidly”, concluding that “the occurrence of variation

depends on the conditions in the outer layers [of the star].” As we know today

(see §1.2.2), all these statements are accurate descriptions of the mechanisms

responsible for Cepheid pulsations.

Lastly, it is of interest that Eddington (1926) used the lack of changes in the

period of δ Cephei from 1785 until the publication of his work as evidence against

the “contraction” hypothesis and in favor of the “sub-atomic” hypothesis for the

mechanism responsible for energy generation in stars. That same year, Hubble

(1926) published his discovery of Cepheid variables in Messier 33, thus establishing

the extragalactic nature of the “spiral nebulae”.

Our increased understanding of the physical properties and processes associated

with stellar structure and evolution since the days of Eddington has resulted in a

clear picture of the mechanisms responsible for the origin of pulsations in Cepheid

variables. These are described in the following sub-section.


1.2.2 A modern introduction to Cepheid variables

Briefly stated, Cepheid variables are stars with masses between 4 − 10M� that

are in the evolutionary stage where helium is fused into carbon in their cores,

and hydrogen is fused into helium in a shell outside the core. During this phase,

their outer stellar envelope becomes vibrationally unstable and starts to pulsate.

The period of pulsation is related to the mean density of the star, which is in

turn related to its mass. The latter determines the luminosity of the star, thus

resulting in a relation between period and luminosity, known as the Cepheid

Period-Luminosity Relation.

Let us expand upon this brief summary as follows. First, we will describe the

evolutionary history of a 7M� star, to put the Cepheid phase in context. Second,

we will describe the physical processes that drive the evolution of high-mass stars

and the mechanisms responsible for the onset of vibrational instabilities. These

descriptions are based on material from Kippenhahn & Weigert (1991).

Figure 1.3 shows the evolutionary track of a 7M� star with a composition

similar to the Sun (Z = 0.02, Y = 0.28), based on the models of Siess et al. (2000)

(for evolution up to the zero-age main sequence) and Alibert et al. (1999) (for

evolution after the zero-age main sequence). The total amount of time covered by

the track is 5× 107 years.

At (a), the future Cepheid is a proto-star with R = 61R�, L = 103L�, and

Tc = 8.5 × 105 K, i.e., no nuclear processes are taking place in its core. The

proto-star collapses for some 103 yr, after which time the central temperature

reaches 106 K and deuterium is fused into helium for 4 × 104 yr before becoming

depleted. At this point (b) the proto-star has R = 28R� and L = 3 × 102. It

continues to collapse for another 2.2× 105 yr before any further nuclear processes

take place. When R = 8R�, L = 2× 103L� and Tc = 1.4× 107 K all 12C present in

its core is converted into 14N via the first steps in the CNO cycle; during this time,

the star settles on a short-lived “carbon main sequence” at (c). Once the carbon is

exhausted, the star completes its collapse onto the zero-age main sequence at (d).

The elapsed time from (a) to (d) is about 6× 105 yr.


Fig. 1.3.— Evolutionary track of a 7M� star, based on the models of Siess et al.

(2000) and Alibert et al. (1999). During a short phase of its life, such a star becomes

a Cepheid with a period near 10 days. See text for details.


At the ZAMS, the star has L = 1.7 × 103L�, Teff = 2.05 × 104 K, and

R = 3.2R�. The nuclear fusion reactions of the CNO cycle proceed at a

temperature close to 3× 107 K in a convective core that contains 4.4M� within 0.3

stellar radii. As the nuclear reactions proceed, the ongoing conversion of hydrogen

into helium starts to increase the mean molecular weight of the core and hence

the stellar luminosity. The star reacts by expanding its radius and hence cooling

its photosphere; after 3.8 × 107 yr, it reaches a maximum attainable radius (e) of

R = 6.5R� and a minimum temperature of Teff = 1.67× 104 K. At this point, the

hydrogen content in the core has dropped to only X = 0.05. As the remaining

hydrogen is fused, the radius decreases slightly and the luminosity continues to

increase for another 106 yr, until hydrogen is completely exhausted in the core (f).

Soon thereafter, the mass shell near 0.2m/M contracts slightly and reaches

conditions suitable for hydrogen fusion. This “hydrogen shell burning” has a

tremendous impact on the outer sections of the star, expanding the photosphere

out to R ∼ 60R� in a mere 8×105 yr. By that time, the inert helium core contracts

to the point that its central temperature and density are high enough to initiate

the fusion of helium into carbon (g). The star increases its luminosity and expands

following a track parallel to the Hayashi line, at which time it develops a convective

outer zone that may reach down into areas whose composition was modified during

the initial hydrogen core burning. Thus, the photospheric abundances may be

modified by this dredge-up mechanism. After reaching its maximum expansion in

1.2× 105 yr, it contracts again, following essentially the same track down to (h) in

3.3× 106 yr.

At this point, the stage is set for the beginning of the Cepheid phase. This

phase takes place while the star traverses a “loop” in the H-R diagram, from (h)

to (i) to (j). During this motion, the star passes through the “instability strip” a

region delineated by dashed lines in Figure 1.3 where conditions are favorable for

the onset of pulsational instabilities. The hydrogen content profile of the stellar

interior, prior to the start of hydrogen shell burning, can be thought of as a smooth

increasing function. Once shell burning starts, the profile becomes increasingly

more steep, until there is no hydrogen left below the shell. Above the shell, there is


a region where the hydrogen content increases until reaching the initial value. The

shape of the profile influences the envelope, mainly through a hydrostatic effect; as

the profile steepens and becomes increasingly step-like, the core radius increases

and the envelope contracts, leading to higher effective temperatures and a leftward

motion from (h) to (i) that takes 1.6 × 106 yr. By that point, about 70% of the

helium in the core has been depleted through fusion; the subsequent reduction in

helium content results in a decrease of the core radius, which makes the envelope

expand and cool, moving the star towards the right from (i) to (j) in 4.2× 106 yr.

The total elapsed time from the ZAMS to end of the loop (i.e., from (d) to (j)) is

4.8× 107 yr.

Once the “loop” ends, the stellar core contains a degenerate mixture of carbon

and oxygen, and the formation of an outer convective envelope results in the

cessation of hydrogen shell burning. Only helium shell burning continues to take

place, and it initiates another expansion of the outer envelope along the Hayashi

track. Eventually, the outer convective zone extends inwards to m/M as small as

0.16, and two closely spaced shells (hydrogen- and helium-burning, respectively)

develop. Thermal pulses ensue, leading to mass ejections in the envelope. If

the degenerate C-O core of the Cepheid reaches 1.4M�, it will ignite a runaway

explosive carbon burning and the star will become a supernova. The minimum

initial mass required to generate a 1.4M� C-O core is not well constrained at

present, but it seems clear that the most massive Cepheids are above the lower

limit.

The evolutionary track displayed in Figure 1.3 shows that the 7M� star

described above crosses the instability strip a total of three times during its

post-main-sequence evolution. The first one, while traversing from (f) to (g),

proceeds along the thermal time scale of the star and takes only 1.6× 104 yr. The

two crossings related to the loop take a increasingly longer amount of time, of the

order of 6.1× 104 and 1.5× 105 yr, respectively. Thus, most Cepheids are expected

to be undergoing the last of the crossings.


The timescales for stellar evolution, and thus the amount of time spent in the

Cepheid phase, decrease dramatically as a function of mass. The models in Table 6

of Alibert et al. (1999) indicate that stars with masses of 5, 7, 9 and 11 M� spend

a total of 6.9 × 106, 2.1 × 105, 3.1 × 104 and 9 × 103 yr in the instability strip,

respectively. The combination of decreasing timescales and the intrinsic shape of

the stellar mass function imply that in a survey where the lower flux limit is well

below that of Cepheids, short-period variables will be discovered in greater numbers

than long-period ones. The OGLE survey (Figure 1.2) is a good example of this

case. Below a certain mass, the contraction and expansion of the helium core is not

large enough to drive the envelope into a loop that would cross the instability strip.

This sets a minimum mass (and hence period) for Cepheids, which according to the

models is a function of both helium and metal content. Unfortunately, theoretical

predictions for this short-period cutoff are not yet in agreement with the observed

distributions in the Magellanic Clouds.

Finally, let us turn our attention to the mechanism responsible for Cepheid

pulsations. Stars with effective temperatures near 6000 K contain a zone close to

the surface (at T ∼ 8000 K) where hydrogen becomes ionized, and another zone

deeper in the interior (at T ∼ 40000 K) where helium becomes doubly ionized. In

both zones, the onset of ionization increases the opacity (κ) and lowers the local

value of the adiabatic gradient, favoring instability.

A 7M� star, such as the one described earlier in this section, with an effective

temperature near 6300 K, has the ionization zones located deep enough inside

its surface that their excitation drives the outer stellar envelope outwards. As

the envelope grows in radius, it cools down and its total flux decreases. As

the expansion progresses, the effective temperature drops until the excitation

mechanism becomes ineffective, at which point the expansion is only propelled by

the momentum of the mass shell. Once all kinetic energy is converted into potential

energy, the mass shell contracts again, increasing the effective temperature and the

total flux. Once the contraction increases the temperature back to the initial value,

the cycle starts again. Since this pulsation mechanism is driven by the increase of

opacity in the ionization zones, it is commonly referred to as the “κ mechanism”.


A 7M� star with an effective temperature higher than ∼ 6300 K will have

the ionization zones located very close to each other and to its surface, making

the pulsation mechanism ineffective. Additionally, if the effective temperature is

lower than ∼ 4700 K, non-adiabatic effects in the convective zone of the envelope

also make the pulsation mechanism ineffective. These two processes delineate the

“blue” and “red” edges of the instability strip, which are shown as dashed lines in

Figure 1.3.

Each pass of a star through the instability strip subtends a narrow range of

luminosity, temperature, and radius. Given the mass and the range of radii of the

star during the passage, one can calculate the equivalent range of densities. The

theory of stellar pulsation shows that, to first order, the period of pulsation only

depends on the mean density of the star; thus, a Cepheid of a given mass will cover

a small range in periods during each passage through the instability strip.

The 7M� star described earlier in this introduction will, according to Alibert

et al. (1999), change its period of pulsation from 10.6 d to 6.4 d during the first

half of the “loop”, while the second half will be characterized by periods between

8.2 d and 13.7 d. The different periods and luminosities exhibited by Cepheids

of different masses during their crossings of the instability strip contribute to the

finite width of the P-L relation, as seen in Figure 1.4 (based on the models of

Alibert et al. 1999).


Fig. 1.4.— Period-Luminosity tracks followed by Cepheids of different masses and

solar composition, based on the models of Alibert et al. (1999). Masses range from

4.75M� at the lower left to 11M� at the upper right. The tracks delineate the edges,

and contribute to the finite width, of the observed Period-Luminosity relation.


1.3 The Tully-Fisher relation

The concept that the rotational velocity of a galaxy might be related to its

absolute luminosity was first used by Opik (1922) to determine the distance to the

Andromeda galaxy. Nearly fifty years later, Roberts (1969) conducted a study of

the integral properties of ninety-one spiral and irregular field galaxies and found a

clear correlation between their luminosities (based on photographic magnitudes)

and total H I masses (based on the width of 21-cm profiles).

A few years later, Tully & Fisher (1977) used a sample of eight inclined spiral

galaxies located in the Virgo Cluster to study the relation between 21-cm line widths

(a distance-independent property) and total magnitudes (a distance-dependent

quantity). They also studied the relation between 21-cm line widths and apparent

diameters for the Virgo cluster sample and for a larger ensemble of 22 galaxies

located in the Ursa Major cluster. Both relations exhibited significant correlations,

with log-log slopes of −6.25 and −3.7 and r.m.s. deviations of of 15% and 30%,

respectively. The left panel of Figure 1.5 shows the original relation published by

these authors.

The large slope and small scatter of the line width-luminosity relation made it

a promising extragalactic distance indicator. Tully & Fisher (1977) used distance

estimates to ten galaxies in the Local, M81 and M101 Groups to establish the

absolute zeropoints of the relation and found a distance to the Virgo Cluster of

13 ± 1 Mpc, an estimate that is not too far from the modern value. The line

width-luminosity relation is now commonly referred to as the “Tully-Fisher”

relation.

The galaxy magnitudes used by Tully & Fisher (1977) were obtained using

blue-sensitive photographic plates. That bandpass is far from an ideal indicator of

the total galaxian luminosity, for several reasons. First, it depends on the recent

star formation history of the galaxy, since massive, young stars are blue, while the

older and more significant stellar population has redder colors. Second, blue light

is subject to significant absorption and scattering by interstellar dust and gas.


Fig. 1.5.— The original B- and H-band line width-luminosity relations published by

Tully & Fisher (1977) and Aaronson, Huchra & Mould (1979). They were based

on eight and eleven galaxies, respectively, all of which are members of the Virgo

Cluster.


This so-called “internal extinction” is increasingly more severe for galaxies

with larger inclination angles, because of the additional path length that must

be covered by the light before exiting the host galaxy. Tully & Fisher (1977)

included a correction term to account for this effect, based on the observed axial

ratio of each object (modern derivations of the correction include additional type-

and linewidth- dependences, which can only be reliably determined through the

analysis of large samples).

Aaronson, Huchra & Mould (1979) recognized these limitations of blue light

and proposed the use of near-infrared photometry instead. They characterized the

line width-luminosity relation in the H band using a sample of eleven Virgo Cluster

and eighteen Ursa Major Cluster galaxies, and found an increased correlation with

a log-log slope of −10 and a scatter of 10%. The original relation published by

these authors can be seen in the right panel of Figure 1.5.

A theoretical basis for the Tully-Fisher relation has been sought since the

initial characterizations of the relation; both Tully & Fisher (1977) and Aaronson,

Huchra & Mould (1979) included sections devoted to this matter. The latter

states that, generally speaking, the basis for the Tully-Fisher relation can be

obtained from the virial theorem, under the assumptions that “[...] all [spiral]

galaxies have (a) the same mass profiles and rotation curves as a function of some

dimensionless scale-length; (b) the same central mass surface density; (c) the same

mean mass-to-light ratio.” Recent theoretical work on the origin of the Tully-Fisher

relation (Steinmetz & Navarro 1999; Bell & de Jong 2001) support that initial view,

although the modern studies are based on more complex ideas. They are based on

high-resolution cosmological simulations that include the effects of gas dynamics,

different star formation rates and initial mass functions, and spectrophotometric

galaxy evolution models. These theoretical studies predict log-log slopes around

−9, in agreement with modern observational studies (Giovanelli et al. 1997b; Tully

& Pierce 2000), but cannot easily match the overall normalization of the relation.

It appears that the latter depends strongly on the star formation algorithm used

in the simulations and on the cosmological parameters that determine the baryon

fraction and time of formation of spiral galaxies.


Soon after the initial observational characterizations of the Tully-Fisher

relation, Aaronson et al. (1982a) used the infrared version to derive distances to

300 nearby spiral galaxies and combined that information with measured recession

velocities to map the velocity field of the Local Supercluster and the infall into the

Virgo Cluster. The application of the Tully-Fisher relation to the study of local

and large-scale galaxian velocity field has been one of its main uses over the past

two decades.

As panoramic detectors were developed for astronomical use in the optical

bandpasses during the late 1980s, and in the infrared during the early 1990s,

it became possible to obtain more reliable galaxian magnitudes and axis ratios

through surface photometry techniques. This were pioneered by Bothun & Mould

(1987) and Pierce & Tully (1988). During the 1990s, the Tully-Fisher relation was

extensively applied to samples of hundreds and thousands of field and cluster spiral

galaxies (Willick 1991; Mould et al. 1991; Courteau 1992; Han 1992; Mould et al.

1993; Mathewson & Ford 1994; Giovanelli et al. 1997a; Haynes et al. 1999a; Dale

et al. 1999; Ekholm et al. 1999) to study galaxy flows in and beyond the Local

Supercluster, as well as other cosmological questions of interest. In the near future,

the Two Micron All-Sky Survey (2MASS) will provide near-infrared magnitudes

for nearly one million galaxies, including several thousands that are suitable for

studies based on the Tully-Fisher relation.

The first attempt at the absolute calibration of the near-infrared luminosity–

linewidth relation was carried out by Aaronson, Huchra & Mould (1979) in their

original derivation of the relation at these wavelengths. They had obtained H-band

circular aperture (hereafter, H−0.5) magnitudes for eleven galaxies in the Virgo

cluster and eighteen objects in the Ursa Major cluster, which were coupled with

six “local calibrators” (M31, M81, NGC 2403, NGC 5204, NGC 5585 and Holmberg

IV). Soon thereafter, Aaronson, Mould & Huchra (1980) improved upon their

previous work by extending the calibrator sample to thirteen objects located in the

Local, Sculptor, M81, and M101 groups.


In the early 1980s, the two competing distance scales (deVaucouleurs and

Sandage-Tammann) resulted in alternate calibrations of the H−0.5 luminosity–

linewidth relation (Aaronson & Mould 1983) that differed by 0.65 mag in their

zeropoints, but whose scatter was basically the same (0.36 mag vs. 0.42 mag,

respectively). The dichotomy stood for some time, until Freedman (1990)

applied her Cepheid distances for five galaxies (M31, M33, M81, NGC 300 and

NGC 2403), based on multiwavelength CCD photometry, to the problem. She

found a zeropoint for the relation that was half-way between the deVaucouleurs

and Sandage-Tammann values, and a very small scatter (0.15 mag) which today is

recognized as an artifact of small-number statistics.

A few years later, the Hubble Space Telescope ushered in a new era of precision

Cepheid distances for galaxies located as far as D ∼ 20 Mpc, increasing four-fold

the number of suitable calibrators. It then became crucial to obtain accurate

magnitudes for these galaxies, measured in a consistent manner to avoid introducing

systematic errors in the determination of the Hubble constant. Chapter 5 of this

Thesis presents observations of the calibrator galaxies at optical and near-infrared

wavelengths, using large-format CCD and InSb arrays.

The combination of accurate Cepheid distances and galaxian magnitudes

allowed Sakai et al. (2000) to derive a new calibration of the luminosity–linewidth

relation in the BV RI bands and in the H−0.5 system, based on 21 objects. They

found discrepant values of H0 based on their absolute calibration of the I and H−0.5

relations, which they ascribed to differences in the I −H−0.5 color of the calibrator

and “distant cluster” samples. Chapter 6 of this Thesis presents a new calibration

of the H and K relations, based on total extrapolated magnitudes, which may

solve the aforementioned discrepancy.


Chapter 2

A Cepheid distance to M33

Abstract

This chapter presents the first large-scale CCD-based search for variables in

M33, based on 95 nights of observations at the F. L. Whipple Observatory 1.2 m

telescope and 36 nights on the Michigan-Dartmouth-MIT 1.3 m telescope. The

data was processed using the DAOPHOT/ALLSTAR package and analyzed using

a suite of programs specially developed for this project.

We present a catalog of 56950 stellar objects detected in these fields, and a

catalog of 910 variable objects, including 537 Cepheids and 49 eclipsing binaries.

Based on a subsample of 61 Cepheids with periods between 15 and 60 days,

accurate V and I photometry, and with no signs of blending, we determine

an extinction-corrected distance modulus to M33 of 24.65 ± 0.12 mag, which

corresponds to a distance of 850± 50 Mpc. This distance is based on an assumed

LMC distance modulus of µ0 = 18.50 ± 0.10 mag (D = 50 ± 2.5 kpc) and a

metallicity dependence of the Cepheid P-L relation of γV I = −0.2± 0.2 mag/dex.

Contains material from: i) The Astronomical Journal, volume 121, pages 861-869, “The DIRECTProject: Catalogs of Stellar Objects in Nearby Galaxies. I. The Central Part of M33”, byL.M. Macri, K.Z. Stanek, D.D Sasselov, M. Krockenberger & J. Kaluzny; ii) The AstronomicalJournal, volume 121, pages 870-890, “DIRECT Distances to Nearby Galaxies Using DetachedEclipsing Binaries and Cepheids. VI. Variables in the Central Part of M33”, by L.M. Macri,K.Z. Stanek, D.D. Sasselov, M. Krockenberger & J. Kaluzny.

21


2.1 Introduction

The DIRECT project (as in “direct distances”) started in 1996 with the long-term

goal of obtaining distances to two important galaxies in the cosmological distance

ladder – M31 and M33 – using detached eclipsing binaries (DEBs) and Cepheids.

These two nearby galaxies are the stepping stones in most of the current effort to

understand the evolving universe at large scales. Not only are they essential to the

calibration of the extragalactic distance scale, but they also constrain population

synthesis models for early galaxy formation and evolution. However, accurate

distances are essential to make these calibrations free from large systematic

uncertainties.

Detached eclipsing binaries have the potential to establish distances to M31

and M33 with an unprecedented accuracy of better than 5% and possibly to better

than 1%. Current uncertainties in the distances to these galaxies are in the order

of 10 to 15%, as there are discrepancies of 0.2-0.3 mag between various distance

indicators. Detached eclipsing binaries (Andersen 1991; Paczynski 1997) offer a

single-step distance determination to nearby galaxies and may therefore provide an

accurate zeropoint calibration for other distance indicators, including Cepheids.

Messier 33 (NGC 598) is one of the members of the Local Group of galaxies.

It is classified as a SA(s)cd galaxy in the Third Reference Catalog of Galaxies de

Vaucouleurs et al. (1991) and as a Sc(s)II-III in the Revised Shapley-Ames Catalog

Sandage & Tammann (1981). It is located at a R.A. of 1h34m and a Declination

of 30◦40m (J2000.0), and it has major and minor B25 isophotal diameters of 71′

and 42′, respectively. It has been extensively studied, appearing in more than 1000

publications. One of first was that of Hubble (1926), who stated in the abstract

of his paper that “... [i]ts great angular diameter and high degree of resolution,

suggesting that it is one of the nearest objects of its kind, offer exceptional

opportunities for detailed investigation.”

This work represents the first large-scale CCD-based search for variables in

M33, and the first Cepheid-based determination of the distance to M33 in a decade,


since the publication of Freedman et al. (1991). We first discuss in §2.2 the details

of data acquisition, reduction and calibration. We describe the multiple steps

involved in PSF photometry in §2.3, and the process of variable star detection and

classification in §2.4. Next, we present in §2.5 the analysis of the Cepheid variable

stars and the determination of a distance to M33 based on a subset of these

objects. Our conclusions appear in §2.6, where we also discuss future prospects for

improvements in the absolute calibration of the Cepheid Distance Scale using our

sample of variables.

2.2 Observations and data reduction

The observations of the central region of M33 were primarily carried out at the Fred

L. Whipple Observatory (hereafter FLWO) 1.2-m telescope. We used “AndyCam”

(Szentgyorgyi et al. 2001), a thinned, back-illuminated, AR-coated Loral 20482

pixel CCD camera with a plate scale of 0.317′′/pixel, or an effective field of view of

10prime.8. The filters used during our program were standard Johnson B and V and

Cousins I. Additional I band data were collected at the Michigan-Dartmouth-MIT

Observatory 1.3-m McGraw-Hill telescope. We used “Wilbur” (Metzger et al.

1993), a thick, front-illuminated Loral 20482 pixel CCD camera. The plate scale

and field of view were almost identical to that of “AndyCam.”

We observed three fields located north, south and south-west of the center

of M33, which we labeled M33A, B and C. The J2000.0 center coordinates of the

fields are: M33A, R.A. = 01h34m05′′.1, Dec.= 30◦43′43′′; M33B, R.A. = 01h33m55′′.9,

Dec.= 30◦34′04′′; M33C, R.A. = 01h33m16′′.0, Dec.= 30◦35′15′′. Figure 2.1 shows

the boundaries of these fields overlaid on a digitized image of the galaxy from the

POSS-I survey1, while Figure 2.2 shows a mosaic of the survey fields, created with

our CCD data. At FLWO, we obtained V and I data on 42 nights and B data on

1 The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S.

Government grant NAGW-2166. The National Geographic Society – Palomar Observatory Sky

Atlas (POSS-I) was made by the California Institute of Technology with grants from the National

Geographic Society.


Fig. 2.1.— Location of DIRECT M33 fields, overlaid on top of a POSS image of

the galaxy. Note the significant overlap between the fields.


Fig. 2.2.— Mosaic of DIRECT M33 fields, created from our CCD frames.


13 nights. At MDM, we obtained I data on 10 nights. Exposure times were 1200s

in B, 900s in V and 600s in I. Fields were observed repeatedly on each night in V

and I, so the actual number of exposures per field in those filters is around 110 and

60, respectively. Standard star fields from Landolt (1992) were observed on two

photometric nights.

The CCD frames were processed with the standard CCDPROC routines under

IRAF2, using bias frames and dome flats obtained on every night of observations.

Bad pixel masks were created to suppress small cosmetic defects found throughout

the detectors and a small region in the top-left corner of Andycam that does not

receive illumination.

2.3 Photometry

The photometric reduction of our data was carried out with a highly automated

Tcl/Tk-based pipeline, which used the standard DAOPHOT and ALLSTAR

programs (Stetson 1987, 1992), the MRJ suite of programs (Alard 2000), and

a suite of programs developed by the DIRECT team. We describe the different

stages of this pipeline below.

2.3.1 Initial Processing

The first stage of the pipeline consisted of an initial photometric processing using

DAOPHOT and ALLSTAR with the aim of obtaining rough values for the FWHM

of the point-spread function and the sky level of each frame. Once this processing

was completed, we selected a subset of high-quality images (i.e., low sky value and

small sized, low-ellipticity PSF) of each field in each filter (∼ 22 in V, ∼ 17 in I

and ∼ 8 in B).

2IRAF is distributed by the National Optical Astronomy Observatories, which are operated

by the Associations of Universities for Research in Astronomy, Inc., under cooperative agreement

with the NSF.


These high-quality images of each field and filter were combined by the MRJ

program of Alard (2000) to create template images for use in subsequent stages

of the pipeline. There are several reasons for using combined template images

over a single, “best-seeing” frame; since each input frame has a slightly different

center and rotation, the combination of many frames (suitably referenced to a

common system) eliminates cosmetic defects and bleeding features and reduces the

amplitudes of fringes in the I band data, effects that would otherwise result in the

non-detection of some objects; additionally, the signal-to-noise ratio increases as

the square root of the number of frames that are combined, resulting in a 3-5 fold

improvement of the S/N and a higher sensitivity to faint objects.

2.3.2 Photometry of template images

Once the template images were created, they were analyzed using DAOPHOT and

ALLSTAR. First, objects were detected using a 4σ threshold, taking into account

the changes in gain and readout noise stemming from the combination of multiple

frames. Aperture photometry was carried out at radii of 10, 12, 14, 16, 18 and 20

pixels, with a sky annulus extending from 30 to 40 pixels. Next, bright and isolated

stars were selected for the determination of the PSF using the “PICK” routine of

DAOPHOT. The initial list was thinned through repeated iterations by rejecting

any star whose residual was three times larger than the mean. We solved for a PSF

without positional variation, since the inspection of the residuals did not show any

significant correlations.

After the rejection of outliers, the average number of stars used for the

determination of the PSF in each template image was 70, with a minimum of 46

and a maximum of 99. The FWHMs of the PSFs were 0′′.9 in the I band, 1′′.1 in

the V band, and 1′′.3 in the B band. Next, PSF photometry was carried out on

the template images with ALLSTAR, using the lists of aperture photometry as

input. The number of objects that were successfully fit with the determined PSFs

were ∼ 112, 000, ∼ 137, 000 and ∼ 90, 000 in the V, I and B template images,

respectively.


2.3.3 Photometry of individual frames

The PSF of each individual frame was determined with DAOPHOT, using as

input the list of PSF stars from the appropriate template image. Figure 2.3 shows

histograms of the seeing for the three filters; median FWHM values were 1.5′′ for I

and 1.8′′ for B and V. Next, PSF photometry of the individual frames was carried

out in “fixed-position” mode, using the star list of the appropriate template image

as input (suitably transformed to the coordinate system of the individual frame).

Once the PSF photometry of an individual frame had been carried out, the

magnitudes of all objects present in both the master image and that frame were

matched and used to derive the mean magnitude offset between the two. These

offsets were recorded in a log file for future use (see below). The typical uncertainty

in the determination of this offset was ±0.02 mag.

Once the PSF photometry of all individual frames pertaining to a particular

field and filter had been completed, the measurements were transformed to the

magnitude system of the relevant template image (using the previously determined

offsets) and merged into a database. In this fashion, nine final photometry

databases were created (3 fields × 3 filters), containing a total of 1.6 × 107

measurements.

2.3.4 Determination of aperture correction coefficients

The transformation of PSF magnitudes into aperture magnitudes requires the

determination of “aperture correction” coefficients. These coefficients are intended

to compensate for the inability of the best-fit PSF to exactly model the actual PSF.

The coefficients are usually obtained by performing aperture photometry of bright,

isolated stars present in the program frames, using the outermost radius employed

in the photometry of standard stars). This aperture photometry is carried out on

program frames obtained on the same night that standard stars are observed. The

resulting aperture magnitudes are compared with those obtained through PSF


Fig. 2.3.— Histogram of FWHM values of the PSFs from our individual frames.

The median values are 1′′.5 for the I band and 1′′.8 for the B and V bands.


fitting, and the correction coefficients are obtained. Contamination by other

stars must be avoided, so usually all other objects are removed from the frame

prior to these measurements. A more refined approach (Stetson 1990) involves

the determination of “growth curves”, and requires that aperture photometry be

carried out at a variety of radii, extending out enough to ensure that the aperture

magnitudes converge to an asymptotic value.

Unfortunately, the extreme crowding present in our fields, coupled with

the marginal quality of the PSF on those nights that were photometric, made

either approach impossible to implement. Even after removing all other objects

in the object frames, the residual contamination in the apertures was large

enough to impede the convergence of the growth curves. On the other hand, the

growth curves derived from standard stars showed satisfactory convergence. After

some experimentation, we found that the best approach to obtain a satisfactory

correction from PSF to large-aperture magnitudes was to divide the process into

two parts: i) the determination of an “aperture correction” coefficient based on a

10-pixel radius aperture, followed by ii) a “growth curve correction” from 10 to 30

pixels based on the standard star growth curves. Because the 10-pixel aperture is

comparable in size with the FWHM of the PSF (5 to 7 pixels), the “growth curve

correction” had a moderate dependence on seeing. Figure 2.4a shows the growth

curves obtained from the standard stars, and Figures 2.4b-d show the correlation

between the total growth in magnitude and the FWHM of the PSF for the I, V

and B bands, respectively. We estimate the total uncertainty associated with this

two-step correction process to be about ±0.04 mag.

2.3.5 Standard star observations and photometric solutions

Seven standard star fields from Landolt (1992) were observed on two photometric

nights: 1997 September 5 and 1997 October 9. A total of 150 frames were obtained,

spanning a range of airmass between 1.1 and 2.2. As described in the previous

sub-section, aperture photometry was carried out at a variety of radii; only the

outermost one (30 pixels, or 9′′.5) was considered for the determination of the


Fig. 2.4.— (a) (top left) Growth curves of aperture magnitudes for objects located

in the standard star fields. Note the large growth in magnitude between 10 and

20 pixels, and the convergence to asymptotic values after 25 pixels. (b) (top right)

Correlation between growth curve correction (∆m(10−30)) and FWHM of the PSF

for the I band. (c) (bottom left) same as (b) but for the V band. (d) (bottom right)

same as (b) but for the B band.


photometric solution. We used the IRAF PHOTCAL routines to solve for equations

of the form

Mstd,i = mobs,i + χi − k′iX + ξij(Mstd,i −Mstd,j) (2.1)

where Mstd,i and Mstd,j are the magnitudes of a star in the standard system in the

i and J filters, while mobs,i is the instrumental magnitudes of the same star in the

i filter. χi is the magnitude zeropoint at X = 0, k′i is the airmass coefficient for

the i filter, and ξij is the color term. The V-band solution was calculated using

both B–V and V–I for the color term; the latter one was used by default in the

calibration process, unless only B and V data were available for a particular object.

The B-band solution was calculated using B–V for the color term, while the I-band

solution was calculated using V–I for the color term. The values and uncertainties

of the coefficients of each term are presented in Table 2.1; based on those numbers,

we estimate a total uncertainty of ±0.02 mag in our solutions.

Based on the uncertainties associated with PSF magnitude offsets (±0.02 mag,

§2.3.3), aperture correction coefficients (±0.04 mag, §2.3.4) and photometric

solutions (±0.02 mag, previous paragraph), we estimate a total random uncertainty

in our zeropoint calibration of ±0.05 mag.

2.3.6 Photometric comparisons

We used bright stars present in the overlap regions between the survey fields

to check our photometric calibration procedures. A comparison of the mean

magnitudes of ∼ 75 objects brighter than 19.0, 18.5 and 18.0 mag in B, V, and I,

respectively is shown in Figure 2.5. The offsets are < 0.01 mag for V and I and

∼ 0.02 mag for B, indicating that the constant PSF used for the photometry was an

appropriate choice, and that the aperture and growth curve corrections described

in the previous sub-section were properly determined. Table 2.2 summarizes the

results of the comparisons.


Table 2.1. Photometric solutions

Filter χ k′ ξ rms

1997 October 9

B (B-V) −22.953± 0.025 0.212± 0.017 −0.033± 0.011 0.030

V (B-V) −22.714± 0.014 0.123± 0.009 0.035± 0.006 0.016

V (V-I) −22.720± 0.013 0.127± 0.009 0.032± 0.005 0.016

I (V-I) −22.719± 0.016 0.064± 0.010 −0.051± 0.007 0.021

1997 September 4

B (B-V) −22.942± 0.020 0.302± 0.013 −0.021± 0.009 0.018

V (B-V) −22.695± 0.018 0.177± 0.009 0.054± 0.009 0.016

V (V-I) −22.700± 0.013 0.181± 0.011 0.044± 0.007 0.017

I (V-I) −22.692± 0.016 0.105± 0.010 −0.039± 0.006 0.010

Table 2.2. Photometry comparisons

Band ∆ mag mlim N

Internal – overlap regions

V −0.005± 0.003 18.5 64

I +0.009± 0.002 18.0 83

B −0.022± 0.004 19.0 75

Bersier et al. (2001)

V −0.057± 0.045 18.0 15

B −0.042± 0.048 18.5 20


Fig. 2.5.— Test of the internal consistency of our photometry. Each of the three

panels shows the difference in the measured magnitude of stars present in the over-

lapping regions between field B and fields A/C, as a function of magnitude. The

mean value of the offset at bright (m < 18) magnitudes is < 0.01 mag.


We performed an external test of our photometric calibration by matching

objects in common between our Field A and one of the fields of Bersier et al.

(2001). We compared the mean B and V magnitudes of stars brighter than 18.5

and 18.0 mag, respectively (about 20 stars/filter) and found offsets of the order

of −0.05 mag (brighter DIRECT magnitudes). The comparisons are plotted in

Figure 2.6 and summarized in Table 2.2.

2.3.7 Artificial star tests

The differences between our photometry and the Bersier et al. (2001) photometry

in B and V are small but consistent. Furthermore, Bersier et al. (2001) used a

larger telescope (the 3.5-m WIYN) under significantly better seeing conditions than

us. Therefore, we decided to undertake artificial star tests to quantify the level

of photometric bias in our magnitudes that could arise due to the poorer spatial

resolution of our images.

We used DAOPHOT to inject 2,500 artificial stars into the nine master frames,

using the PSFs previously derived by our automated reduction pipeline and taking

into account photon noise and other detector characteristics. We analyzed the

frames using the same procedures as in the automated pipeline. The results were

quite similar for the three frames pertaining to each band, and thus the data files

were merged to improve the statistics. Our results are presented in Table 2.3 and

in Figure 2.7.

Bright stars (15 < m < 18) are affected by crowding at the 0.01 − 0.04 mag

level. The bias becomes stronger for fainter objects (m > 18), reaching

0.05− 0.08 mag. At a given magnitude, the bias increases from B to V to I. In all

cases, the offset induced by crowding is in the same direction as the offset found

between our data and other catalogs.


Fig. 2.6.— Test of the external consistency of our photometry. Each of the two

panels shows ∆ mag as a function of magnitude for objects in common between

our Field A and one of the fields of Bersier et al. (2001), for the B and V bands,

respectively. The mean value of the offsets at bright (m < 18.5) magnitudes is

−0.05 mag.


Fig. 2.7.— Results of the artificial star tests. The bias in recovered magnitude is

plotted against input magnitude. Averages over 0.5 mag bins are plotted using solid

circles and tabulated in Table 2.3.


Table 2.3. Artificial star test results

Band Mag. ∆ mag (meas-input)

median mean σ

V 15.5 -0.004 -0.007 0.019

16.5 -0.009 -0.016 0.025

17.5 -0.016 -0.026 0.040

18.5 -0.028 -0.034 0.053

19.5 -0.041 -0.052 0.092

20.5 -0.062 -0.081 0.158

I 15.5 -0.014 -0.020 0.025

16.5 -0.025 -0.032 0.040

17.5 -0.039 -0.050 0.066

18.5 -0.063 -0.076 0.084

19.5 -0.076 -0.089 0.146

20.5 -0.081 -0.128 0.248

B 16.5 -0.006 -0.012 0.021

17.5 -0.013 -0.020 0.034

18.5 -0.019 -0.030 0.048

19.5 -0.029 -0.039 0.076

20.5 -0.039 -0.055 0.132

21.5 -0.046 -0.068 0.225


2.4 The star catalog

Once the zeropoint calibration was determined, we merged the BV I databases

of each field into a single database and applied the photometric transformations.

Objects were included in the catalog only if they had been detected in the V

band and in either of the B or I bands. As described above, the transformation

for the V band was carried out favoring the V–I color term formulation over the

B-V one if all three bands were available. We also re-determined the magnitude

uncertainties for each object following the precepts established by Kaluzny et al.

(1998), since the magnitude uncertainties reported by DAOPHOT/ALLSTAR are

under-estimated for bright stars and over-estimated for faint ones. Lastly, we used

our time-series data to calculate mean BVI magnitudes and V-band JS variability

indices (Stetson 1996).

As Figure 2.1 shows, there is –by design– a significant overlap between fields

A and B, and between fields C and B. We matched the three field databases and

found ∼ 4, 800 objects in common; only one entry from each object was kept in the

common database, to avoid duplication. We saved the matched entries to test the

internal consistency of our photometric calibration (as described in §2.3.6). Once

the matching process was completed, we obtained a single database containing

56950 objects; 40005 with two-color photometry, and 16945 with three-color

photometry.

Next, we transformed the (x,y) coordinates of the objects into the FK5 system

using stars from the USNO-A2.0 catalog (Monet et al. 1998). We solved for a

cubic-order transformation using the IMWCS program (Mink 1999). The solution

used 17 stars and had rms values of 0.3′′ in both R.A. And Dec.

Figure 2.8 shows the cumulative luminosity functions of the objects in our

catalog. The turnovers in these luminosity functions indicate incompleteness below

∼ 22 mag for B and V, and ∼ 20 mag for I. Figure 2.9 shows color-magnitude

diagrams of our catalog stars. A plume of foreground stars from our Galaxy can be

seen in the region 0.4 < B − V < 1.2, V < 20. The feature is substantially


Fig. 2.8.— Cumulative luminosity functions of the stars detected in our frames with

two- or three-band photometry. Based on these histograms, we estimate complete-

ness limits of I∼20 mag, V∼ 22 mag, and B∼22 mag.


Fig. 2.9.— Color-magnitude diagram of 56950 stars in M33. Note the plume of

foreground Galactic stars at 0.4 <B-V< 1.2 mag, V< 20 mag.


diminished relative to the one seen in the CMD of M31 in Kaluzny et al. (1998)

due to the difference in galactic latitude between these two objects (l ∼ −22◦

for M31 and l ∼ −31◦ for M33).The displacement induced by an extinction of

AV = 1 mag is indicated by an arrow.

2.5 Variable search and classification

We calculated the JS variability index (Stetson 1996) for all 56950 objects in our

database, using the V band data since it has the best sampling. We flagged 1226

objects with JS,V ≥ 0.75 as candidate variables. Periods were determined using the

V band data only, employing a variant of the Lafler-Kinman technique proposed

by Stetson (1996). We searched for periods between 0.25 and 400 days, which

corresponds to the time span of the observations. Figure 2.10 shows our phase

coverage as a function of period. The ten most likely periods of each object were

saved for the next step in the analysis procedure, involving the classification of

variables.

We classified variables into three categories: Cepheids, eclipsing binaries, and

miscellaneous. The classification process started with an automated procedure that

employed Cepheid and eclipsing binary template light curves, followed by visual

examinations of every phased light curve to confirm the classification.

A variable star was classified as a Cepheid if the χ2ν of a fit of its time series

to a template Cepheid light curve (from Stetson 1996) was smaller than the χ2ν

of a fit to a template EB light curve and 3 times smaller than the χ2ν of a fit to a

straight line. We further required that the V-band amplitude be equal to or larger

than 0.1 mag. 341 objects were classified as Cepheids.

A variable star was classified as an eclipsing binary (EB) if the χ2ν of a fit of

its time series to a EB light curve was smaller than the χ2ν of a fit to a template

Cepheid light curve and 1.75 times smaller than the χ2ν of a fit to a straight line.

The EB light curve was modeled using nine parameters: the period (P ), the zero

point of the phase (T0), the eccentricity (e), the longitude of periastron (ω), the


Fig. 2.10.— Phase coverage as a function of period, calculated from the mid-

exposure dates of our V band images. The vertical axis shows the size of the largest

gap in phase as a function of period.


radii of the two stars relative to the binary separation (r1 and r2), the inclination

angle (i), and the magnitudes of the primary and of the uneclipsed system. We

further required that the larger stellar radius be less than 90% of the binary

separation and that the light of the brighter star be less than 90% of the total

light. Lastly, we rejected periods within 0.025d of 1 and 2 days, to avoid spurious

classifications due to aliasing of long-period variables. 49 objects were classified as

EBs.

In other cases, the classification routine could not obtain a satisfactory match

to a Cepheid or EB template, but the V-band JS index of the object being analyzed

was equal or greater than 1.2, implying a well-established variability. These 292

objects were classified as “miscellaneous”. An additional 544 objects, which did

not match the Cepheid or EB templates and which had a V-band JS < 1.2, were

discarded.

There could be additional variables in our fields with data in one band only.

This situation could arise in regions of high extinction, where only the I band

flux would be detected. Additionally, some objects could have been detected

in the V band and missed in the I band due to close proximity to a bright red

object. Therefore, we decided to repeat our variable search and classification for

single-band objects in our V- and I-band databases.

We searched the V-band database for objects with no counterparts in other

bands and with JS ≥ 0.75. We found 203 such objects and analyzed them in

manner described above. 17 were classified as Cepheids, 5 were classified as EBs,

27 were classified as “miscellaneous”, and 154 were rejected.

We searched the I-band database for objects with no counterparts in other

bands and with JS ≥ 0.75. We were aware that our observing strategy had not

included obtaining back-to-back images in this band, a fact that affects the meaning

of the JS statistic. Therefore, a substantially larger number of objects (2173)

passed the selection criterion. We decided to only retain the variables that fitted a

Cepheid or EB template and reject the rest. Since EBs are blue objects, it is not

surprising that none were found. However, 179 objects were classified as Cepheids.


In summary, our classification of candidate variables resulted in the selection

of 910 objects, of which 537 were classified as Cepheids, 54 as eclipsing binaries,

and 319 as miscellaneous variables. These numbers include 17 Cepheids, 5 EBs and

27 miscellaneous variables detected only in the V band and 179 Cepheids detected

only in the I band. Figures 2.11-2.13 contain representative light curves of each

class of variables.

Tables 2.4-2.6 list the properties of the Cepheids, EBs and miscellaneous

variables, respectively, discovered in our search. We list their designations (based

on their J2000.0 coordinates), periods (or JS values for miscellaneous variables), V,

I, and B magnitudes, and their errors. In the case of Cepheids, the magnitudes were

determined through numerical integration of the best fit templates; in the case of

EBs, they represent the mean magnitude out of eclipse; in the case of miscellaneous

variables, they are the mean magnitudes. Regarding the errors in magnitude, they

represent the r.m.s. deviation of the data from the best-fit templates (for Cepheids

and EBs) or from the mean magnitude (for miscellaneous variables). Additionally,

we list the V-band (or I-band if its the only one available) amplitudes of the

Cepheids, and the best-fit inclinations and primary and secondary radii of the EBs.

Figure 2.14 shows color-magnitude diagrams of the variables which have data

in more than one band. EBs are represented by filled circles; Cepheids are plotted

using open circles; and miscellaneous variables are indicated with starred symbols.

The displacement induced by an extinction of AV = 1 mag is indicated by an

arrow.

The segregation of EBs in the blue part of the diagram, and of Cepheids

in the instability strip, is quite clear in both panels. Variables labeled as

“miscellaneous” seem to fall into two well-defined categories: i) luminous blue

variables (V < 18, V −I < 1.5) and ii) AGB stars (V < 20.5, V −I > 2), while other

miscellaneous variables populate the lower regions of the CMD (V > 21, V −I ∼ 2).

Lastly, Figure 2.15 shows the correlation between periods and I-band

magnitudes for the objects listed in Table 2.4. Variables detected in both the V

and I bands are plotted using open symbols, while objects found only in the I band


Fig. 2.11.— Light curves for 6 of the 537 Cepheid variables. BV I data are rep-

resented by starred, filled and open symbols, respectively. The best-fit model light

curves are overplotted using solid lines.


Fig. 2.12.— Light curves for 4 of the 54 eclipsing binaries. BV I data are represented

by starred, filled and open symbols, respectively. The best-fit model light curves are

overplotted using solid lines.


Fig. 2.13.— Light Curves for 8 of the 319 miscellaneous variables. BV I data are

represented by starred, filled and open symbols, respectively.


Table 2.4. Cepheids

Designation P (d) V I B σV σI σB Amp.

D33J013420.14+303401.0 3.22 21.00 21.04 21.14 0.10 0.17 0.10 0.23D33J013356.69+304110.6 3.62 21.06 · · · 21.58 0.11 · · · 0.10 0.22D33J013334.18+303058.6 3.72 21.18 20.80 21.50 0.12 0.26 0.11 0.30D33J013329.43+303614.3 3.76 21.17 · · · 21.93 0.10 · · · 0.24 0.22D33J013341.17+302856.9 3.97 21.42 20.48 21.93 0.13 0.14 0.14 0.26D33J013310.09+303355.1 4.02 21.15 20.20 21.87 0.11 0.08 0.15 0.32D33J013413.03+304210.3 4.11 21.15 20.76 21.75 0.12 0.17 0.10 0.30D33J013305.37+303433.9 4.18 21.47 20.88 22.10 0.12 0.12 0.11 0.30D33J013327.20+303747.3 4.25 20.91 · · · 21.42 0.09 · · · 0.07 0.22D33J013337.02+303741.5 4.34 20.89 19.92 · · · 0.10 0.09 · · · 0.17D33J013336.80+303710.0 4.36 20.95 19.59 21.66 0.12 0.09 0.13 0.25D33J013330.33+303019.9 4.41 21.55 20.74 · · · 0.13 0.12 · · · 0.38D33J013319.13+303419.4 4.43 21.30 20.67 22.00 0.12 0.10 0.16 0.41D33J013305.84+303040.7 4.47 21.59 21.46 21.91 0.18 0.43 0.10 0.47D33J013402.60+303945.2 4.47 21.22 · · · 22.27 0.11 · · · 0.11 0.33D33J013303.16+303631.3 4.50 21.40 20.80 21.91 0.12 0.09 0.20 0.42D33J013355.88+304720.3 4.54 21.89 21.92 21.98 0.33 0.32 0.11 0.66D33J013255.35+303753.4 4.56 21.29 21.07 21.74 0.11 0.17 0.17 0.33D33J013336.87+303020.5 4.57 19.19 · · · 19.26 0.04 · · · 0.06 0.13D33J013322.04+303731.9 4.59 21.03 20.14 21.69 0.07 0.08 0.05 0.14D33J013254.46+303944.0 4.60 21.09 20.50 21.78 0.09 0.12 0.10 0.20D33J013309.36+303933.6 4.60 21.13 20.46 21.64 0.08 0.15 0.05 0.22D33J013326.43+303959.6 4.61 19.79 18.93 20.29 0.04 0.05 0.04 0.10D33J013327.28+304024.7 4.74 21.70 · · · 22.40 0.16 · · · 0.26 0.40D33J013409.67+304350.1 4.77 21.07 20.60 21.70 0.13 0.13 0.09 0.32D33J013359.36+304213.8 4.78 21.72 20.89 · · · 0.22 0.28 · · · 0.45D33J013356.19+303228.1 4.79 21.41 19.75 22.09 0.16 0.08 0.27 0.26D33J013256.15+303850.2 4.80 20.98 20.36 21.52 0.07 0.10 0.07 0.22D33J013315.35+303004.3 4.80 21.43 20.52 22.34 0.14 0.18 0.18 0.32D33J013339.02+303714.1 4.83 21.32 21.11 22.24 0.13 0.27 0.12 0.36D33J013347.62+304626.5 4.85 20.80 20.41 21.36 0.08 0.12 0.05 0.18D33J013305.08+303648.4 4.92 22.10 21.06 22.66 0.20 0.20 0.25 0.33D33J013336.31+303438.6 4.98 21.52 20.46 · · · 0.16 0.12 · · · 0.37D33J013331.55+303408.2 5.01 21.43 19.52 · · · 0.13 0.12 · · · 0.23D33J013359.36+304337.9 5.03 21.26 · · · 21.98 0.14 · · · 0.11 0.39D33J013421.40+303959.8 5.03 21.58 20.79 22.13 0.13 0.19 0.07 0.31D33J013341.35+304736.6 5.19 22.04 21.09 · · · 0.26 0.30 · · · 0.55D33J013358.12+302958.7 5.24 21.11 19.90 · · · 0.11 0.08 · · · 0.24D33J013321.75+303235.1 5.28 21.34 · · · 22.02 0.10 · · · 0.08 0.32D33J013405.95+303454.0 5.28 20.61 · · · 20.92 0.08 · · · 0.07 0.23D33J013342.58+303330.1 5.31 20.51 19.96 21.08 0.05 0.05 0.08 0.15D33J013408.59+303754.8 5.32 21.10 · · · 21.96 0.11 · · · 0.16 0.32D33J013340.76+303434.9 5.34 21.12 20.50 · · · 0.15 0.14 · · · 0.40D33J013421.47+304415.6 5.36 20.76 19.54 21.75 0.08 0.06 0.11 0.16


Table 2.4—Continued


D33J013321.87+303249.9 5.41 21.49 20.72 21.96 0.23 0.16 0.24 0.59D33J013359.46+303846.9 5.45 21.23 · · · · · · 0.19 · · · · · · 0.42D33J013258.67+303505.2 5.48 21.27 20.65 21.79 0.11 0.12 0.17 0.34D33J013307.02+303224.6 5.49 21.31 20.72 · · · 0.13 0.12 · · · 0.38D33J013355.27+304637.7 5.49 20.89 20.16 21.76 0.13 0.11 0.16 0.27D33J013357.00+303117.7 5.55 20.58 19.60 21.23 0.06 0.07 0.05 0.14D33J013343.94+304557.2 5.56 20.74 20.08 21.09 0.08 0.11 0.05 0.19D33J013351.17+303001.3 5.60 20.46 19.82 21.18 0.05 0.08 0.07 0.15D33J013330.69+303449.8 5.61 21.92 21.38 22.23 0.25 0.35 0.18 0.73D33J013428.97+303836.0 5.62 21.15 20.26 21.70 0.17 0.15 0.19 0.37D33J013401.29+304325.8 5.67 20.78 20.02 21.31 0.11 0.10 0.12 0.30D33J013420.52+304243.8 5.70 21.30 20.44 21.92 0.13 0.12 0.13 0.35D33J013350.48+304733.9 5.74 21.60 20.72 · · · 0.14 0.14 · · · 0.33D33J013312.23+303053.0 5.75 20.63 19.67 21.21 0.06 0.05 0.05 0.17D33J013311.23+303115.4 5.76 21.26 20.60 21.86 0.11 0.10 0.11 0.30D33J013332.10+303002.7 5.79 21.34 · · · 22.38 0.18 · · · 0.30 0.53D33J013420.04+304502.8 5.85 20.38 19.24 21.16 0.06 0.05 0.07 0.14D33J013413.51+304210.1 5.87 19.95 19.47 20.39 0.04 0.05 0.02 0.11D33J013325.23+303158.0 5.88 21.72 20.22 22.45 0.19 0.07 0.18 0.42D33J013350.93+303156.7 5.89 20.59 20.09 21.14 0.11 0.08 0.07 0.27D33J013404.96+303557.8 5.89 21.19 20.50 21.76 0.11 0.13 0.25 0.35D33J013407.31+303048.7 5.90 21.79 20.89 22.42 0.17 0.16 0.18 0.42D33J013407.88+303831.7 5.90 20.28 · · · 20.94 0.09 · · · 0.08 0.20D33J013343.80+304512.9 5.91 20.04 · · · · · · 0.06 · · · · · · 0.15D33J013424.70+304430.9 5.91 21.26 20.18 22.19 0.09 0.09 0.14 0.25D33J013303.59+303620.4 5.94 21.55 · · · 22.33 0.18 · · · 0.16 0.39D33J013352.30+304602.7 5.96 21.42 20.39 22.13 0.12 0.12 0.14 0.33D33J013341.79+303452.7 5.97 21.12 · · · 21.67 0.15 · · · 0.10 0.31D33J013359.85+303800.1 5.99 21.23 20.41 22.24 0.17 0.14 0.15 0.45D33J013346.78+304333.6 6.00 20.90 · · · 21.36 0.10 · · · 0.11 0.30D33J013408.40+304430.2 6.00 21.54 20.73 21.97 0.13 0.16 0.10 0.29D33J013349.52+304743.8 6.01 21.74 20.45 22.66 0.15 0.13 0.30 0.30D33J013403.10+304331.6 6.07 20.89 · · · · · · 0.10 · · · · · · 0.24D33J013416.99+302923.2 6.11 21.20 20.63 21.75 0.16 0.13 0.25 0.55D33J013325.59+303510.9 6.12 21.07 20.14 21.90 0.08 0.12 0.14 0.33D33J013356.65+304837.8 6.12 20.80 · · · 21.27 0.11 · · · 0.09 0.35D33J013405.53+304120.2 6.12 21.60 20.35 22.21 0.19 0.13 0.25 0.41D33J013324.85+303708.1 6.13 21.08 19.84 21.64 0.08 0.11 0.10 0.22D33J013302.88+303636.4 6.18 21.32 20.56 21.94 0.13 0.13 0.10 0.46D33J013403.63+304528.0 6.19 20.90 20.20 21.38 0.10 0.10 0.08 0.36D33J013310.30+304011.6 6.20 21.24 20.50 21.99 0.10 0.18 0.14 0.30D33J013416.96+303415.6 6.25 20.96 · · · · · · 0.13 · · · · · · 0.26D33J013349.57+304401.0 6.28 21.53 20.83 · · · 0.18 0.17 · · · 0.38D33J013349.26+304701.0 6.34 21.27 · · · 22.07 0.14 · · · 0.23 0.39




D33J013427.70+304131.7 6.37 20.66 20.02 21.13 0.07 0.08 0.04 0.13D33J013310.45+303817.7 6.48 21.32 20.66 22.10 0.17 0.16 0.21 0.53D33J013329.20+303136.2 6.53 21.24 · · · 22.40 0.13 · · · 0.20 0.34D33J013315.68+303319.3 6.55 · · · 20.19 · · · · · · 0.10 · · · · · ·D33J013424.82+304129.2 6.55 21.29 20.34 21.98 0.14 0.12 0.17 0.48D33J013304.63+303148.9 6.61 21.11 · · · · · · 0.13 · · · · · · 0.39D33J013325.95+303742.5 6.64 20.84 · · · 21.52 0.10 · · · 0.14 0.41D33J013301.99+303519.6 6.75 21.95 20.87 22.72 0.20 0.27 0.21 0.52D33J013349.33+303009.7 6.78 20.94 20.43 21.53 0.09 0.11 0.09 0.37D33J013352.00+304702.0 6.87 20.62 20.11 21.35 0.09 0.16 0.07 0.25D33J013355.70+304416.0 6.88 21.26 20.83 21.86 0.16 0.18 0.16 0.45D33J013406.40+304003.5 6.93 20.58 19.42 20.92 0.11 0.11 0.11 0.28D33J013428.19+303900.4 6.99 21.15 20.32 21.72 0.10 0.12 0.13 0.32D33J013332.38+303409.8 7.06 21.18 20.64 · · · 0.21 0.28 · · · 0.55D33J013333.69+303428.6 7.06 20.71 19.80 21.67 0.10 0.13 0.26 0.23D33J013402.95+304727.3 7.09 21.00 20.34 21.67 0.08 0.09 0.05 0.27D33J013404.04+304328.8 7.09 20.53 19.08 · · · 0.10 0.11 · · · 0.25D33J013410.27+303934.7 7.10 21.56 21.08 21.84 0.17 0.18 0.09 0.41D33J013324.90+303854.7 7.13 20.53 19.71 21.23 0.08 0.06 0.05 0.21D33J013429.03+304015.4 7.14 21.31 20.56 21.86 0.16 0.18 0.15 0.53D33J013330.90+303051.4 7.18 21.27 20.29 21.93 0.12 0.09 0.13 0.30D33J013331.55+302905.5 7.21 19.96 19.63 · · · 0.06 0.10 · · · 0.16D33J013356.42+304643.5 7.30 20.74 19.92 · · · 0.08 0.09 · · · 0.17D33J013413.52+303027.7 7.30 21.23 20.38 21.97 0.11 0.08 0.11 0.26D33J013402.15+303741.9 7.32 20.85 20.78 · · · 0.13 0.23 · · · 0.36D33J013340.54+304542.4 7.38 21.70 20.80 22.38 0.17 0.24 0.06 0.47D33J013343.02+304501.6 7.38 20.06 19.73 20.44 0.05 0.09 0.02 0.14D33J013327.02+303959.9 7.51 21.97 20.89 22.61 0.25 0.19 0.19 0.69D33J013251.40+303615.5 7.59 21.33 20.48 21.98 0.11 0.11 0.15 0.30D33J013336.47+303053.9 7.59 21.12 20.73 · · · 0.18 0.18 · · · 0.70D33J013347.87+302943.9 7.62 21.20 19.93 22.22 0.13 0.11 0.11 0.26D33J013422.38+304408.0 7.66 21.27 20.24 22.10 0.13 0.08 0.13 0.25D33J013424.20+304738.9 7.68 20.49 19.74 21.27 0.08 0.09 0.10 0.28D33J013308.75+303057.9 7.72 20.86 20.14 21.41 0.08 0.10 0.06 0.24D33J013402.20+304242.5 7.84 20.92 20.32 21.49 0.09 0.15 0.08 0.40D33J013417.27+303211.7 7.96 21.00 20.13 21.67 0.11 0.09 0.07 0.43D33J013332.37+303144.1 7.97 21.13 20.28 · · · 0.11 0.16 · · · 0.26D33J013348.81+303416.2 7.97 20.26 19.34 20.89 0.08 0.10 0.07 0.24D33J013429.40+304137.8 7.98 · · · 20.04 · · · · · · 0.10 · · · · · ·D33J013314.70+303907.1 8.01 20.43 19.82 21.01 0.09 0.08 0.07 0.31D33J013341.64+304311.7 8.06 21.40 20.48 22.34 0.12 0.27 0.09 0.40D33J013329.80+303453.1 8.10 20.76 20.10 21.48 0.07 0.10 0.09 0.28D33J013417.63+304507.7 8.14 20.20 19.17 20.89 0.05 0.06 0.06 0.25D33J013336.24+303244.4 8.18 21.28 20.68 22.45 0.13 0.14 0.16 0.27




D33J013348.74+303045.3 8.18 21.13 20.26 22.09 0.10 0.09 0.06 0.28D33J013412.55+304126.3 8.32 20.96 19.95 21.91 0.09 0.06 0.10 0.17D33J013320.16+303519.5 8.34 20.63 19.67 21.30 0.07 0.05 0.06 0.29D33J013328.78+303829.4 8.37 20.96 · · · 22.10 0.11 · · · 0.14 0.26D33J013339.74+303413.0 8.37 20.95 20.21 21.54 0.19 0.17 0.30 0.47D33J013318.37+303916.6 8.54 20.69 19.76 21.47 0.07 0.07 0.10 0.42D33J013413.26+304306.9 8.55 21.36 20.61 21.89 0.14 0.13 0.10 0.37D33J013406.55+303816.9 8.58 20.31 · · · · · · 0.07 · · · · · · 0.23D33J013356.24+303909.2 8.59 20.50 19.24 · · · 0.15 0.11 · · · 0.22D33J013328.73+303131.9 8.69 21.69 20.67 22.38 0.14 0.18 0.23 0.50D33J013409.24+304238.2 8.71 20.89 19.67 21.82 0.12 0.10 0.10 0.23D33J013322.94+303040.2 8.74 20.47 19.65 21.04 0.06 0.08 0.07 0.30D33J013423.87+304858.8 8.83 20.76 19.74 · · · 0.09 0.10 · · · 0.18D33J013328.74+303440.5 8.90 20.69 19.80 21.26 0.09 0.06 0.19 0.35D33J013331.19+303355.8 8.92 20.65 · · · 21.76 0.10 · · · 0.19 0.13D33J013337.49+303305.8 8.98 20.93 20.13 21.67 0.11 0.11 0.14 0.28D33J013337.87+303355.4 8.98 21.16 20.07 21.76 0.15 0.09 0.06 0.28D33J013333.43+303321.3 9.00 19.87 19.45 19.96 0.07 0.09 0.09 0.18D33J013336.75+303435.1 9.06 20.31 19.65 21.04 0.07 0.08 0.06 0.26D33J013343.49+303121.9 9.08 20.91 19.94 21.48 0.11 0.10 0.16 0.17D33J013413.83+303212.5 9.09 20.74 20.05 21.20 0.09 0.11 0.09 0.24D33J013346.21+302909.2 9.12 20.65 20.00 20.95 0.10 0.11 0.06 0.27D33J013338.93+303414.2 9.13 20.76 · · · 20.97 0.13 · · · 0.04 0.27D33J013413.40+304334.2 9.13 20.62 20.19 20.96 0.10 0.11 0.05 0.28D33J013409.32+302956.8 9.16 20.68 19.92 21.46 0.08 0.06 0.06 0.19D33J013352.73+303416.5 9.22 21.04 · · · 21.62 0.15 · · · 0.06 0.32D33J013426.74+304003.1 9.26 20.55 19.68 21.15 0.07 0.08 0.12 0.24D33J013351.88+302856.1 9.32 21.01 20.38 21.59 0.10 0.19 0.12 0.26D33J013347.74+303814.0 9.38 20.03 19.21 20.70 0.07 0.11 0.09 0.16D33J013419.13+303430.5 9.39 21.04 20.16 · · · 0.11 0.08 · · · 0.24D33J013349.48+304500.4 9.58 21.11 20.28 · · · 0.19 0.16 · · · 0.29D33J013325.77+303158.5 9.59 20.95 · · · · · · 0.11 · · · · · · 0.35D33J013343.11+303649.4 9.59 20.60 19.61 · · · 0.08 0.07 · · · 0.21D33J013353.08+304834.2 9.59 19.88 · · · · · · 0.06 · · · · · · 0.19D33J013350.65+304714.6 9.72 20.72 20.08 21.26 0.11 0.11 0.06 0.34D33J013341.01+304340.1 9.84 20.78 · · · 21.71 0.10 · · · 0.16 0.16D33J013420.99+304415.1 9.98 20.54 19.86 21.13 0.08 0.08 0.06 0.34D33J013333.10+303345.4 10.09 20.67 20.01 · · · 0.12 0.14 · · · 0.33D33J013354.97+303537.3 10.12 20.52 19.64 21.05 0.10 0.10 0.12 0.36D33J013408.79+303946.3 10.12 20.59 19.43 21.15 0.09 0.07 0.12 0.26D33J013325.47+303102.6 10.27 21.83 20.84 · · · 0.27 0.18 · · · 0.58D33J013258.14+303858.1 10.30 20.64 19.94 21.16 0.06 0.07 0.05 0.19D33J013416.43+303728.9 10.33 20.57 19.70 · · · 0.11 0.09 · · · 0.34D33J013332.54+303116.2 10.36 22.45 · · · · · · 0.28 · · · · · · 0.45




D33J013342.06+303211.3 10.38 20.88 · · · · · · 0.15 · · · · · · 0.36D33J013356.09+303903.0 10.42 20.55 · · · · · · 0.11 · · · · · · 0.33D33J013410.15+304450.1 10.45 20.60 19.77 21.34 0.08 0.06 0.05 0.34D33J013416.91+304639.8 10.56 20.67 19.43 21.57 0.12 0.07 0.07 0.26D33J013338.80+303423.4 10.57 · · · 19.81 · · · · · · 0.10 · · · · · ·D33J013341.85+302952.2 10.59 20.96 19.96 21.91 0.12 0.11 0.16 0.35D33J013338.79+303423.3 10.60 20.50 19.59 · · · 0.09 0.08 · · · 0.32D33J013413.79+304418.3 10.61 21.60 20.38 22.42 0.20 0.16 0.16 0.55D33J013335.51+303650.0 10.70 20.85 20.41 21.80 0.13 0.15 0.24 0.49D33J013333.14+303327.4 10.95 21.11 · · · · · · 0.13 · · · · · · 0.28D33J013302.17+303455.1 10.99 20.98 19.95 21.79 0.10 0.09 0.11 0.22D33J013419.65+303419.1 11.03 21.47 · · · · · · 0.22 · · · · · · 0.60D33J013323.01+303216.6 11.13 20.83 20.04 21.55 0.08 0.08 0.08 0.22D33J013352.79+303836.6 11.15 20.37 · · · · · · 0.11 · · · · · · 0.28D33J013358.50+304359.6 11.15 20.44 19.58 21.24 0.07 0.08 0.08 0.29D33J013313.79+303208.4 11.20 20.49 19.65 21.08 0.10 0.07 0.17 0.42D33J013327.29+303551.5 11.20 20.53 19.66 21.32 0.08 0.08 0.17 0.29D33J013412.45+303839.4 11.23 20.18 19.01 · · · 0.10 0.09 · · · 0.25D33J013412.44+303839.7 11.25 20.09 18.98 · · · 0.08 0.06 · · · 0.21D33J013306.38+303142.9 11.26 20.43 19.48 21.21 0.09 0.06 0.11 0.36D33J013415.39+303727.8 11.28 20.84 19.98 · · · 0.12 0.10 · · · 0.28D33J013257.84+303240.4 11.37 20.55 19.46 21.28 0.09 0.10 0.13 0.23D33J013355.90+304231.0 11.37 20.58 19.70 20.78 0.13 0.12 0.09 0.27D33J013338.31+303639.5 11.41 19.89 18.99 21.04 0.12 0.16 0.10 0.30D33J013341.89+304728.6 11.44 18.38 18.13 · · · 0.05 0.07 · · · 0.09D33J013411.34+303535.4 11.45 20.39 19.68 20.94 0.08 0.08 0.06 0.25D33J013325.53+303427.4 11.46 20.08 19.43 20.86 0.07 0.07 0.07 0.28D33J013326.68+303112.9 11.49 20.65 19.80 21.42 0.09 0.07 0.13 0.48D33J013340.13+304740.6 11.50 20.91 19.85 22.08 0.09 0.08 0.05 0.28D33J013353.40+303308.8 11.50 21.31 20.75 21.73 0.17 0.17 0.22 0.52D33J013335.47+303331.0 11.52 20.61 19.68 21.57 0.12 0.08 0.09 0.44D33J013413.39+303318.0 11.52 21.15 19.98 21.57 0.11 0.07 0.05 0.36D33J013357.33+304113.6 11.61 20.29 19.25 20.93 0.08 0.11 0.10 0.26D33J013414.69+304609.7 11.77 21.73 19.79 · · · 0.20 0.08 · · · 0.34D33J013336.22+303731.5 11.79 20.99 19.77 22.14 0.12 0.11 0.08 0.26D33J013337.65+303219.8 11.88 20.84 19.85 · · · 0.11 0.10 · · · 0.32D33J013420.17+304351.5 11.97 20.23 19.48 20.97 0.09 0.08 0.07 0.38D33J013356.12+304342.5 11.98 20.75 19.63 21.47 0.11 0.11 0.14 0.42D33J013317.57+303154.5 12.07 20.71 19.92 21.44 0.08 0.07 0.10 0.32D33J013318.41+303534.1 12.09 20.08 19.50 20.50 0.08 0.07 0.07 0.28D33J013341.18+304755.0 12.12 20.26 19.14 21.21 0.07 0.08 0.14 0.33D33J013255.91+303438.2 12.33 · · · 19.63 · · · · · · 0.08 · · · · · ·D33J013351.02+304359.9 12.35 21.16 20.24 21.93 0.30 0.21 0.27 0.66D33J013357.56+303805.5 12.35 20.41 19.77 21.02 0.15 0.14 0.13 0.51




D33J013346.49+304820.6 12.37 20.06 18.38 21.26 0.06 0.05 0.08 0.15D33J013336.44+303651.0 12.38 21.06 19.39 · · · 0.13 0.08 · · · 0.39D33J013411.19+304754.7 12.41 20.15 19.37 20.76 0.09 0.07 0.11 0.35D33J013308.58+303122.3 12.53 20.16 19.35 20.94 0.09 0.07 0.10 0.36D33J013322.14+303258.5 12.62 20.75 19.78 21.57 0.08 0.08 0.14 0.45D33J013354.94+304642.3 12.88 20.02 19.32 20.61 0.05 0.05 0.07 0.14D33J013345.93+304231.5 12.92 20.28 19.17 20.95 0.08 0.05 0.07 0.47D33J013349.78+303758.9 12.92 20.22 19.71 · · · 0.17 0.11 · · · 0.46D33J013349.97+303015.2 12.98 20.60 19.39 21.40 0.07 0.06 0.08 0.35D33J013402.76+304145.4 13.04 20.01 18.87 20.69 0.06 0.05 0.06 0.37D33J013312.49+303020.9 13.08 19.49 19.21 19.63 0.05 0.06 0.08 0.09D33J013345.79+304420.8 13.13 20.49 · · · 21.33 0.08 · · · 0.09 0.45D33J013331.59+303931.7 13.17 20.09 19.35 20.77 0.08 0.08 0.10 0.50D33J013359.94+303910.4 13.25 20.59 19.57 · · · 0.14 0.18 · · · 0.39D33J013356.42+304631.4 13.29 22.31 20.76 · · · 0.29 0.23 · · · 1.00D33J013408.11+303931.8 13.29 20.19 19.94 · · · 0.14 0.15 · · · 0.28D33J013411.86+302947.7 13.30 20.43 19.54 21.24 0.09 0.09 0.08 0.51D33J013329.56+303109.0 13.33 20.63 19.54 21.59 0.11 0.05 0.12 0.45D33J013351.95+304848.6 13.33 20.42 19.51 21.22 0.11 0.10 0.16 0.60D33J013415.05+304435.0 13.35 20.59 19.34 21.32 0.08 0.07 0.11 0.25D33J013411.94+303519.3 13.37 20.72 19.48 21.62 0.14 0.06 0.10 0.51D33J013305.51+303824.8 13.53 20.60 19.69 21.54 0.07 0.07 0.07 0.48D33J013408.71+304543.0 13.53 20.71 19.71 21.53 0.07 0.07 0.13 0.54D33J013351.23+303758.4 13.57 19.89 19.14 20.78 0.08 0.08 0.09 0.40D33J013336.58+303154.8 13.64 19.91 · · · · · · 0.06 · · · · · · 0.16D33J013402.53+303628.2 13.65 20.37 19.45 20.95 0.10 0.10 0.11 0.32D33J013331.51+303705.3 13.76 21.23 20.05 · · · 0.24 0.20 · · · 0.47D33J013338.75+303751.7 13.77 21.21 20.12 22.30 0.18 0.15 0.11 0.52D33J013311.78+303709.8 13.88 20.54 18.99 21.47 0.06 0.05 0.14 0.29D33J013336.45+302934.2 13.94 21.47 19.99 · · · 0.20 0.12 · · · 0.52D33J013408.35+303817.3 14.34 20.18 · · · 20.66 0.06 · · · 0.09 0.40D33J013405.87+303928.6 14.59 19.89 19.11 20.38 0.06 0.06 0.07 0.38D33J013404.89+304022.4 14.61 20.17 18.67 21.03 0.11 0.08 0.16 0.52D33J013409.05+303629.8 14.62 19.44 19.01 · · · 0.04 0.04 · · · 0.12D33J013348.18+304319.0 14.63 20.56 19.39 21.44 0.11 0.06 0.11 0.30D33J013429.12+304338.7 14.77 20.14 19.35 20.81 0.07 0.08 0.15 0.56D33J013401.32+304026.7 14.86 20.09 19.39 20.37 0.11 0.16 0.12 0.43D33J013427.81+304101.0 14.89 20.52 19.55 · · · 0.08 0.08 · · · 0.53D33J013342.22+303747.6 14.90 19.78 18.89 · · · 0.11 0.10 · · · 0.35D33J013415.00+304452.9 14.91 20.41 19.40 21.18 0.06 0.06 0.06 0.29D33J013347.58+303634.5 14.92 20.60 19.81 21.46 0.10 0.10 0.03 0.45D33J013332.10+303946.0 14.97 20.41 19.38 21.23 0.06 0.09 0.11 0.42D33J013334.89+303337.4 15.07 20.16 19.33 20.88 0.09 0.08 0.09 0.54D33J013346.20+303744.5 15.07 20.36 18.80 · · · 0.24 0.09 · · · 0.49




D33J013348.16+303800.4 15.10 19.88 19.28 · · · 0.13 0.12 · · · 0.42D33J013338.31+303603.3 15.13 21.21 20.07 · · · 0.30 0.16 · · · 0.62D33J013400.96+304340.9 15.65 19.92 19.11 · · · 0.04 0.06 · · · 0.20D33J013334.89+302912.9 15.66 22.80 20.86 · · · 0.34 0.31 · · · 0.41D33J013315.30+303212.5 15.69 · · · 19.04 · · · · · · 0.04 · · · · · ·D33J013334.20+303501.2 15.69 20.50 19.51 21.70 0.18 0.12 0.14 0.48D33J013328.01+303213.8 15.75 21.18 20.01 22.10 0.08 0.10 0.11 0.37D33J013401.60+303103.4 15.79 20.35 19.38 21.28 0.08 0.05 0.03 0.42D33J013334.33+303531.0 15.83 19.85 18.86 20.36 0.05 0.09 0.04 0.20D33J013420.35+304101.0 15.95 20.21 19.18 21.04 0.04 0.06 0.08 0.43D33J013329.26+303100.7 15.96 21.09 19.84 22.30 0.11 0.08 0.14 0.46D33J013356.09+304205.0 15.97 20.40 20.14 20.73 0.09 0.15 0.04 0.11D33J013342.65+303300.5 16.04 19.90 19.13 · · · 0.07 0.10 · · · 0.47D33J013403.99+304709.4 16.06 20.90 19.68 21.91 0.11 0.09 0.08 0.46D33J013403.95+303616.0 16.27 20.35 19.23 21.32 0.11 0.10 0.07 0.42D33J013417.74+303707.7 16.28 21.21 20.00 · · · 0.19 0.10 · · · 0.55D33J013412.12+303636.4 16.41 20.29 19.35 · · · 0.06 0.06 · · · 0.34D33J013417.85+303558.1 16.51 20.16 19.18 20.66 0.07 0.07 0.04 0.31D33J013400.54+304027.5 16.67 19.88 · · · 20.58 0.04 · · · 0.06 0.17D33J013336.32+302856.5 16.81 20.68 19.50 21.85 0.10 0.07 0.11 0.47D33J013353.41+303535.6 17.47 19.70 19.08 20.29 0.07 0.07 0.12 0.51D33J013344.98+303952.3 17.53 19.91 18.81 20.66 0.16 0.14 0.14 0.50D33J013330.78+303111.6 17.54 20.56 19.59 21.48 0.06 0.08 0.17 0.48D33J013331.23+302947.7 17.55 20.33 19.45 · · · 0.12 0.11 · · · 0.64D33J013421.20+304536.8 17.83 19.85 18.93 20.74 0.04 0.06 0.07 0.42D33J013330.07+303638.4 17.97 19.74 18.77 20.52 0.05 0.07 0.06 0.52D33J013316.39+303658.0 18.57 20.08 19.08 21.01 0.06 0.07 0.15 0.50D33J013414.56+304413.4 18.61 20.09 19.01 20.99 0.08 0.11 0.09 0.63D33J013346.51+304645.0 18.81 19.74 18.93 20.74 0.06 0.08 0.06 0.53D33J013406.74+303940.0 18.89 19.82 18.95 20.65 0.06 0.08 0.06 0.49D33J013408.74+302857.7 19.14 20.45 19.01 21.44 0.05 0.06 0.07 0.39D33J013410.21+303408.0 19.36 20.51 19.45 21.70 0.08 0.07 0.14 0.45D33J013321.14+303116.4 19.61 20.68 19.57 21.62 0.07 0.05 0.10 0.36D33J013326.07+303320.2 19.98 20.15 19.19 21.09 0.04 0.06 0.05 0.50D33J013330.10+303804.4 19.98 19.88 19.13 20.45 0.07 0.08 0.10 0.37D33J013341.29+303213.2 20.13 18.05 17.92 18.12 0.02 0.06 0.02 0.09D33J013331.39+303352.1 20.18 19.19 17.47 · · · 0.06 0.06 · · · 0.26D33J013343.29+304355.8 20.19 19.40 18.87 19.72 0.06 0.08 0.07 0.26D33J013418.86+304441.1 20.21 20.17 18.84 21.33 0.07 0.06 0.08 0.43D33J013324.59+303518.0 20.49 19.97 18.79 20.99 0.08 0.06 0.13 0.55D33J013255.13+303514.0 21.08 · · · 19.06 · · · · · · 0.06 · · · · · ·D33J013331.65+302958.6 21.48 19.84 · · · · · · 0.07 · · · · · · 0.41D33J013304.05+303534.3 21.60 · · · 19.92 · · · · · · 0.11 · · · · · ·D33J013401.74+303923.0 21.65 19.95 18.81 20.83 0.07 0.16 0.08 0.50




D33J013351.44+303830.8 21.81 20.14 18.91 · · · 0.17 0.20 · · · 0.55D33J013420.43+304543.4 21.82 19.35 18.52 20.13 0.04 0.06 0.06 0.44D33J013424.01+303953.1 21.90 19.77 18.74 20.63 0.05 0.08 0.05 0.52D33J013330.35+303555.7 22.12 19.37 · · · 20.18 0.05 · · · 0.12 0.56D33J013344.51+304313.6 22.41 19.71 18.69 20.59 0.06 0.06 0.06 0.33D33J013253.04+303003.7 22.52 22.20 20.22 · · · 0.19 0.23 · · · 0.35D33J013259.16+303957.6 22.63 · · · 20.02 · · · · · · 0.12 · · · · · ·D33J013333.21+303747.8 22.66 20.61 19.31 · · · 0.07 0.10 · · · 0.42D33J013322.59+303455.0 23.00 · · · 19.12 · · · · · · 0.06 · · · · · ·D33J013350.71+303544.6 23.30 19.94 18.94 20.97 0.09 0.05 0.08 0.57D33J013417.51+303819.8 23.31 20.28 19.18 21.49 0.06 0.05 0.06 0.42D33J013358.81+303719.9 24.55 19.99 18.83 21.13 0.05 0.06 0.08 0.51D33J013339.24+303033.6 24.62 21.94 21.75 · · · 0.26 0.31 · · · 0.69D33J013401.17+303113.9 24.89 19.19 18.28 19.75 0.04 0.05 0.04 0.39D33J013409.52+304535.6 25.26 20.06 18.95 21.21 0.06 0.05 0.08 0.40D33J013355.20+304343.0 26.38 19.94 18.98 21.00 0.07 0.05 0.07 0.37D33J013350.47+304753.7 26.48 19.92 18.68 21.14 0.05 0.06 0.11 0.29D33J013347.15+303536.6 26.51 19.89 18.87 20.70 0.07 0.07 0.07 0.50D33J013411.21+304155.9 26.56 19.33 18.24 20.12 0.03 0.05 0.10 0.37D33J013357.57+303844.7 26.69 18.48 18.00 18.82 0.06 0.10 0.05 0.25D33J013331.34+303017.2 27.02 20.37 19.18 · · · 0.09 0.06 · · · 0.54D33J013423.44+304204.2 27.27 19.33 18.52 20.21 0.07 0.08 0.11 0.56D33J013354.25+304110.9 27.93 19.19 18.09 19.92 0.09 0.09 0.11 0.42D33J013332.86+303549.3 30.30 19.53 18.54 20.52 0.05 0.07 0.03 0.49D33J013400.99+304309.8 30.47 19.51 18.61 20.58 0.06 0.06 0.06 0.47D33J013301.95+303633.9 30.54 19.48 18.58 20.39 0.08 0.06 0.08 0.59D33J013329.41+303557.6 30.58 19.61 18.62 20.57 0.05 0.05 0.07 0.51D33J013415.84+304612.3 31.27 19.93 18.62 20.91 0.09 0.07 0.24 0.64D33J013358.07+304556.8 31.53 19.82 18.70 20.63 0.05 0.05 0.06 0.26D33J013354.74+304106.3 33.91 19.24 18.15 20.14 0.05 0.06 0.08 0.48D33J013354.80+304531.8 35.60 18.98 18.13 · · · 0.07 0.05 · · · 0.49D33J013412.15+304640.9 35.87 19.25 18.21 20.13 0.08 0.06 0.08 0.55D33J013352.42+303844.3 35.90 19.18 18.13 19.74 0.11 0.08 0.05 0.59D33J013341.16+303550.5 36.09 19.89 18.64 · · · 0.07 0.06 · · · 0.73D33J013415.77+303618.0 36.35 19.61 18.45 20.79 0.04 0.04 0.02 0.26D33J013327.40+303707.9 37.04 · · · 18.16 · · · · · · 0.06 · · · · · ·D33J013341.54+303609.7 37.35 19.35 18.32 20.52 0.04 0.05 0.06 0.61D33J013350.85+303336.5 37.57 20.55 19.09 21.71 0.06 0.05 0.05 0.38D33J013252.15+303714.6 37.58 19.16 18.23 20.03 0.06 0.07 0.07 0.51D33J013353.61+304850.4 38.74 · · · 20.39 · · · · · · 0.22 · · · · · ·D33J013329.18+303745.0 45.88 19.17 18.03 20.33 0.04 0.04 0.10 0.56D33J013328.28+303815.8 46.10 · · · 19.17 · · · · · · 0.07 · · · · · ·D33J013257.15+303935.8 46.74 20.88 19.71 21.99 0.07 0.09 0.13 0.31D33J013405.37+303632.5 48.12 19.37 19.13 19.66 0.06 0.06 0.03 0.16




D33J013359.42+303227.0 50.21 19.83 18.47 20.83 0.06 0.04 0.08 0.37D33J013339.91+303508.4 51.11 18.25 · · · · · · 0.03 · · · · · · 0.23D33J013420.65+303942.6 52.83 18.01 17.85 18.18 0.03 0.07 0.06 0.14D33J013338.75+303505.9 53.14 · · · 20.55 · · · · · · 0.26 · · · · · ·D33J013345.18+304419.5 53.34 · · · 17.99 · · · · · · 0.05 · · · · · ·D33J013339.18+303414.5 55.19 · · · 20.55 · · · · · · 0.30 · · · · · ·D33J013331.04+303143.9 55.39 19.25 18.08 20.41 0.04 0.04 0.04 0.29D33J013412.59+303644.6 55.87 20.00 18.93 20.63 0.10 0.05 0.07 0.55D33J013347.40+304422.6 55.91 19.60 18.31 20.79 0.05 0.05 0.07 0.29D33J013422.92+304847.6 55.92 21.02 18.97 22.67 0.09 0.07 0.19 0.43D33J013408.36+303414.2 56.43 · · · 20.24 · · · · · · 0.13 · · · · · ·D33J013254.27+303804.9 56.57 19.30 18.53 19.95 0.07 0.06 0.05 0.35D33J013405.11+303851.3 56.69 18.99 17.83 20.12 0.04 0.06 0.04 0.25D33J013403.81+303911.0 57.40 19.63 18.24 · · · 0.05 0.07 · · · 0.36D33J013337.43+303139.2 57.48 19.20 18.06 · · · 0.04 0.04 · · · 0.41D33J013335.15+303407.0 57.97 · · · 20.91 · · · · · · 0.29 · · · · · ·D33J013351.33+303901.1 61.80 17.56 · · · 18.33 0.05 · · · 0.05 0.18D33J013337.68+303830.8 61.89 · · · 20.03 · · · · · · 0.16 · · · · · ·D33J013349.53+303109.9 61.94 · · · 19.88 · · · · · · 0.12 · · · · · ·D33J013419.15+304510.7 62.11 · · · 20.16 · · · · · · 0.11 · · · · · ·D33J013403.82+303921.7 62.36 · · · 19.88 · · · · · · 0.14 · · · · · ·D33J013342.05+304314.9 62.55 · · · 20.91 · · · · · · 0.31 · · · · · ·D33J013407.13+304236.7 62.92 · · · 20.70 · · · · · · 0.35 · · · · · ·D33J013346.64+304219.3 62.98 · · · 20.11 · · · · · · 0.13 · · · · · ·D33J013409.66+303625.6 63.00 · · · 20.31 · · · · · · 0.15 · · · · · ·D33J013351.33+303847.1 63.26 · · · 20.08 · · · · · · 0.26 · · · · · ·D33J013410.62+304111.3 63.29 · · · 19.89 · · · · · · 0.14 · · · · · ·D33J013401.08+304702.6 63.34 · · · 20.02 · · · · · · 0.14 · · · · · ·D33J013341.07+303914.7 63.43 · · · 20.57 · · · · · · 0.45 · · · · · ·D33J013428.18+304115.9 63.50 · · · 20.90 · · · · · · 0.29 · · · · · ·D33J013346.55+304418.4 63.78 · · · 20.16 · · · · · · 0.17 · · · · · ·D33J013346.98+304129.6 63.84 · · · 20.38 · · · · · · 0.16 · · · · · ·D33J013303.58+303018.5 63.93 · · · 21.21 · · · · · · 0.25 · · · · · ·D33J013325.72+303837.0 64.41 · · · 20.58 · · · · · · 0.14 · · · · · ·D33J013413.73+303544.1 64.68 · · · 21.15 · · · · · · 0.35 · · · · · ·D33J013339.18+303740.1 65.06 · · · 21.06 · · · · · · 0.32 · · · · · ·D33J013402.22+304347.8 65.21 · · · 20.47 · · · · · · 0.26 · · · · · ·D33J013338.45+303447.5 65.23 · · · 20.83 · · · · · · 0.25 · · · · · ·D33J013333.39+303157.4 65.46 · · · 20.48 · · · · · · 0.14 · · · · · ·D33J013413.21+304355.0 65.58 · · · 20.71 · · · · · · 0.30 · · · · · ·D33J013408.48+304748.8 66.13 · · · 20.26 · · · · · · 0.22 · · · · · ·D33J013351.81+303951.0 67.05 18.38 17.39 19.27 0.07 0.09 0.14 0.35D33J013422.73+304328.4 67.49 · · · 20.01 · · · · · · 0.14 · · · · · ·D33J013359.94+304831.6 68.46 · · · 19.71 · · · · · · 0.10 · · · · · ·




D33J013400.09+303525.6 69.84 · · · 20.16 · · · · · · 0.18 · · · · · ·D33J013354.56+303659.8 70.18 · · · 20.62 · · · · · · 0.18 · · · · · ·D33J013356.75+304256.5 71.89 · · · 20.95 · · · · · · 0.34 · · · · · ·D33J013402.15+303414.3 73.78 · · · 20.36 · · · · · · 0.26 · · · · · ·D33J013343.85+303245.6 73.94 18.57 17.43 19.56 0.06 0.04 0.04 0.33D33J013420.32+303117.7 74.35 · · · 20.13 · · · · · · 0.17 · · · · · ·D33J013345.19+303547.7 74.69 · · · 21.33 · · · · · · 0.35 · · · · · ·D33J013328.59+303052.9 75.21 · · · 20.14 · · · · · · 0.11 · · · · · ·D33J013343.30+303641.0 75.49 · · · 20.47 · · · · · · 0.22 · · · · · ·D33J013404.32+304424.5 75.87 · · · 19.78 · · · · · · 0.14 · · · · · ·D33J013415.81+303429.8 76.09 · · · 20.62 · · · · · · 0.26 · · · · · ·D33J013308.07+303238.5 76.62 · · · 20.40 · · · · · · 0.10 · · · · · ·D33J013412.72+303914.6 76.91 20.36 18.16 · · · 0.21 0.06 · · · 0.34D33J013321.91+303114.2 77.17 19.94 18.31 21.44 0.04 0.04 0.06 0.15D33J013338.88+303653.3 77.26 · · · 20.63 · · · · · · 0.18 · · · · · ·D33J013317.74+303326.5 77.64 · · · 21.29 · · · · · · 0.33 · · · · · ·D33J013401.69+304159.2 77.83 · · · 20.92 · · · · · · 0.29 · · · · · ·D33J013352.98+304254.5 79.10 · · · 19.68 · · · · · · 0.08 · · · · · ·D33J013423.38+304731.4 79.72 · · · 19.99 · · · · · · 0.07 · · · · · ·D33J013400.12+304435.3 79.84 · · · 20.01 · · · · · · 0.11 · · · · · ·D33J013427.46+304334.5 80.43 · · · 20.76 · · · · · · 0.32 · · · · · ·D33J013427.42+303951.0 80.62 · · · 20.90 · · · · · · 0.33 · · · · · ·D33J013256.32+303910.9 83.02 · · · 18.45 · · · · · · 0.06 · · · · · ·D33J013316.35+303110.5 83.68 20.49 19.73 21.11 0.06 0.06 0.05 0.27D33J013335.11+303400.3 83.75 · · · 18.85 · · · · · · 0.05 · · · · · ·D33J013422.31+304116.1 84.16 · · · 19.38 · · · · · · 0.14 · · · · · ·D33J013318.47+303923.9 84.18 · · · 20.23 · · · · · · 0.20 · · · · · ·D33J013422.90+304733.5 84.34 · · · 18.32 · · · · · · 0.09 · · · · · ·D33J013332.70+303427.6 84.47 · · · 19.68 · · · · · · 0.12 · · · · · ·D33J013335.90+303717.7 84.54 · · · 20.34 · · · · · · 0.21 · · · · · ·D33J013403.57+304305.6 84.76 · · · 20.75 · · · · · · 0.35 · · · · · ·D33J013338.65+303029.1 84.80 · · · 21.41 · · · · · · 0.43 · · · · · ·D33J013302.64+303051.5 84.87 · · · 20.11 · · · · · · 0.13 · · · · · ·D33J013307.95+303209.9 84.91 · · · 19.59 · · · · · · 0.07 · · · · · ·D33J013259.49+303328.6 84.93 · · · 19.20 · · · · · · 0.04 · · · · · ·D33J013357.19+303631.6 84.93 · · · 19.74 · · · · · · 0.11 · · · · · ·D33J013427.08+303952.4 85.00 · · · 19.67 · · · · · · 0.19 · · · · · ·D33J013352.82+304817.8 85.08 · · · 20.06 · · · · · · 0.19 · · · · · ·D33J013412.40+304606.7 85.18 · · · 19.23 · · · · · · 0.08 · · · · · ·D33J013413.29+303938.9 85.41 · · · 20.20 · · · · · · 0.15 · · · · · ·D33J013412.90+303639.4 85.55 · · · 19.62 · · · · · · 0.10 · · · · · ·D33J013414.51+304311.0 85.57 · · · 20.00 · · · · · · 0.18 · · · · · ·D33J013320.76+303312.5 85.58 · · · 20.24 · · · · · · 0.13 · · · · · ·D33J013356.49+303649.9 85.61 · · · 19.30 · · · · · · 0.11 · · · · · ·




D33J013309.20+303238.9 85.71 · · · 20.06 · · · · · · 0.17 · · · · · ·D33J013354.73+303815.1 85.84 · · · 20.17 · · · · · · 0.21 · · · · · ·D33J013337.09+303337.9 85.88 · · · 20.68 · · · · · · 0.28 · · · · · ·D33J013259.45+303358.9 85.93 · · · 19.63 · · · · · · 0.10 · · · · · ·D33J013336.42+303112.7 85.97 · · · 19.26 · · · · · · 0.11 · · · · · ·D33J013310.34+303922.0 86.02 · · · 20.60 · · · · · · 0.22 · · · · · ·D33J013336.47+303112.7 86.05 · · · 19.21 · · · · · · 0.12 · · · · · ·D33J013334.74+303426.3 86.08 · · · 19.67 · · · · · · 0.12 · · · · · ·D33J013405.86+303249.1 86.12 · · · 19.73 · · · · · · 0.13 · · · · · ·D33J013351.60+303134.5 86.15 · · · 20.29 · · · · · · 0.16 · · · · · ·D33J013403.29+303708.5 86.31 · · · 20.21 · · · · · · 0.27 · · · · · ·D33J013403.15+304505.4 86.33 · · · 19.88 · · · · · · 0.15 · · · · · ·D33J013409.66+303959.7 86.33 · · · 20.12 · · · · · · 0.20 · · · · · ·D33J013357.45+304656.1 86.44 · · · 20.19 · · · · · · 0.12 · · · · · ·D33J013421.03+304515.2 86.49 · · · 20.35 · · · · · · 0.21 · · · · · ·D33J013334.71+303836.3 86.56 · · · 19.56 · · · · · · 0.19 · · · · · ·D33J013412.37+303124.6 86.66 · · · 20.13 · · · · · · 0.15 · · · · · ·D33J013426.89+304230.9 86.68 · · · 20.21 · · · · · · 0.21 · · · · · ·D33J013253.25+303243.7 86.69 · · · 20.57 · · · · · · 0.19 · · · · · ·D33J013302.88+303545.2 86.70 · · · 20.22 · · · · · · 0.11 · · · · · ·D33J013400.11+304231.7 86.81 · · · 19.78 · · · · · · 0.13 · · · · · ·D33J013319.96+303152.4 86.82 · · · 20.57 · · · · · · 0.21 · · · · · ·D33J013427.50+303941.6 87.05 · · · 20.16 · · · · · · 0.17 · · · · · ·D33J013419.06+304347.6 87.13 · · · 21.00 · · · · · · 0.30 · · · · · ·D33J013306.72+303250.3 87.16 · · · 19.95 · · · · · · 0.12 · · · · · ·D33J013422.93+304616.4 87.23 · · · 19.98 · · · · · · 0.11 · · · · · ·D33J013425.25+304811.2 87.39 · · · 20.39 · · · · · · 0.14 · · · · · ·D33J013402.88+303028.8 87.45 · · · 19.12 · · · · · · 0.07 · · · · · ·D33J013357.00+304645.6 87.46 · · · 19.18 · · · · · · 0.10 · · · · · ·D33J013350.03+304620.3 87.56 · · · 19.75 · · · · · · 0.14 · · · · · ·D33J013344.10+304503.6 87.63 · · · 20.19 · · · · · · 0.18 · · · · · ·D33J013421.12+304624.5 88.12 · · · 20.49 · · · · · · 0.15 · · · · · ·D33J013410.57+303751.0 88.60 20.66 20.14 21.05 0.09 0.17 0.09 0.24D33J013354.20+303149.8 88.70 · · · 19.83 · · · · · · 0.19 · · · · · ·D33J013410.26+303035.1 89.15 · · · 20.45 · · · · · · 0.20 · · · · · ·D33J013318.30+303248.3 89.27 · · · 19.07 · · · · · · 0.07 · · · · · ·D33J013321.01+303849.3 89.61 · · · 20.74 · · · · · · 0.25 · · · · · ·D33J013426.22+304647.7 89.80 · · · 20.49 · · · · · · 0.19 · · · · · ·D33J013352.66+304801.6 90.36 · · · 21.06 · · · · · · 0.22 · · · · · ·D33J013258.97+303652.7 90.44 · · · 20.23 · · · · · · 0.15 · · · · · ·D33J013302.56+303201.2 91.05 · · · 20.60 · · · · · · 0.18 · · · · · ·D33J013351.99+303147.5 91.43 · · · 19.96 · · · · · · 0.17 · · · · · ·D33J013401.15+304226.9 91.87 · · · 19.27 · · · · · · 0.08 · · · · · ·D33J013407.57+304109.8 91.88 · · · 19.46 · · · · · · 0.07 · · · · · ·




D33J013313.33+303228.4 92.05 · · · 20.51 · · · · · · 0.15 · · · · · ·D33J013325.14+303545.3 92.05 · · · 19.75 · · · · · · 0.12 · · · · · ·D33J013358.11+304352.2 92.20 · · · 20.33 · · · · · · 0.15 · · · · · ·D33J013410.87+304758.0 92.30 · · · 18.75 · · · · · · 0.09 · · · · · ·D33J013411.34+303931.0 92.33 · · · 20.55 · · · · · · 0.26 · · · · · ·D33J013339.99+304600.0 92.34 · · · 20.58 · · · · · · 0.19 · · · · · ·D33J013324.66+303726.3 92.43 · · · 20.86 · · · · · · 0.31 · · · · · ·D33J013334.66+303724.8 92.48 · · · 19.92 · · · · · · 0.16 · · · · · ·D33J013409.70+302936.0 92.55 · · · 20.41 · · · · · · 0.19 · · · · · ·D33J013322.57+303327.1 92.62 · · · 19.74 · · · · · · 0.12 · · · · · ·D33J013347.64+304302.4 92.67 · · · 19.56 · · · · · · 0.14 · · · · · ·D33J013402.73+303409.2 92.76 · · · 20.03 · · · · · · 0.16 · · · · · ·D33J013324.12+303759.6 92.79 · · · 19.74 · · · · · · 0.13 · · · · · ·D33J013412.52+304309.4 92.83 · · · 20.09 · · · · · · 0.14 · · · · · ·D33J013304.37+303058.9 93.11 · · · 21.39 · · · · · · 0.33 · · · · · ·D33J013315.76+303816.1 93.12 · · · 20.24 · · · · · · 0.10 · · · · · ·D33J013334.08+303613.6 93.25 · · · 20.40 · · · · · · 0.26 · · · · · ·D33J013358.34+304200.0 93.50 · · · 20.56 · · · · · · 0.29 · · · · · ·D33J013342.85+303409.7 93.59 · · · 19.54 · · · · · · 0.10 · · · · · ·D33J013353.95+304048.0 93.70 · · · 20.56 · · · · · · 0.31 · · · · · ·D33J013308.79+304025.3 93.92 · · · 20.57 · · · · · · 0.21 · · · · · ·D33J013410.27+303709.9 93.97 · · · 19.78 · · · · · · 0.11 · · · · · ·D33J013343.34+303606.7 94.04 · · · 20.68 · · · · · · 0.20 · · · · · ·D33J013348.87+304338.3 94.04 · · · 19.57 · · · · · · 0.12 · · · · · ·D33J013351.57+304300.0 94.07 · · · 20.38 · · · · · · 0.31 · · · · · ·D33J013336.58+303034.2 94.33 · · · 20.73 · · · · · · 0.28 · · · · · ·D33J013343.31+303558.2 94.37 · · · 20.31 · · · · · · 0.24 · · · · · ·D33J013327.51+303209.5 94.43 · · · 20.01 · · · · · · 0.10 · · · · · ·D33J013343.44+303909.7 94.45 · · · 19.39 · · · · · · 0.11 · · · · · ·D33J013410.44+304155.1 94.49 · · · 21.00 · · · · · · 0.27 · · · · · ·D33J013326.88+303241.3 94.53 · · · 20.26 · · · · · · 0.15 · · · · · ·D33J013305.46+303819.3 94.63 · · · 19.95 · · · · · · 0.14 · · · · · ·D33J013319.90+303846.7 94.76 · · · 19.63 · · · · · · 0.07 · · · · · ·D33J013354.48+304446.5 94.90 · · · 20.37 · · · · · · 0.24 · · · · · ·D33J013408.21+303420.9 94.92 · · · 20.29 · · · · · · 0.12 · · · · · ·D33J013411.27+303126.9 95.01 · · · 20.56 · · · · · · 0.14 · · · · · ·D33J013310.45+303154.4 95.67 · · · 20.14 · · · · · · 0.17 · · · · · ·D33J013334.63+303109.1 95.77 · · · 19.83 · · · · · · 0.10 · · · · · ·D33J013321.64+303234.9 96.40 · · · 19.53 · · · · · · 0.08 · · · · · ·D33J013414.14+304408.0 96.50 · · · 20.60 · · · · · · 0.33 · · · · · ·D33J013401.93+303908.5 96.87 · · · 20.30 · · · · · · 0.36 · · · · · ·D33J013415.19+304241.7 97.07 · · · 20.47 · · · · · · 0.18 · · · · · ·D33J013418.75+304441.2 97.43 · · · 18.82 · · · · · · 0.07 · · · · · ·D33J013333.76+302917.1 97.82 · · · 19.30 · · · · · · 0.13 · · · · · ·




D33J013419.91+304613.3 98.08 · · · 19.80 · · · · · · 0.11 · · · · · ·D33J013416.22+303843.0 98.61 · · · 20.17 · · · · · · 0.12 · · · · · ·D33J013333.81+303438.0 98.97 · · · 20.09 · · · · · · 0.17 · · · · · ·D33J013325.43+303127.9 99.32 · · · 19.43 · · · · · · 0.12 · · · · · ·D33J013338.37+303823.3 99.52 · · · 20.08 · · · · · · 0.12 · · · · · ·D33J013349.22+303851.9 100.17 · · · 19.71 · · · · · · 0.15 · · · · · ·D33J013417.84+304144.7 100.37 · · · 20.99 · · · · · · 0.29 · · · · · ·D33J013418.60+302941.8 101.45 · · · 20.08 · · · · · · 0.13 · · · · · ·D33J013356.78+304640.5 103.00 · · · 20.12 · · · · · · 0.15 · · · · · ·


Tab

le2.

5.E

clip

sing

Bin

arie

s

Des

igna

tion

P(d

)V

IB

σV

σI

σB

i(◦

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r 2

D33

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337.

83+

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35.3

1.03

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220

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61.3

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0.30

D33

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421.

93+

3047

10.1

1.05

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19.8

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0.08

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63.1

0.66

0.33

D33

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331.

89+

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39.8

1.66

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···

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0.51

0.30

D33

J013

417.

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69.6

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0.36

D33

J013

414.

97+

3034

31.7

1.87

7419

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19.5

619

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0.05

0.06

0.06

57.9

0.61

0.31

D33

J013

347.

42+

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49.4

1.89

7020

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20.1

720

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0.09

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81.2

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0.30

D33

J013

337.

52+

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03.7

1.90

2120

.98

···

20.9

90.

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0.05

87.7

0.37

0.31

D33

J013

253.

23+

3036

40.0

1.93

8820

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20.2

220

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0.06

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77.1

0.50

0.32

D33

J013

350.

23+

3033

18.2

2.09

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0.39

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D33

J013

309.

79+

3032

53.6

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D33

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345.

39+

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42.3

2.14

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19.6

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72.8

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D33

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310.

35+

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01.7

2.29

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20.8

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D33

J013

319.

79+

3036

29.8

2.30

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20.3

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61.0

0.59

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D33

J013

319.

42+

3030

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2.30

6720

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22.0

920

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0.12

0.33

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89.4

0.44

0.34

D33

J013

356.

24+

3033

58.9

2.33

7118

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···

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80.

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0.51

0.49

D33

J013

419.

29+

3033

21.8

2.50

2120

.35

20.5

920

.35

0.06

0.12

0.04

88.4

0.61

0.38

D33

J013

402.

21+

3044

09.1

2.66

2519

.48

20.1

719

.36

0.04

0.11

0.03

64.7

0.46

0.43

D33

J013

354.

29+

3040

30.4

2.70

7918

.97

···

···

0.06

···

···

71.8

0.47

0.46

D33

J013

343.

07+

3038

45.4

2.88

7218

.62

19.0

4···

0.02

0.07

···

49.7

0.66

0.34

D33

J013

307.

81+

3032

42.2

2.94

5320

.87

···

20.7

50.

09···

0.06

80.2

0.46

0.35

D33

J013

351.

94+

3039

05.1

2.96

8019

.14

···

···

0.07

···

···

81.0

0.61

0.38

D33

J013

315.

92+

3035

23.5

3.02

0520

.53

20.1

120

.67

0.08

0.13

0.05

83.3

0.40

0.34

D33

J013

337.

84+

3031

21.4

3.06

7719

.62

19.8

619

.55

0.05

0.10

0.03

70.3

0.49

0.44

D33

J013

346.

40+

3034

08.1

3.15

3519

.52

20.0

019

.35

0.04

0.12

0.03

76.2

0.55

0.37

D33

J013

351.

92+

3043

11.8

3.64

8820

.07

20.3

820

.12

0.06

0.20

0.03

71.4

0.56

0.44

D33

J013

419.

68+

3033

44.5

3.69

5419

.59

20.0

019

.70

0.06

0.09

0.05

65.9

0.62

0.38

D33

J013

355.

43+

3037

42.2

3.78

5020

.96

···

20.7

10.

15···

0.10

85.2

0.45

0.36

D33

J013

349.

24+

3040

37.1

3.84

6219

.38

···

19.4

50.

08···

0.06

76.1

0.45

0.31


Tab

le2.

5—C

onti

nued

Des

igna

tion

P(d

)V

IB

σV

σI

σB

i(◦

)r 1

r 2

D33

J013

400.

90+

3035

45.3

3.91

3419

.88

19.4

519

.96

0.07

0.10

0.03

69.5

0.44

0.35

D33

J013

304.

49+

3034

06.9

3.96

3520

.02

20.5

920

.03

0.06

0.09

0.05

80.3

0.29

0.25

D33

J013

407.

19+

3046

35.0

4.42

4019

.69

20.3

519

.60

0.04

0.14

0.02

73.7

0.62

0.35

D33

J013

347.

83+

3043

01.1

4.43

2919

.62

···

19.6

30.

05···

0.03

77.8

0.56

0.43

D33

J013

314.

47+

3037

17.9

4.65

1720

.14

20.2

920

.10

0.05

0.08

0.04

70.9

0.45

0.30

D33

J013

346.

05+

3044

39.2

4.89

3819

.38

19.6

819

.33

0.05

0.12

0.05

85.3

0.23

0.19

D33

J013

355.

07+

3029

57.6

5.09

4820

.03

20.7

019

.91

0.06

0.16

0.04

89.8

0.35

0.30

D33

J013

338.

50+

3031

24.8

5.54

2018

.86

19.1

618

.79

0.03

0.07

0.03

57.9

0.61

0.39

D33

J013

307.

32+

3037

23.0

5.82

4719

.51

19.7

119

.54

0.03

0.05

0.02

50.7

0.65

0.35

D33

J013

336.

97+

3030

33.4

6.16

1319

.66

19.9

219

.58

0.05

0.10

0.04

88.8

0.24

0.16

D33

J013

426.

52+

3043

34.4

6.21

2219

.64

20.0

219

.57

0.03

0.07

0.02

62.9

0.66

0.34

D33

J013

257.

18+

3031

57.3

6.62

5018

.16

18.3

118

.20

0.05

0.06

0.04

89.8

0.55

0.44

D33

J013

340.

97+

3045

00.9

6.81

6519

.51

···

···

0.04

···

···

75.5

0.49

0.37

D33

J013

334.

78+

3032

12.2

6.82

8918

.69

18.5

718

.75

0.03

0.05

0.04

49.4

0.61

0.37

D33

J013

335.

27+

3040

24.6

6.85

2119

.38

19.4

419

.43

0.04

0.08

0.02

78.6

0.45

0.39

D33

J013

415.

97+

3033

37.8

7.10

0218

.25

18.5

318

.22

0.04

0.04

0.04

54.4

0.49

0.32

D33

J013

404.

84+

3043

17.9

7.31

7320

.19

20.1

820

.17

0.08

0.11

0.08

75.8

0.62

0.38

D33

J013

302.

77+

3030

55.7

7.90

2319

.18

19.5

319

.21

0.05

0.07

0.05

78.8

0.42

0.32

D33

J013

354.

03+

3033

04.9

8.77

4418

.77

18.4

918

.92

0.06

0.08

0.03

76.8

0.43

0.43

D33

J013

354.

79+

3032

49.2

9.79

5818

.19

18.4

418

.15

0.02

0.03

0.03

44.8

0.68

0.32

D33

J013

420.

35+

3044

31.2

10.2

534

19.7

320

.36

19.5

90.

050.

110.

0287

.00.

100.

06D

33J0

1335

8.56

+30

3422

.410

.381

919

.04

···

···

0.07

···

···

61.9

0.62

0.38

D33

J013

321.

57+

3035

03.1

23.1

091

20.3

220

.10

20.4

90.

070.

100.

0571

.40.

640.

35D

33J0

1330

6.50

+30

3213

.827

.044

419

.39

19.2

219

.54

0.06

0.08

0.06

87.9

0.59

0.41

D33

J013

344.

76+

3044

32.6

27.8

209

17.9

917

.64

18.2

40.

040.

080.

0766

.20.

460.

37D

33J0

1325

1.35

+30

3737

.834

.694

419

.84

19.3

520

.18

0.06

0.07

0.06

86.3

0.64

0.35


Table 2.6. Miscellaneous variables

Designation JS V I B σV σI σB

D33J013251.16+303639.7 1.85 21.86 19.82 · · · 0.59 0.16 · · ·D33J013251.35+303737.8 1.45 20.13 20.14 19.98 0.10 0.11 0.08D33J013251.93+303506.6 1.62 19.76 20.00 19.71 0.08 0.10 0.08D33J013253.68+303208.5 1.70 19.19 16.74 20.96 0.08 0.05 0.03D33J013253.77+303524.8 3.00 17.77 16.45 19.30 0.11 0.07 0.11D33J013256.40+303844.5 1.41 16.88 16.72 17.11 0.03 0.02 0.01D33J013256.57+303146.0 1.59 19.02 17.01 20.51 0.11 0.06 0.08D33J013256.65+303903.3 2.57 18.77 16.53 · · · 0.12 0.05 · · ·D33J013256.93+303530.1 2.00 19.08 16.83 20.59 0.09 0.04 0.06D33J013257.70+303216.9 1.24 21.66 19.95 22.50 0.39 0.20 0.07D33J013257.81+303554.6 2.33 18.93 16.61 21.00 0.09 0.06 0.06D33J013258.13+303606.0 2.44 18.56 15.93 20.31 0.06 0.08 0.02D33J013259.29+303504.7 2.19 17.49 17.02 17.89 0.04 0.04 0.02D33J013259.66+303136.9 2.21 19.27 16.83 21.36 0.10 0.05 0.05D33J013300.98+303500.4 2.27 18.80 16.96 19.83 0.09 0.04 0.02D33J013301.21+303051.2 1.24 18.09 · · · 18.39 0.08 · · · 0.05D33J013301.68+303050.5 1.27 21.25 21.83 21.18 0.38 0.29 0.08D33J013301.71+303954.0 2.11 18.96 16.51 20.94 0.07 0.05 0.05D33J013302.97+303550.8 1.55 20.65 20.95 20.71 0.12 0.24 0.03D33J013303.06+303101.6 2.20 16.92 16.76 · · · 0.06 0.05 · · ·D33J013303.37+303051.1 2.96 17.45 16.65 18.28 0.07 0.04 0.02D33J013303.50+303201.0 7.65 18.32 15.60 20.98 0.37 0.19 0.21D33J013303.52+303139.0 1.27 19.61 17.01 21.49 0.06 0.04 0.05D33J013303.85+303041.1 2.57 19.16 16.68 20.60 0.11 0.07 0.06D33J013303.99+303215.1 1.41 19.31 16.59 · · · 0.09 0.05 · · ·D33J013304.48+303234.9 4.20 19.17 16.89 20.68 0.13 0.07 0.12D33J013304.52+303043.2 1.58 19.80 · · · · · · 0.13 · · · · · ·D33J013305.00+303706.8 1.96 20.87 18.58 22.22 0.20 0.08 0.10D33J013305.45+303138.5 3.54 18.63 15.63 20.32 0.11 0.04 0.05D33J013305.72+303719.8 2.77 18.06 16.93 19.29 0.07 0.05 0.05D33J013305.93+303014.5 1.47 18.76 16.64 20.53 0.06 0.04 0.05D33J013305.95+303944.9 1.80 22.12 21.16 22.93 0.53 0.47 0.32D33J013306.55+304029.8 1.31 22.75 · · · · · · 0.53 · · · · · ·D33J013306.80+303039.4 1.37 19.57 17.50 20.52 0.06 0.05 0.02D33J013306.91+303506.0 1.98 19.01 16.32 20.92 0.10 0.06 0.06D33J013307.57+303116.8 1.38 19.02 17.38 19.72 0.06 0.10 0.05D33J013307.66+303105.3 1.31 21.18 21.19 20.97 0.20 0.30 0.10D33J013308.05+303040.5 1.22 19.96 · · · 19.99 0.08 · · · 0.01D33J013308.11+303551.2 1.30 22.25 · · · 23.21 0.41 · · · 0.29D33J013308.36+303315.7 1.95 20.39 17.63 22.43 0.15 0.07 0.10D33J013308.66+303409.2 1.87 19.25 16.79 21.24 0.11 0.06 0.10D33J013309.36+303429.4 1.56 16.97 17.01 17.08 0.03 0.04 0.02D33J013310.06+303330.7 1.40 19.69 17.82 21.37 0.07 0.04 0.05D33J013310.17+303314.4 4.22 19.79 16.70 21.24 0.24 0.06 0.06




D33J013310.23+303211.4 5.64 20.41 18.78 21.80 0.45 0.13 0.14D33J013310.36+303849.2 1.20 17.48 17.26 17.68 0.03 0.04 0.01D33J013310.95+302957.2 1.88 20.03 19.24 · · · 0.25 0.17 · · ·D33J013311.12+303421.8 2.39 16.28 16.06 · · · 0.04 0.04 · · ·D33J013311.75+303420.3 1.29 21.84 20.13 · · · 0.35 0.19 · · ·D33J013312.33+303034.0 2.11 18.41 15.86 · · · 0.09 0.06 · · ·D33J013312.56+303252.6 3.31 18.90 16.45 20.39 0.13 0.08 0.10D33J013312.68+303946.0 5.08 20.61 17.15 · · · 0.84 0.20 · · ·D33J013312.79+303012.6 3.35 17.84 17.77 17.73 0.13 0.15 0.12D33J013312.93+303905.3 3.04 19.29 16.70 21.02 0.12 0.06 0.06D33J013313.39+303654.7 1.53 22.32 19.48 · · · 0.57 0.23 · · ·D33J013313.79+303018.1 3.96 19.89 17.28 22.08 0.32 0.16 0.12D33J013315.25+303011.3 1.49 19.20 16.95 20.75 0.07 0.04 0.05D33J013315.64+303550.8 1.49 20.70 20.60 20.89 0.13 0.16 0.04D33J013315.70+303821.6 4.44 17.51 16.82 18.21 0.07 0.07 0.04D33J013315.84+303952.0 1.48 20.10 19.22 20.41 0.09 0.10 0.05D33J013316.48+303212.3 1.54 16.75 16.42 17.05 0.03 0.04 0.01D33J013316.55+303052.1 2.65 19.47 16.43 21.50 0.13 0.09 0.07D33J013316.80+303807.1 1.20 20.83 21.12 20.82 0.13 0.24 0.04D33J013317.00+303116.4 1.30 19.70 17.33 21.14 0.07 0.04 0.04D33J013317.22+303313.9 3.08 19.31 16.95 20.99 0.11 0.04 0.04D33J013317.36+303210.9 6.25 17.97 15.76 20.73 0.56 0.25 0.28D33J013318.08+303704.0 1.26 21.14 17.77 · · · 0.54 0.88 · · ·D33J013318.17+303134.3 4.45 17.02 · · · 18.61 0.12 · · · 0.11D33J013318.26+303209.5 1.21 20.89 · · · 22.00 0.14 · · · 0.06D33J013319.07+303642.5 5.45 18.72 15.93 21.07 0.30 0.15 0.17D33J013319.08+303032.2 3.15 21.95 19.24 · · · 0.60 0.30 · · ·D33J013320.72+303205.0 3.03 19.71 16.80 · · · 0.27 0.08 · · ·D33J013322.15+303050.3 1.69 21.63 19.72 · · · 0.68 0.25 · · ·D33J013322.83+303012.7 1.23 21.82 19.95 · · · 0.44 0.23 · · ·D33J013324.67+303423.9 5.45 20.39 17.01 · · · 0.36 0.19 · · ·D33J013325.20+303758.1 1.84 19.78 17.16 · · · 0.15 0.09 · · ·D33J013325.35+303417.7 1.32 20.98 18.92 22.12 0.16 0.12 0.07D33J013325.46+303849.9 1.42 21.42 · · · · · · 0.39 · · · · · ·D33J013325.67+303258.6 2.20 22.38 20.20 22.98 0.71 0.17 0.37D33J013326.89+303058.7 1.81 21.29 · · · 21.83 0.30 · · · 0.08D33J013327.06+303917.7 1.69 21.34 17.06 22.18 0.52 0.56 0.12D33J013327.14+303311.9 1.94 21.73 19.33 · · · 0.51 0.59 · · ·D33J013327.38+303029.7 2.03 17.45 16.77 · · · 0.07 0.05 · · ·D33J013328.87+303058.3 1.38 20.45 16.92 22.12 0.16 0.08 0.10D33J013331.01+303503.4 1.44 20.04 16.81 · · · 0.12 0.16 · · ·D33J013331.41+303256.1 2.13 20.95 20.88 · · · 0.28 0.46 · · ·D33J013333.08+303506.6 1.56 17.42 17.30 17.53 0.04 0.04 0.03D33J013333.28+303147.6 1.97 20.55 17.05 · · · 0.21 0.07 · · ·




D33J013333.33+303351.6 6.27 18.90 16.25 21.84 0.43 0.24 0.36D33J013333.45+303150.0 1.74 19.63 16.94 · · · 0.12 0.09 · · ·D33J013333.78+303403.4 2.59 19.37 16.85 21.15 0.20 0.08 0.07D33J013334.65+303912.7 2.66 21.85 19.68 · · · 0.67 0.96 · · ·D33J013334.83+303355.0 1.43 17.24 15.38 · · · 0.12 0.08 · · ·D33J013335.09+303600.7 10.56 16.18 15.93 16.87 0.27 0.29 0.17D33J013335.19+303041.3 1.59 19.39 16.76 21.09 0.11 0.05 0.03D33J013335.42+303835.5 1.60 17.18 17.14 17.33 0.04 0.03 0.05D33J013335.80+303912.4 1.24 22.27 18.93 · · · 0.69 0.11 · · ·D33J013335.86+303344.8 8.19 19.68 16.39 · · · 0.56 0.23 · · ·D33J013336.39+303531.4 1.40 18.00 · · · 18.00 0.07 · · · 0.01D33J013336.59+303532.6 2.32 18.16 · · · 20.08 0.09 · · · 0.02D33J013337.23+304005.4 1.38 18.73 17.12 20.21 0.06 0.03 0.04D33J013337.99+303236.3 1.82 20.46 17.31 22.02 0.15 0.05 0.17D33J013338.61+303109.3 1.89 19.96 16.94 · · · 0.15 0.07 · · ·D33J013338.92+303506.3 5.17 19.54 16.80 20.30 0.27 0.15 0.10D33J013338.92+303829.5 13.35 18.82 15.89 · · · 0.43 0.41 · · ·D33J013339.01+302944.6 3.90 20.53 18.38 22.39 0.72 0.16 0.18D33J013339.24+303119.3 5.67 17.13 · · · 18.50 0.20 · · · 0.16D33J013339.25+303050.0 3.51 19.36 · · · 20.16 0.23 · · · 0.03D33J013340.02+302846.3 1.35 15.96 · · · · · · 0.04 · · · · · ·D33J013340.34+303131.7 1.44 20.92 17.12 · · · 0.23 0.13 · · ·D33J013340.44+304256.8 1.74 16.37 16.17 · · · 0.04 0.06 · · ·D33J013340.48+303159.1 1.20 17.95 18.07 17.99 0.04 0.04 0.02D33J013340.58+304206.1 1.26 20.54 · · · · · · 0.23 · · · · · ·D33J013340.75+303236.7 1.40 20.04 17.27 · · · 0.11 0.06 · · ·D33J013341.60+303220.9 4.19 16.31 · · · 17.11 0.06 · · · 0.03D33J013341.80+304021.1 1.37 20.75 17.26 · · · 0.36 0.48 · · ·D33J013342.30+303608.5 2.15 19.75 16.82 21.48 0.13 0.06 0.08D33J013342.34+303911.2 1.24 20.44 19.67 · · · 0.20 0.15 · · ·D33J013342.40+303631.5 1.60 19.40 17.27 21.23 0.08 0.04 0.09D33J013342.57+303534.9 2.88 20.11 16.85 21.27 0.19 0.14 0.01D33J013342.72+303256.6 1.26 17.94 17.80 18.00 0.04 0.05 0.02D33J013342.84+303235.0 2.39 19.15 16.75 19.66 0.09 0.06 0.01D33J013343.04+303904.8 1.89 18.09 16.62 · · · 0.10 0.06 · · ·D33J013343.42+302938.7 3.60 20.27 17.38 21.91 0.20 0.07 0.07D33J013343.65+304450.8 7.67 19.67 · · · 21.67 0.80 · · · 0.07D33J013343.79+304848.4 1.36 22.20 · · · · · · 0.69 · · · · · ·D33J013343.91+303916.3 1.82 20.24 · · · · · · 0.33 · · · · · ·D33J013344.09+303206.1 2.50 17.11 16.21 17.79 0.05 0.04 0.07D33J013344.28+303636.2 1.27 18.99 16.69 19.08 0.06 0.11 0.02D33J013344.38+303228.3 2.50 19.37 17.08 20.71 0.11 0.03 0.04D33J013344.96+303008.6 1.77 21.23 19.16 · · · 0.36 0.15 · · ·D33J013344.97+304714.3 1.37 21.21 19.29 · · · 0.27 0.11 · · ·




D33J013345.10+303620.2 2.10 16.57 16.03 16.97 0.05 0.05 0.02D33J013345.11+303606.8 1.66 20.48 17.41 · · · 0.18 0.07 · · ·D33J013345.16+303138.7 3.92 18.14 15.90 20.08 0.17 0.13 0.13D33J013345.67+303609.8 1.72 19.16 16.40 · · · 0.15 0.05 · · ·D33J013345.76+304311.9 1.49 20.43 19.66 20.75 0.13 0.08 0.05D33J013346.09+303653.8 1.55 15.97 15.56 16.27 0.03 0.04 0.01D33J013346.56+304125.6 4.69 18.78 16.11 21.20 0.30 0.12 0.15D33J013346.66+304210.2 1.97 20.27 · · · · · · 0.28 · · · · · ·D33J013346.96+303950.7 1.23 20.42 · · · · · · 0.23 · · · · · ·D33J013347.38+304630.1 3.12 19.91 17.03 21.90 0.35 0.10 0.16D33J013347.46+304155.2 1.92 19.66 · · · · · · 0.12 · · · · · ·D33J013348.12+304809.2 1.73 21.86 19.95 · · · 0.55 0.26 · · ·D33J013348.32+304242.3 1.47 16.70 16.31 17.11 0.03 0.04 0.01D33J013348.58+304658.1 1.30 21.25 · · · 21.63 0.26 · · · 0.05D33J013348.71+304211.7 1.96 19.61 · · · 20.27 0.14 · · · 0.05D33J013348.82+303709.5 1.75 20.25 17.48 21.62 0.15 0.09 0.07D33J013348.82+304821.9 1.44 20.85 18.94 · · · 0.20 0.13 · · ·D33J013348.83+303842.4 1.23 19.71 · · · · · · 0.13 · · · · · ·D33J013348.85+304423.5 1.65 21.26 · · · 21.85 0.75 · · · 0.19D33J013349.09+304148.2 1.28 21.41 19.64 · · · 0.38 0.19 · · ·D33J013349.63+304045.3 1.48 21.16 · · · · · · 0.33 · · · · · ·D33J013349.68+303913.1 1.22 20.08 · · · · · · 0.25 · · · · · ·D33J013349.71+304500.0 1.70 20.07 17.00 · · · 0.18 0.09 · · ·D33J013349.75+304257.0 2.51 19.30 16.88 · · · 0.15 0.13 · · ·D33J013349.77+303225.0 3.19 19.25 16.77 20.70 0.12 0.09 0.05D33J013349.80+303246.4 1.43 16.02 · · · 16.89 0.02 · · · 0.01D33J013349.83+303836.0 1.22 19.05 · · · 19.13 0.26 · · · 0.03D33J013349.89+302929.1 2.74 18.32 16.06 19.01 0.09 0.12 0.01D33J013349.96+304314.3 3.05 19.68 · · · 21.54 0.15 · · · 0.12D33J013350.00+304610.5 1.46 22.37 20.17 · · · 0.51 0.29 · · ·D33J013350.35+303914.1 1.38 20.34 · · · · · · 0.32 · · · · · ·D33J013350.50+303225.7 1.54 19.77 · · · 21.64 0.11 · · · 0.09D33J013350.56+303230.6 4.03 18.03 · · · 19.41 0.16 · · · 0.06D33J013350.57+303836.3 1.33 19.16 · · · · · · 0.14 · · · · · ·D33J013350.61+303617.4 1.36 19.72 16.84 21.32 0.10 0.06 0.08D33J013350.95+303819.1 3.89 16.52 16.45 · · · 0.09 0.08 · · ·D33J013351.42+303640.3 2.01 19.66 16.22 · · · 0.22 0.15 · · ·D33J013351.60+303226.2 3.18 16.69 16.12 17.21 0.04 0.03 0.01D33J013351.60+303454.9 2.06 16.98 16.92 17.06 0.03 0.04 0.02D33J013351.79+303827.7 2.67 16.43 15.80 17.18 0.04 0.03 0.01D33J013352.11+303902.5 1.21 20.66 16.53 · · · 0.29 0.07 · · ·D33J013352.26+302908.0 1.53 21.24 19.68 · · · 0.32 0.22 · · ·D33J013352.37+303736.6 1.22 20.20 17.01 · · · 0.12 0.15 · · ·D33J013352.37+303909.9 3.43 16.36 15.92 · · · 0.06 0.05 · · ·




D33J013352.51+303816.2 6.13 16.91 16.01 17.52 0.10 0.06 0.01D33J013352.57+304403.5 1.68 21.56 20.19 · · · 0.86 0.42 · · ·D33J013353.47+303816.5 1.59 20.77 18.21 · · · 0.32 0.19 · · ·D33J013353.53+303520.2 1.80 19.46 17.03 20.17 0.11 0.09 0.04D33J013353.60+304005.5 1.25 19.96 17.48 · · · 0.15 0.15 · · ·D33J013353.68+303916.3 1.45 20.29 · · · · · · 0.43 · · · · · ·D33J013353.73+303028.2 1.80 22.24 19.54 · · · 0.78 0.37 · · ·D33J013353.96+304059.7 1.40 21.61 18.99 23.24 0.42 0.11 0.25D33J013354.80+303223.1 2.18 18.28 18.15 18.39 0.07 0.06 0.06D33J013355.13+304035.8 1.25 21.09 · · · 21.87 0.50 · · · 0.22D33J013355.53+304121.1 1.80 20.50 16.60 · · · 0.29 0.11 · · ·D33J013355.62+304153.4 1.30 21.89 19.16 · · · 0.50 0.13 · · ·D33J013356.04+303834.8 1.87 19.67 17.56 19.99 0.15 0.16 0.02D33J013356.21+303259.1 1.37 19.37 17.32 · · · 0.12 0.06 · · ·D33J013356.58+303316.7 1.88 17.01 17.14 · · · 0.03 0.03 · · ·D33J013356.93+303703.2 1.47 20.81 · · · 21.40 0.26 · · · 0.11D33J013356.98+303517.2 1.67 19.99 17.45 · · · 0.15 0.08 · · ·D33J013357.02+303818.1 6.48 19.83 16.56 20.79 0.38 0.22 0.02D33J013357.03+303355.6 2.62 19.44 16.85 21.24 0.14 0.09 0.04D33J013357.43+303821.7 2.96 17.23 16.32 18.29 0.10 0.06 0.03D33J013357.43+304810.1 2.19 21.46 19.53 · · · 0.65 0.32 · · ·D33J013357.66+304824.1 2.68 16.79 16.07 17.77 0.06 0.06 0.08D33J013357.80+303718.0 2.28 19.41 16.85 21.31 0.25 0.07 0.17D33J013358.02+304539.9 3.31 16.01 · · · 16.98 0.04 · · · 0.06D33J013358.09+304337.2 1.21 21.06 18.87 · · · 0.25 0.08 · · ·D33J013358.11+303321.0 1.70 16.60 16.50 16.67 0.03 0.04 0.02D33J013358.49+303420.1 3.40 17.32 · · · · · · 0.17 · · · · · ·D33J013358.52+303812.9 1.97 19.82 · · · · · · 0.14 · · · · · ·D33J013358.53+303251.9 1.37 20.46 21.02 20.25 0.14 0.37 0.02D33J013358.92+304139.6 4.84 16.75 16.06 17.82 0.09 0.04 0.07D33J013359.02+303756.5 1.29 21.22 20.47 · · · 0.38 0.25 · · ·D33J013359.05+304354.8 2.52 20.03 17.28 22.39 0.24 0.08 0.20D33J013359.14+303212.5 2.53 19.65 16.41 22.09 0.26 0.15 0.23D33J013359.19+303742.1 1.24 21.82 19.16 · · · 0.37 0.12 · · ·D33J013359.44+303734.1 2.20 19.72 17.09 21.10 0.15 0.08 0.10D33J013359.83+303355.1 1.36 17.75 · · · · · · 0.09 · · · · · ·D33J013359.87+304703.4 1.56 19.46 16.79 21.25 0.08 0.06 0.06D33J013359.93+304453.3 1.97 21.02 · · · · · · 0.30 · · · · · ·D33J013400.00+304622.2 1.28 19.70 17.83 · · · 0.09 0.30 · · ·D33J013400.09+304831.6 1.51 20.56 17.54 · · · 0.14 0.11 · · ·D33J013400.34+303338.3 1.21 19.55 17.47 · · · 0.07 0.05 · · ·D33J013400.50+302951.6 2.76 19.75 17.62 21.16 0.17 0.13 0.09D33J013400.78+304149.6 1.25 21.51 19.97 22.21 0.36 0.23 0.18D33J013400.86+303415.1 4.33 17.53 15.61 19.39 0.11 0.07 0.07




D33J013401.04+303432.4 3.75 19.44 16.53 · · · 0.28 0.09 · · ·D33J013401.60+303129.1 3.50 20.79 17.02 · · · 0.34 0.15 · · ·D33J013401.83+303858.3 2.65 16.72 · · · 17.91 0.06 · · · 0.04D33J013402.02+303133.0 1.44 22.09 19.87 · · · 0.59 0.25 · · ·D33J013402.02+304117.2 1.22 17.69 17.56 17.86 0.03 0.03 0.01D33J013402.08+304257.7 1.93 17.06 16.96 17.22 0.03 0.04 0.02D33J013402.27+303828.4 1.58 18.73 16.21 20.26 0.06 0.06 0.04D33J013402.45+303513.4 1.24 21.13 20.03 · · · 0.26 0.30 · · ·D33J013402.50+304107.8 1.77 19.35 16.63 21.25 0.10 0.06 0.06D33J013402.74+304836.5 3.64 18.20 · · · 19.76 0.10 · · · 0.05D33J013403.15+304645.8 1.84 21.33 19.28 · · · 0.40 0.13 · · ·D33J013403.56+303143.2 2.77 19.64 16.70 21.39 0.12 0.04 0.07D33J013403.70+304202.5 3.08 19.49 16.20 21.52 0.24 0.15 0.10D33J013403.82+303753.1 2.75 19.82 16.40 · · · 0.90 0.41 · · ·D33J013404.00+303817.3 1.49 21.11 19.30 · · · 0.61 0.34 · · ·D33J013404.22+304115.3 1.35 21.54 · · · 21.70 0.43 · · · 0.42D33J013404.29+303018.6 1.23 21.62 20.30 · · · 0.42 0.20 · · ·D33J013404.48+303257.3 1.70 21.83 19.54 · · · 0.66 0.75 · · ·D33J013404.54+303315.6 1.89 20.55 17.58 22.54 0.47 0.16 0.07D33J013405.41+303719.3 1.61 18.80 17.24 20.10 0.07 0.04 0.05D33J013405.46+303443.4 6.04 19.80 18.49 21.30 0.36 0.20 0.15D33J013405.50+303419.2 1.56 20.45 19.25 20.91 0.13 0.07 0.04D33J013405.53+303905.7 2.16 20.45 · · · · · · 0.25 · · · · · ·D33J013405.65+303906.2 1.21 20.84 · · · · · · 0.20 · · · · · ·D33J013406.15+304632.3 1.98 19.57 16.87 · · · 0.17 0.08 · · ·D33J013406.55+304250.2 1.21 22.11 20.12 · · · 0.58 0.20 · · ·D33J013406.60+304147.8 2.74 16.04 15.74 16.23 0.04 0.04 0.03D33J013406.83+304623.3 1.31 21.04 · · · 22.25 0.28 · · · 0.10D33J013407.07+303918.8 1.91 19.17 16.61 · · · 0.14 0.16 · · ·D33J013407.29+304732.3 1.46 18.29 17.57 18.80 0.05 0.05 0.03D33J013407.67+304628.4 3.60 19.43 16.54 20.79 0.16 0.08 0.03D33J013408.21+304548.3 1.25 19.78 17.56 21.33 0.07 0.05 0.07D33J013408.47+304555.2 1.30 22.34 · · · · · · 0.66 · · · · · ·D33J013409.13+303846.9 1.28 20.47 16.85 · · · 0.18 0.08 · · ·D33J013409.18+303423.4 7.22 17.67 16.80 18.80 0.22 0.23 0.02D33J013409.32+304526.8 1.51 20.32 17.18 22.01 0.12 0.04 0.06D33J013409.42+303706.2 2.94 21.18 19.01 · · · 0.42 0.13 · · ·D33J013409.54+303621.7 1.51 20.57 19.72 20.90 0.21 0.14 0.11D33J013409.58+303907.9 5.72 19.84 · · · · · · 0.46 · · · · · ·D33J013409.76+304643.2 2.27 19.50 17.05 21.09 0.14 0.08 0.07D33J013409.83+303814.5 2.15 20.63 18.42 21.31 0.23 0.24 0.09D33J013409.86+304738.0 1.48 21.82 19.91 · · · 0.47 0.30 · · ·D33J013410.17+304728.1 1.27 19.50 17.29 20.85 0.09 0.04 0.04D33J013410.46+304650.9 2.86 17.75 17.51 17.94 0.05 0.04 0.02




D33J013410.79+304708.1 1.97 20.99 · · · 21.13 0.30 · · · 0.08D33J013410.89+303437.7 6.18 15.98 · · · · · · 0.08 · · · · · ·D33J013411.03+303954.7 1.50 17.73 17.77 17.82 0.03 0.04 0.01D33J013411.50+303312.8 4.84 18.83 · · · 20.37 0.20 · · · 0.09D33J013411.68+304003.2 1.65 19.77 17.22 · · · 0.13 0.11 · · ·D33J013411.69+303343.5 1.52 22.28 19.89 · · · 0.55 0.39 · · ·D33J013412.15+303241.9 1.21 21.48 19.61 · · · 0.45 0.11 · · ·D33J013412.21+303320.8 1.97 19.38 16.85 21.22 0.10 0.04 0.06D33J013412.62+304208.0 1.44 21.68 19.67 22.68 0.34 0.19 0.12D33J013412.63+303828.5 1.47 21.77 19.38 22.48 0.49 0.41 0.20D33J013412.84+303310.1 1.52 19.87 17.05 · · · 0.10 0.06 · · ·D33J013412.92+303104.8 1.36 21.72 · · · · · · 0.42 · · · · · ·D33J013413.42+304402.1 1.25 22.25 19.14 22.77 0.43 0.24 0.17D33J013413.65+304026.7 1.23 21.50 19.82 · · · 0.25 0.14 · · ·D33J013413.94+304837.3 1.46 21.17 20.41 21.45 0.45 0.18 0.27D33J013414.24+304254.2 1.34 19.55 17.10 21.14 0.07 0.05 0.03D33J013414.45+303511.7 3.35 19.81 16.38 21.02 0.21 0.14 0.06D33J013414.50+303557.9 2.50 19.47 16.71 21.16 0.10 0.06 0.07D33J013414.84+303401.4 1.54 19.18 16.82 · · · 0.15 0.07 · · ·D33J013415.26+304850.3 1.28 22.30 20.00 · · · 0.49 0.32 · · ·D33J013415.71+304526.5 1.63 21.72 20.13 22.11 0.39 0.18 0.09D33J013415.80+303732.2 2.13 19.13 16.87 · · · 0.10 0.06 · · ·D33J013415.82+302919.4 1.63 22.36 · · · · · · 0.55 · · · · · ·D33J013415.90+304115.0 4.57 20.11 16.51 21.30 0.25 0.18 0.09D33J013416.24+303801.7 1.94 20.33 17.64 · · · 0.17 0.07 · · ·D33J013416.25+303353.7 5.42 18.55 16.22 20.29 0.23 0.14 0.09D33J013416.29+303158.8 1.23 19.49 17.29 21.08 0.06 0.04 0.04D33J013416.40+303121.1 1.83 17.12 17.09 17.06 0.04 0.06 0.03D33J013416.44+304750.5 1.33 19.49 17.29 21.15 0.08 0.06 0.05D33J013416.72+304518.4 2.39 20.26 17.19 21.82 0.17 0.12 0.12D33J013417.17+304826.4 1.20 20.91 17.03 · · · 0.16 0.09 · · ·D33J013417.54+304155.3 1.30 19.16 18.73 19.42 0.06 0.04 0.02D33J013417.79+303356.2 2.77 19.24 16.18 21.00 0.13 0.05 0.07D33J013418.09+304147.5 1.37 20.79 · · · 20.82 0.14 · · · 0.03D33J013418.40+304108.2 1.71 21.78 19.78 22.93 0.47 0.14 0.27D33J013418.67+304338.0 3.18 21.66 19.55 · · · 0.48 0.20 · · ·D33J013418.74+303942.6 1.33 21.68 · · · 22.50 0.31 · · · 0.18D33J013419.07+304226.0 2.04 21.70 · · · 22.67 0.40 · · · 0.12D33J013419.58+303303.5 1.78 20.89 17.50 · · · 0.20 0.10 · · ·D33J013419.65+303700.3 1.46 19.49 17.10 21.28 0.09 0.06 0.07D33J013419.95+304436.6 1.48 19.94 17.16 21.51 0.13 0.07 0.07D33J013420.23+304848.6 3.14 20.04 17.32 21.58 0.17 0.09 0.11D33J013420.31+304545.5 1.45 17.16 16.05 18.41 0.03 0.05 0.05D33J013420.76+304407.0 1.59 20.44 17.82 22.05 0.16 0.06 0.07




D33J013422.21+304629.1 1.40 21.96 19.78 · · · 0.48 0.20 · · ·D33J013425.24+303940.2 1.53 21.21 19.51 · · · 0.34 0.23 · · ·D33J013425.49+304415.7 1.78 21.25 19.55 22.62 0.39 0.18 0.09D33J013425.84+304615.0 1.33 19.70 17.56 21.52 0.07 0.05 0.07D33J013426.31+304844.8 1.86 22.02 19.96 22.95 0.48 0.33 0.19D33J013426.43+304754.2 1.82 21.75 19.52 23.59 0.48 0.24 0.23D33J013427.12+304407.0 1.55 21.14 20.08 21.81 0.32 0.20 0.04D33J013427.65+304355.9 1.57 21.48 19.99 21.93 0.29 0.25 0.12D33J013428.62+304820.6 2.13 21.70 20.77 22.05 0.40 0.24 0.28D33J013428.72+304223.1 1.36 21.81 19.75 · · · 0.34 0.20 · · ·D33J013428.72+304752.2 1.37 21.88 · · · 22.37 0.43 · · · 0.07


Fig. 2.14.— Color-magnitude diagram of 682 variables in M33 with two- or three-

color data. EBs, Cepheids and miscellaneous variables are plotted using filled, open

and starred symbols, respectively. An additional 177 variables with data in a single

band could not be plotted.


Fig. 2.15.— Observed I-band P-L relation for all Cepheids listed in Table 2.4. Most

of the objects detected in the I band only (filled symbols) appear to be Population

II Cepheids.


are indicated with filled symbols. Most of the latter appear to be Population

II Cepheids; this sample represents the largest extragalactic ensemble of such

variables ever observed.

2.5.1 Previously-known variables in M33

The search for variables in M33 has a long and venerable history. Duncan (1922)

(hereafter, Du22) discovered three variables in this galaxy while searching for

novae. The first two of these are irregular variables, while the third one turned out

to be a 42-day Cepheid. Hubble (1926) (hereafter Hu26) undertook an extensive

observational program which resulted in the discovery of 41 variables, including 35

Cepheids and one eclipsing variable. Later, Hubble & Sandage (1953) (hereafter,

HS53) discovered an additional three bright irregular variables. After a long hiatus,

van den Bergh, Herbst & Kowal (1975) (hereafter VHK75) discovered 36 new

variables but were unable to determine periods and classifications for them, due

to the rather poor quality of their magnitudes. Lastly, Sandage & Carlson (1983)

(hereafter, SC83) discovered an additional 12 Cepheids.

Table 2.7 lists the properties of all these “classical” variables, and their

DIRECT counterparts, where available. Coordinates are from our catalog, if

the variable was present in it. Otherwise, they were obtained from the original

publication or from a digitized POSS image of M33. We hope this table, which to

our knowledge is the first compilation of all M33 classical variables, will serve as

reference for future work.

In general, there is good agreement between the classical and the DIRECT

periods and classification of these variables. In two cases (Hu26-V04 and

VHK75-76), it seems that the original finding charts may be erroneously indicating

a nearby star as the variable instead of the actual object. Apparently, van den

Bergh, Herbst & Kowal (1975) did not notice the mis-identification of V04 by

Hubble (1926), and designated it VHK75-49, thinking it was a new variable.


Some classical variables which had been not been classified as Cepheids were

found to be so by our automated template fitting program. Such was the case

for Hu26-V15 (re-classified as a 50-day Cepheid), Hu26-V21 (re-classified as a

67-day Cepheid) and Hu26-V45 (re-classified as a 74-day Cepheid). One classical

Cepheid (Hu26-V19) is present in our star catalog, but it did not meet the criteria

to be classified as a variable. Indeed, the amplitude of its pulsation seems to have

decreased from ∼ 1 mag at the beginning of the century to a few hundredths of a

magnitude at present. See Macri et al. (2001) for details.

The only modern search for variables in M33 was undertaken by Kinman,

Mould & Wood (1987) (hereafter, KMW87). The observations were carried out

using plates, but these were digitized using a PDS machine, and the search for

variables was performed using automated routines. They discovered 65 Cepheids,

44 long-period variables, 6 periodic variables and 224 miscellaneous variables over

a large area of the disk of M33. We were able to retrieve 35/36 Cepheids, 1/1 W

Vir variable, 14/27 long-period variables, and 63/103 unclassified variables present

in our fields.

2.6 A Cepheid Distance to M33

As described in the previous section, numerous searches for Cepheids in M33 have

been conducted over the past 75 years. Most of these have also determined a

distance to the galaxy based on the variables that were discovered. Given the

fluid nature of the absolute calibration of the Distance Scale during the twentieth

century, these distance estimates cannot be compared directly.

Our determination of the distance to M33 will be based on a subset of the

Cepheids presented in Table 2.4, with periods longer than 15 days and no evidence

of blends, individually corrected for extinction. Our analysis will make use of

fiducial Period-Luminosity Relations, based on Cepheids located in the Large

Magellanic Cloud. We will describe these points in reverse order.


Table 2.7. M33 Classical variables

Designation R.A. Dec. Type Per (d)Classical DIRECT (J2000.0) Cl. DI. Cl. DI.

Du22-V01 D33J013409.83+303814.5 01:34:09.83 30:38:14.5 V V · · · · · ·Du22-V02 D33J013418.35+303837.0 01:34:18.35 30:38:37.0 V N · · · · · ·Hu26-V03 · · · 01:33:25.9 30:48:34 C O 41.68 · · ·Hu26-V04 D33J013423.44+304204.2 01:34:23.44 30:42:04.2 C C 27.37 27.27 [1]Hu26-V05 D33J013404.89+304022.4 01:34:04.89 30:40:22.4 C C 14.60 14.61Hu26-V06 · · · 01:34:45.1 30:49:25 V O · · · · · ·Hu26-V07 D33J013411.21+304155.9 01:34:11.21 30:41:55.9 C C 26.56 26.56Hu26-V08 D33J013355.07+302957.6 01:33:55.07 30:29:57.6 E E · · · 5.095Hu26-V09 D33J013406.74+303940.0 01:34:06.74 30:39:40.0 C C 18.90 18.89Hu26-V10 D33J013405.11+303851.3 01:34:05.11 30:38:51.3 C C 69.50 56.69Hu26-V11 D33J013402.76+304145.4 01:34:02.76 30:41:45.4 C C 23.43 13.04Hu26-V12 D33J013401.74+303923.0 01:34:01.74 30:39:23.0 C C 21.68 21.65Hu26-V13 D33J013359.73+303937.1 01:33:59.73 30:39:37.1 V N · · · · · ·Hu26-V14 D33J013331.04+303143.9 01:33:31.04 30:31:43.9 V C · · · 55.39Hu26-V15 D33J013359.42+303227.0 01:33:59.42 30:32:27.0 V C · · · 50.21Hu26-V16 D33J013353.41+303535.6 01:33:53.41 30:35:35.6 C C 17.50 17.47Hu26-V17 D33J013350.71+303544.6 01:33:50.71 30:35:44.6 C C 23.30 23.30Hu26-V18 D33J013354.74+304106.3 01:33:54.74 30:41:06.3 C C 34.00 33.91Hu26-V19 D33J013357.04+304511.8 01:33:57.04 30:45:11.8 C N 54.71 · · ·Hu26-V20 D33J013352.42+303844.3 01:33:52.42 30:38:44.3 C C 35.95 35.90Hu26-V21 D33J013351.81+303951.0 01:33:51.82 30:39:50.9 V C · · · 67.05Hu26-V22 D33J013351.44+303830.8 01:33:51.44 30:38:30.8 C C 21.82 21.81Hu26-V23 D33J013351.23+303758.4 01:33:51.23 30:37:58.4 C C 13.56 13.57Hu26-V24 D33J013349.78+303758.9 01:33:49.78 30:37:58.9 C C 12.89 12.92Hu26-V25 D33J013358.81+303719.9 01:33:58.81 30:37:19.9 C C 13.44 24.55Hu26-V26 · · · 01:34:37.9 30:41:26 C O 23.26 · · ·Hu26-V27 D33J013344.51+304313.6 01:33:44.51 30:43:13.6 C C 22.45 22.41Hu26-V28 D33J013414.56+304413.4 01:34:14.56 30:44:13.4 C C 18.58 18.61Hu26-V29 D33J013341.54+303609.7 01:33:41.54 30:36:09.7 C C 36.31 37.35Hu26-V30 D33J013329.18+303745.0 01:33:29.18 30:37:45.0 C C 46.03 45.88Hu26-V31 D33J013327.40+303707.9 01:33:27.40 30:37:07.9 C C 37.33 37.04Hu26-V32 D33J013326.07+303320.2 01:33:26.07 30:33:20.2 V C · · · 19.98Hu26-V33 D33J013324.59+303518.0 01:33:24.59 30:35:18.0 C C 20.50 20.49Hu26-V34 · · · 01:33:22.4 30:48:48 C O 22.16 · · ·Hu26-V35 D33J013301.95+303633.9 01:33:01.95 30:36:33.9 C C 30.51 30.54Hu26-V36 D33J013412.15+304640.9 01:34:12.15 30:46:40.9 C C 35.80 35.87Hu26-V37 D33J013344.98+303952.3 01:33:44.98 30:39:52.3 C C 17.60 17.53Hu26-V38 D33J013401.17+303113.9 01:34:01.17 30:31:13.9 C C 25.04 24.89Hu26-V39 · · · 01:34:13.9 30:50:35 C O 16.17 · · ·Hu26-V40 D33J013345.93+304231.5 01:33:45.93 30:42:31.5 C C 12.92 12.92Hu26-V41 D33J013330.07+303638.4 01:33:30.07 30:36:38.4 C C 17.98 17.97Hu26-V42 D33J013332.86+303549.3 01:33:32.86 30:35:49.3 C C 30.34 30.30Hu26-V43 D33J013331.39+303352.1 01:33:31.39 30:33:52.1 C C 20.17 20.18




Hu26-V44 D33J013329.41+303557.6 01:33:29.41 30:35:57.6 C C 30.12 30.58Hu26-V45 D33J013343.85+303245.6 01:33:43.85 30:32:45.6 V C · · · 73.94HS53-A · · · 01:32:33.0 30:30:25 V O · · · · · ·HS53-B D33J013349.18+303809.5 01:33:49.18 30:38:09.5 V · · · · · · · · · [2]HS53-C D33J013335.09+303600.7 01:33:35.09 30:36:00.7 V V · · · · · ·VHK75-46 D33J013408.98+303300.6 01:34:08.98 30:33:00.6 V N · · · · · ·VHK75-47 · · · 01:34:23.2 30:56:53 V O · · · · · ·VHK75-48 · · · 01:33:07.2 30:45:43 V O · · · · · ·VHK75-49 D33J013423.44+304204.2 01:34:23.44 30:42:04.2 V C · · · 27.27 [3]VHK75-50 · · · 01:34:21.4 30:55:39 V O · · · · · ·VHK75-51 · · · 01:33:00.2 30:46:46 V O · · · · · ·VHK75-52 · · · 01:34:25.3 30:54:37 V O · · · · · ·VHK75-53 · · · 01:35:01.4 30:32:05 V O · · · · · ·VHK75-54 D33J013410.77+303317.0 01:34:10.77 30:33:17.0 V N · · · · · ·VHK75-55 · · · 01:32:45.4 30:35:19 V O · · · · · ·VHK75-56 · · · 01:34:34.3 30:26:28 V O · · · · · ·VHK75-57 · · · 01:33:24.8 30:17:54 V O · · · · · ·VHK75-58 D33J013317.36+303210.9 01:33:17.36 30:32:10.9 V V · · · · · ·VHK75-59 D33J013403.07+304221.1 01:34:03.07 30:42:21.1 V F · · · · · ·VHK75-60 D33J013336.59+303532.6 01:33:36.59 30:35:32.6 V V · · · · · ·VHK75-61 D33J013411.50+303312.8 01:34:11.50 30:33:12.8 V V · · · · · ·VHK75-62 D33J013345.16+303138.7 01:33:45.16 30:31:38.7 V V · · · · · ·VHK75-63 · · · 01:33:39.4 30:21:11 V O · · · · · ·VHK75-64 · · · 01:33:29.4 30:18:49 V O · · · · · ·VHK75-65 · · · 01:34:54.2 30:41:10 V O · · · · · ·VHK75-66 D33J013319.07+303642.5 01:33:19.07 30:36:42.5 V V · · · · · ·VHK75-67 D33J013257.18+303157.3 01:32:57.18 30:31:57.3 V E · · · 6.62VHK75-68 D33J013357.51+304214.7 01:33:57.51 30:42:14.7 V F · · · · · ·VHK75-69 · · · 01:33:31.8 30:19:54 V O · · · · · ·VHK75-70 · · · 01:34:30.7 30:32:17 V O · · · · · ·VHK75-71 · · · 01:34:12.1 30:53:13 V O · · · · · ·VHK75-72 D33J013415.90+304115.0 01:34:15.90 30:41:15.0 V V · · · · · ·VHK75-73 · · · 01:33:49.1 30:52:21 V O · · · · · ·VHK75-74 · · · 01:33:28.8 31:00:40 V O · · · · · ·VHK75-75 · · · 01:34:14.0 30:52:47 V O · · · · · ·VHK75-76 D33J013416.25+303353.7 01:34:16.25 30:33:53.7 V V · · · · · · [4]VHK75-77 · · · 01:33:55.7 30:27:25 V O · · · · · ·VHK75-78 · · · 01:33:09.3 30:25:58 V O · · · · · ·VHK75-79 D33J013329.18+303745.0 01:33:29.18 30:37:45.0 V C · · · 45.88 [5]VHK75-80 · · · 01:33:53.8 30:26:42 V O · · · · · ·VHK75-81 · · · 01:34:55.5 30:43:49 V O · · · · · ·VHK75-82 · · · 01:33:49.1 30:51:35 V O · · · · · ·VHK75-83 D33J013410.89+303437.7 01:34:10.89 30:34:37.7 V V · · · · · ·




SC83-A01 D33J013318.37+303916.6 01:33:18.37 30:39:16.6 C C 8.54 8.54SC83-B01 D33J013252.15+303714.6 01:32:52.15 30:37:14.6 C C 37.62 37.58SC83-B08 D33J013253.12+303810.5 01:32:53.12 30:38:10.5 C F 3.23 · · ·SC83-D54 D33J013322.94+303040.2 01:33:22.94 30:30:40.2 C C 8.74 8.74SC83-E14 D33J013255.91+303438.2 01:32:55.91 30:34:38.2 C C 12.82 12.33SC83-F08 · · · 01:32:32.3 30:31:08 C O 21.28 · · ·SC83-F09 · · · 01:32:36.3 30:31:42 C O 18.10 · · ·SC83-F12 · · · 01:32:34.7 30:36:52 C O 18.48 · · ·SC83-G01 D33J013331.23+302947.7 01:33:31.23 30:29:47.7 C C 17.56 17.55SC83-G04 · · · 01:33:20.3 30:29:05 C O 13.00 · · ·SC83-G05 · · · 01:33:20.3 30:28:54 C O 8.78 · · ·SC83-G06 · · · 01:33:18.9 30:27:09 C O 26.32 · · ·

References. — Du22: Duncan (1922); Hu26: Hubble (1926); HS53: Hubble & Sandage (1953);VHK75: van den Bergh, Herbst & Kowal (1975); SC83: Sandage & Carlson (1983)

Note. — Key to types: C: Cepheid; E: Eclipsing binary; V: miscellaneous variable; N: does notdisplay variability in the DIRECT database; F: faint and/or fuzzy object present in our templateframe, but below our detection threshold; O: outside the boundaries of our catalog. [1]: possiblymis-identified with nearby star in original finding chart; [2]: saturated in DIRECT images; [3]:same object as Hu26-V04; [4]: possibly mis-identified with nearby star in original finding chart;[5]: same object as Hu26-V30.


2.6.1 The P-L relation of LMC Cepheids

All modern determinations of distances based on Cepheids use the Period-

Luminosity Relations of these variables in the Large Magellanic Cloud as fiducial

relations to determine relative distances and extinction corrections. The choice of

the LMC is motivated by several factors: it is relatively close (∼ 50 kpc) to the

Milky Way, hence its Cepheids are bright and well separated from other objects;

the amount of intervening dust and gas along the line of sight is relatively low; it

has a young stellar content, hence Cepheids are plentiful.

Cepheids in the Large Magellanic Cloud have been heavily studied over the

past century, and many P-L relations have stemmed from those studies. The first

self-consistent, multi-wavelength and modern (i.e., photoelectric or CCD based)

relations were derived by Madore & Freedman (1991). They consisted of 32 (25)

Cepheids with data in the BVRI(JHK) bands, with periods ranging from 4 to 60

days. They were corrected for extinction using a fixed value of EB−V =0.10 mag

derived by Bessell (1991) (see §2.6.2 for a definition of EB−V ).

During the past decade, surveys for microlensing events towards the Magellanic

Clouds have resulted in the discovery of thousands of variables, including many

hundreds of Cepheids. In particular, the OGLE project Udalski et al. (1997)

observes in the standard BVI bands, so their Cepheid data can be readily used

for extragalactic work. Udalski et al. (1999) determined VI P-L relations using

∼ 650 Cepheids, individually corrected for extinction using values of EB−V

determined towards 84 different lines of sight, based on the mean magnitudes of

red clump giants. We used the published OGLE B-band extinction-corrected mean

magnitudes for ∼ 300 of these objects to determine the P-L relation in that band

as well. The relations are plotted in Figure 2.16 and listed below:

mB,0 = −2.39 (±0.05) [log P− 1] + 14.91 (±0.07), (2.2)

mV,0 = −2.76 (±0.02) [log P− 1] + 14.28 (±0.02), (2.3)

mI,0 = −2.96 (±0.02) [log P− 1] + 13.60 (±0.01). (2.4)


Fig. 2.16.— Period-Luminosity Relations of Cepheids located in the Large Magel-

lanic Cloud, in the B (top), V (center) and I (bottom) bands. The data was obtained

by the OGLE microlensing experiment Udalski et al. (1997).


These equations can be combined to form period-color relations:

(B − V )0 = 0.37 (±0.05) [log P− 1] + 0.63 (±0.07), (2.5)

(V − I)0 = 0.20 (±0.03) [log P− 1] + 0.68 (±0.02). (2.6)

These relations are distance-independent and can be used to determine the

extinction towards Cepheids in other galaxies (see §2.6.2). The most significant

difference between Madore & Freedman (1991) and Udalski et al. (1999) was a

change of −0.2 mag/dex in the slope of the I-band P-L relation. This affected

the V–I period-color relation and resulted in an increase in the mean extinction of

extragalactic Cepheids and a corresponding decrease in the distances to their host

galaxies.

The P-L relations of LMC Cepheids are well characterized, and thus form an

excellent primary distance indicator that can yield relative distances with internal

errors of a few percent, provided that a fair number of Cepheids are discovered in a

target galaxy. The limiting factors in the accuracy of Cepheid distances are related

to external sources of error, such as extinction, blending, metallicity effects, and

the absolute distance to the LMC. We describe these below.

2.6.2 Extinction corrections

Observations of extragalactic Cepheids are always affected by the scatter and

absorption of a fraction of the incoming flux by dust located along the line of

sight, both in our Galaxy and in a target galaxy. This absorption is commonly

referred to as “extinction” and denoted by Ai, where i is replaced by the symbol of

a particular bandpass or a specific wavelength. Dust is more efficient at scattering

blue light than red light, so obscured objects will not only appear fainter, but

also redder than they actually are. The wavelength dependence of extinction is

commonly referred to as “reddening” and denoted by Ei−j ≡ Ai − Aj. The most

common reddening index is the ratio of extinction between the B and V bands,

represented by EB−V .


The wavelength dependence of extinction in the interstellar medium of our

Galaxy was characterized in detail by Cardelli et al. (1989). Figure 2.17 shows

extinction curves, based on their model, for the wavelength range corresponding

to the ultraviolet, optical and near-infrared bandpasses. These curves are

parameterized by only two quantities: the total extinction in the V band (AV ), and

the ratio of EB−V to AV , denoted by RV . Determinations of RV towards different

lines of sight in our Galaxy yield a mean value of 3.1, with extrema as low as 2.6

and as high as 5.6 (both shown as dotted lines in Figure 2.17).

Given a set of period-color relations of Cepheids such as those presented in

Equations 2.5 and 2.6, and the characterization of the extinction law by Cardelli

et al. (1989), one can calculate the change in any observed color (i.e., V–I) as

a function of AV and RV for a Cepheid of a particular period. Then, standard

minimization techniques can be used to determine the best-fit value of AV and RV

for any given set of observed colors. The application of this technique is shown in

Figure 2.18. Once the best-fit extinction curve is found, it can be applied to correct

the observed magnitudes. Then, the P-L relations of LMC Cepheids can be applied

to the corrected magnitudes to determine the relative distance modulus between

the LMC and the target galaxy. This is the method used in §2.7 to determine the

distance to M33.

An additional advantage of using two or more period-color relations for the

determination of EB−V is that this technique can be used to reject Cepheids that

are contaminated by blends (see §2.6.3). Figure 2.19 shows two examples of this

type of contamination: one by a red star, and one by a blue star. In these cases,

the value of EB−V derived from the B–V data is markedly different than the value

derived from the V–I data. Such contaminated Cepheids can then be rejected from

further consideration; however, the technique has limited power because it cannot

detect the blend of a Cepheid with another star of similar spectral type.

Most searches for Cepheids (including our own) are conducted using a limited

number of bandpasses in the optical portion of the spectrum. Given such a small

coverage in wavelength, it is not possible to solve for the value of RV , so this


Fig. 2.17.— Interstellar extinction curves for different values of RV , based on the

formulation of Cardelli et al. (1989).

Fig. 2.18.— Determination of the extinction towards a particular Cepheid in our

sample (D33J013316.39+303658.0), based on the fit of a standard (RV = 3.1) in-

terstellar extinction curve to the crowding-corrected B, V and I magnitudes. The

best-fit value of EB−V is 0.18± 0.01 mag.


Fig. 2.19.— Effect of blends on Cepheid colors and the derived values of

EB−V . The top and bottom panels show the best-fit values of E(B-V) for

D33J013358.07+304556.8, a 31-day Cepheid blended with a blue companion, and

D33J013325.53+303427.4, an 11-day Cepheid blended with a red companion, re-

spectively. The solid line represents the best-fit solution using all three bands, while

the dotted and dashed lines show the solutions based on the B&V and V&I data,

respectively.


parameter is kept fixed at 3.1. The practice of fixing the value of RV raises the issue

of a possible systematic bias in the determination of distances, since there is no a

priori reason why the extinction law of the interstellar medium of other galaxies

should be the same as the one observed in the Milky Way. Chapter 4 of this Thesis

presents an observational investigation into the validity of this assumption.

An alternative method to simultaneously determine the distance to a galaxy

and correct for extinction is to fit the extinction-corrected LMC P-L relations to

the observed P-L relation of Cepheids in the target galaxy. Given the wavelength

dependence of extinction, the resulting distance moduli will be affected by different

amounts. For example, in the case where only V and I data are available,

µV = µ0 + AV , (2.7)

µI = µ0 + AI . (2.8)

The extinction law of Cardelli et al. (1989) specifies that AI = 0.59AV , for the

mean Galactic value RV = 3.1. Thus, we can combined the measured values of µV

and µI to determine AV as follows:

µV − AV = µI − AI (2.9)

AV − AI = µV − µI (2.10)

0.41AV = µV − µI (2.11)

AV = 2.45(µV − µI). (2.12)

Lastly, we can replace AV in Equation 2.7 by its equivalent formulation in

Equation 2.12 to arrive at:

µ0 = µV − AV (2.13)

µ0 = µV − 2.45(µV − µI). (2.14)

This is the methodology that is used in HST-based Cepheid distance

determinations, such as the one presented in Chapter 3 of this Thesis. A


similar formulation by Madore (1982) combines the V-band P-L relation

(Equation 2.3) with the V–I period-color relation (Equation 2.6) to arrive at the

extinction-corrected LMC-relative distance modulus for an individual Cepheid:

µ0 = V − 2.45(V − I) + 3.26(±0.01) [log P− 1] + 24.40(±0.01). (2.15)

2.6.3 Blending bias

Cepheids are young stars and therefore are preferentially found in regions of active

star formation, such as the arms of spiral galaxies. Given this fact, and the limited

angular resolution provided by any telescope and detector combination, one might

expect that in some cases, a nearby star will fall within the same resolution element

as a Cepheid. If the separation between the Cepheid and the other star is small

compared to the size of the resolution element, the PSF of the combined object

will be indistinguishable from that of an isolated star. We denote such a close

association as “blending”, and note that the bias that results from this process is

different from the bias due to “crowding” (described in §2.3.7), which is akin to

confusion noise and impacts one’s ability to determine a reliable value of the sky

background.

The size of our resolution element is given by the FWHM of the stellar PSF in

our images, ∼ 1− 1.5′′. This translates to 4-6 pc for an assumed distance to M33 of

840 kpc. Thus, blends can be expected to arise both from physically related (i.e.,

binary companions) and unrelated objects (i.e., field stars). If one could improve

the FWHM by a factor of 10, the physical size of a resolution element would

decrease to 0.4-0.6 pc and then only binary companions would elude detection.

Such an increase in resolution is provided by archival HST/WFPC2 images of

the disk of M33, obtained over the past five years for a variety of scientific goals.

Mochejska et al. (2001) have analyzed such images for 91 Cepheids present in our

sample (56 with P < 15 d and 35 with P ≥ 15 d). The data listed in Table 1 of

that paper is reproduced in Figure 2.20.


Fig. 2.20.— Blending data for 91 Cepheids in our sample, from Table 1 of Mochejska

et al. (2001). The level of blending is parameterized by the ratio of the fluxes of the

contaminating star(s) and the affected Cepheid. B, V and I data is plotted using

starred, filled, and open symbols, respectively.


We are interested in the statistics of the long-period (P > 15 d) subset, since

these are the Cepheids typically used for distance determinations. Approximately

half of them (55% in V, 40% in I, 50% in B) show no companions in the HST

data. However, the other half of the sample (45% in V, 57% in I, 42% in B) has

companions whose median (mean) V, I and B fluxes are 11% (17%), 17% (20%) and

22% (25%), respectively, of the flux of the Cepheid they contaminate. In compiling

these statistics, we rejected from consideration a few objects with companions that

contribute more than 60% of the flux of the Cepheid, since these are very obvious

blends that would be identified under any analysis due to their strong impact on

the amplitudes and/or colors of the Cepheids. Given these statistics, one would

expect that a determination of the distance to M33 based on all Cepheids with

P > 15 d would be biased by about 6% in V, 9% in I, and 11% in B. One can lower

this bias even in the absence of HST images, by applying cuts based on several

properties, provided one has good sampling of the light curves in the different

bands. We followed such a procedure, described below, and compared the resulting

distance modulus with the one obtained from the Cepheids that are known to have

no companions.

1. Require P ≥ 15 d and the existence of both V and I data. This was motivated

by the observation that short-period Cepheids suffer from more blending

than long-period ones, and the necessity of color information for extinction

correction. Out of 537 variables, 99 passed these criteria.

2. Require that ∆µI(M33− LMC) ≤ 9.5 mag. This was motivated by the need

to reject Population II Cepheids from the sample. 90 Cepheids passed this

criterion.

3. Require that the r.m.s. deviation of the phased data points about the best-fit

template light curves in the V and I bands be less than or equal to 0.12 mag.

80 Cepheids passed this criterion.

4. Require that the I-band to V-band amplitude of the light curves be within

0.6 ± 0.125. This was motivated by the observation that Cepheids suffering


from a red (blue) blend will display a light curve in the I (V) band with

diminished amplitude. The value of 0.6 was obtained from the analysis of

OGLE Cepheids in the LMC. 65 Cepheids passed this criterion.

5. Require that the value of EB−V derived from the V–I period-color relation

be greater than or equal to zero, and less than or equal to 0.5 mag. This

criterion is similar (but not identical) to the requirement that the observed

V–I color be within 1± 0.5 mag. These criteria help reject blue blends (which

would display negative values of EB−V ) and red blends or highly reddened

Cepheids (which would display very large values of EB−V ). 61 Cepheids

passed this criterion.

Figure 2.21 shows the observed V and I band P-L relations of the 61 Cepheids

that passed all five cuts. These criteria are similar in spirit to those applied by the

HST Key Project on the Extragalactic Distance Scale (Freedman et al. 2001) in their

determination of Cepheid distances. Thus, it is of interest to compare the distance

moduli determined with their techniques to the distance modulus derived by our

technique. The solid lines in Figure 2.21 show the best fit of Equations 2.3 and 2.4

to the data, while the dashed lines show the r.m.s. uncertainty of the fits. This

method yields LMC-relative observed distance moduli of ∆µV = 6.73 ± 0.05 mag

and ∆µI = 6.47 ± 0.04 mag. The application of Equations 2.12 and 2.14 (the

earlier method employed by the Key Project) yields a mean value of extinction of

EB−V = 0.20 mag and an extinction-corrected LMC-relative distance modulus of

∆µ0 = 6.09 ± 0.04 mag. The application of Equation 2.15 (the current method

employed by the Key Project) results in ∆µ0 = 6.09 ± 0.03 mag. Our approach,

based on the fitting of the standard extinction curve of Cardelli et al. (1989) to the

V and I data of each variable, is shown in Figure 2.22; it yields a mean extinction

of EB−V = 0.20± 0.11 mag and a mean extinction-corrected LMC-relative distance

modulus of ∆µ0 = 6.12 ± 0.03 mag. For comparison, Freedman et al. (2001)

determined EB−V = 0.21 ± 0.05 mag and ∆µ0 = 6.06 ± 0.08 mag, based on 11

variables.


Fig. 2.21.— V and I P-L relations of 61 Cepheids in M33 that passed five selection

criteria aimed at rejecting blended variables. The solid lines indicate the best fit

of Equations 2.3 and 2.4 to the data, while the dashed lines indicate the r.m.s

uncertainty of the fits. The best-fit values are µV = 6.73 ± 0.05 mag and µI =

6.47± 0.04 mag.


Fig. 2.22.— Distribution of ∆µ0 vs. P for 61 Cepheids with V & I data. Each

Cepheid was individually corrected for extinction as described in §2.6.2. The mean

extinction-corrected LMC-relative distance modulus is 6.12± 0.03 mag.


The addition of data in our third bandpass (B) may increase our sensitivity

to reject blended Cepheids and yield better estimates of the individual values of

EB−V . However, we are limited by the sparse nature of our B band coverage, which

results in light curves with large phase gaps and hence uncertain amplitudes and

mean magnitudes. 50 of the selected 61 Cepheids have B band data with r.m.s.

deviations of the data points about the best-fit light curve of less than 0.15 mag.

33 variables have a ratio of B-band to V-band amplitudes that is within the values

seen in LMC OGLE Cepheids (1.48± 0.25). After applying these cuts, we can be

confident that we have accurate B band magnitudes. In the absence of blends, the

values of EB−V derived from the V–I and the B–V period-color relations should

track each other fairly well, while red or blue blends will introduce asymmetries

such as the ones previously shown in Figure 2.19. We found that 20 variables had

values of EB−V determined from the two period-color relations that were within

±0.125 mag of each other. The distribution of ∆µ0 vs. P for these Cepheids is

shown in Figure 2.23. A comparison with Figure 2.22 shows a modest decrease in

the r.m.s. scatter from 0.24 mag to 0.17 mag, while the mean value ∆µ0 remains

constant within the errors (6.12± 0.03 mag vs. 6.11± 0.04 mag).

Lastly, there are four Cepheids from the catalog of Mochejska et al. (2001)

which are known to have no companions in either of the three bands, and that are

present in both our subsets (61 variables selected through their V & I properties,

and 20 Cepheids selected through their B, V & I properties). These four unblended

Cepheids yield a mean value of ∆µ0 = 6.09± 0.11 mag.

In conclusion, our selection criteria seem to help in the rejection of blended

Cepheids, and the addition of a third band decreases the r.m.s. scatter of the

distribution of individual distance moduli. Given the good agreement between the

mean distance moduli of four unblended Cepheids and our selected subsample, we

are fairly confident that our extinction-corrected LMC-relative distance modulus

of ∆µ0 = 6.12 ± 0.03 based on 61 Cepheids with V & I data is not substantially

affected by blending.


Fig. 2.23.— Distribution of ∆µ0 vs. P for 20 Cepheids with B, V & I data. Each

Cepheid was individually corrected for extinction as described in §2.6.2. The mean

extinction-corrected LMC-relative distance modulus is 6.11± 0.04 mag. The y-axis

is identical to that of Figure 2.22; note the absence of most Cepheids seen in the

previous Figure with P < 30 d and µ0 < 5.8 mag.


2.6.4 The metallicity dependence of the P-L relation

The period-luminosity and period-color relations used in the previous sub-section to

determine extinction corrections and distance moduli galaxy are based on Cepheids

located in the Large Magellanic Cloud. This galaxy is a low-metallicity system,

with [O/H]LMC = −0.4 dex (Kennicutt et al. 1998). However, most spiral galaxies

where Cepheids have been discovered (including M33) are systems with metallicities

closer to solar (i.e.,[O/H] ≡ 0 dex). This difference in metal content could increase

the opacity of the photosphere, thus altering the observed flux and colors of the

variables. The first investigations into the possibility of this effect were based on

observations of Galactic and Magellanic Cloud Cepheids (Payne-Gaposchkin 1974;

Martin, Warren & Feast 1979; Caldwell & Coulson 1985).

The change in observed distance modulus for a sample of Cepheids due to the

metallicity effect is commonly denoted by the symbol γλ, where λ represents the

band(s) of interest. Most current extragalactic Cepheid distances are based on

V and I data, so it is of special interest to determine an accurate value for γV I .

Recent theoretical models of Cepheids predict γV I = −0.2 mag/dex (Baraffe &

Alibert 2001) to γV I = −0.06 mag/dex (Caputo, Marconi & Musella 2000).

The first observational attempt to quantify the metallicity effect in other

spiral galaxies was undertaken by Freedman & Madore (1990), who compared

the distance moduli of Cepheids located in three regions of M31 with different

galactocentric distances. They found a null result that is not surprising, given

the shallow metallicity gradient of M31. More recently, three studies appeared

within a short period of time addressing this issue from different observational

perspectives. Kochanek (1997) performed a global analysis of Cepheids located

in a dozen galaxies, observed in the V and I bands as part of HST-based efforts

to determine the Hubble Constant. He found a change in the zeropoints for

those bands of −0.14 ± 0.14 mag/dex, as well as a change in color, amounting to

0.13± 0.04 mag/dex, which had the larger impact on derived distances. Sasselov et

al. (1997) performed a differential analysis using Cepheids located in the Large and

Small Magellanic Clouds; the latter is even more metal-poor than the former, with

[O/H]SMC = −0.7 mag/dex. They found an effect of γV I = −0.44+0.2−0.1 mag/dex.


Lastly, Kennicutt et al. (1998) performed another differential analysis using

Cepheids located in the central (metal-rich) and in the outer (metal-poor) regions

of M101 and found a smaller effect of γV I = −0.24± 0.17 mag/dex.

The final paper of the HST Key Project on the Extragalactic Distance Scale

Freedman et al. (2001) adopted a correction of γV I = −0.2± 0.2 mag/dex. Such a

large error bar associated with this parameter introduces a non-negligible source of

uncertainty in the derived distances of the most metal-rich galaxies, making a more

precise determination of this effect highly desirable.

The abundance gradient of M33 has been extensively studied over the past

twenty five years through observations of H II regions (Smith 1975; Kwitter &

Aller 1981; McCall 1982; Vilchez et al. 1988; Garnett et al. 1992; Zaritsky et al.

1989) and supernova remnants (Dopita et al. 1980; Blair & Kirshner, 1985; Smith

et al. 1993). More recently, spectra of individual supergiants in this galaxy have

been used to derive the abundance gradient (McCarthy et al. 1995; Monteverde et

al. 1997; Monteverde & Herrero 1998; Monteverde et al. 2000). Henry & Howard

(1995) performed a combined analysis of all the H II region data and derived

[O/H] = 0.20 − 0.55ρ dex, where ρ = r/r0 and r0 = 12.′2 is the effective radius

of the galaxy. They also found a possible steepening of the gradient inside 8.′3 to

[O/H] = 0.28− 0.68ρ dex, although the latter fit is dominated by a single region at

a very small galactocentric distance. Nevertheless, the total change in abundance

is quite impressive, and is one of the largest among spiral galaxies in the Local

Supercluster. This makes M33 ideally suited for a precise determination of the

metallicity dependence of the Cepheid P-L relation.

A plot of the correlation between ∆µ0 and galactocentric radius for the

selected 20 Cepheids with B, V & I data can be found in Figure 2.24. No significant

correlation is seen, due to the limited range in galactocentric distance and

photometric uncertainties of our sample. However, we expect to have higher quality

data with increased wavelength coverage for these and other Cepheids located at

larger galactocentric distances. That data set ought to yield a determination of the

metallicity effect that is competitive with, and hopefully more precise than,


Fig. 2.24.— Distribution of ∆µ0 vs. galactocentric radius for the 20 selected

Cepheids with B, V & I data. No significant correlation is seen. The expected

trends for metallicity dependences of γV I = −0.2, –0.4 and 0 mag/dex (based on

the gradient of Henry & Howard 1995) are overplotted using solid, dashed and

dotted lines, respectively.


previous findings.

Based on the abundance gradient of Henry & Howard (1995) and the median

galactocentric distance of our variables (r = 9′), the median abundance of our

sample is [O/H] ∼ −0.2 dex, or 0.2 dex greater than that of the LMC. This

corresponds to a correction to the derived distance modulus of 0.04 to 0.08 mag (for

γV I = −0.2 mag/dex to −0.4 mag/dex). We shall adopt the smaller correction,

in order to keep M33 in the distance scale of Freedman et al. (2001), as are the

other Tully-Fisher calibrator spirals to be used in Chapter 6. This implies a

metallicity-corrected LMC-relative distance modulus for M33 of ∆µ0,z = 6.15±0.06

mag. The quoted uncertainty includes the statistical error determined previously

and the external uncertainty related to the metallicity correction.

2.6.5 The distance to the LMC

The determination of an absolute distance to M33 requires the use of a distance

to the Large Magellanic Cloud. This is a topic of considerable debate among the

community (for a recent review, see Gibson 2000), since there is a considerable

range in the estimates that come out of different distance indicators.

Detached eclipsing binaries offer great promise in this endeavor, and two

systems have been studied in detail thus far (HV2274 and HV 982). The group

at Villanova University has obtained µLMC = 18.30 ± 0.07 mag based on the

former system (Guinan et al. 1998) and µLMC = 18.31 ± 0.10 mag based on

the latter one (Fitzpatrick et al. 2000). However, other studies of HV 2274 by

Nelson et al. (2000); Groenewegen & Salaris (2001) yield lower values of EB−V and

corresponding larger distance moduli for the LMC, of µLMC = 18.40 ± 0.07 and

18.42 ± 0.07 mag, respectively. Near-infrared observations of these systems will

likely resolve this relatively small discrepancy in the near future.

Another method used to determine the distance to the LMC relies on the

absolute magnitude of intermediate-age, degenerate helium core-burning stars.

They occupy a well-defined, narrow region of the color-magnitude diagram,


commonly referred to as the “red clump” (Paczynski & Stanek 1998). These stars

are plentiful in the solar neighborhood, and the Hipparcos mission obtained accurate

(σπ/π < 10%) parallaxes for many hundreds of these stars. Udalski (2000) used

284 of these objects which also had high-quality spectra (and hence, well known

metallicities) to obtain an absolute calibration of MI,0(RC) = −0.26 ± 0.02 mag

for [Fe/H]= -0.25 dex, and a metallicity dependence of 0.13± 0.07 mag/dex. Based

upon this calibration, he obtained µLMC = 18.24± 0.08 mag.

The luminosity function of red giant branch stars is another distance indicator

that can be applied to the Large Magellanic Cloud. This method is commonly

referred to as “tip of the red giant branch” and is based on the detection of a

discontinuity in the first or second derivative of the stellar luminosity function,

related to the maximum magnitude of the core helium flash of first-ascent red giant

branch stars. Two recent determinations by Sakai, Zaritsky & Kennicutt (2000)

and Cioni et al. (2000) yield µLMC = 18.59± 0.24 and 18.55± 0.09 mag.

Galactic RR Lyraes, Cepheids and Miras can also be calibrated using

Hipparcos parallaxes, but these calibrations are less certain. In the case of RR

Lyraes, one must first determine the distances to the Galactic globular clusters

where these objects reside, using the “subdwarf fitting technique.” Two different

applications of this technique yield widely different values of MV (RR), and hence

of the distance to the LMC: µLMC = 18.64 ± 0.12 mag (Carretta et al. 2000)

and µLMC = 18.24 ± 0.14 mag (Gould & Popowski, 1998). Cepheids and Miras

are present directly in the Hipparcos catalog, but the typically low S/N of their

parallax measurements yield poorly constrained distances. Cepheids (Groenewegen

& Oudmaijer 2000) yield values of µLMC between 18.45±0.18 and 18.86±0.12 mag,

depending on the choice of bandpass, slope of the P-L relation, and metallicity

correction. The K-band P-L relation of Mira variables (Whitelock & Feast 2000)

yields µLMC = 18.64± 0.14 mag. More accurate parallaxes to be obtained by the

FAME mission will result in competitive determinations of the distance to the

LMC based on these methods.

In summary, the distance to the Large Magellanic Cloud is still poorly known,


with estimates ranging from 18.24 mag to 18.86 mag. Thus, the adoption of a

fiducial LMC distance modulus of µLMC = 18.50 ± 0.10 mag, as proposed by

Freedman et al. (2001), seems warranted until new measurements settle the issue.

2.6.6 An absolute distance to M33

In conclusion, we find an absolute distance modulus to M33 of µM33 =

24.65±0.12 mag, which corresponds to an absolute distance of DM33 = 850±50 kpc.

Our determination is based on V & I photometry of 61 Cepheids with periods

between 15 and 80 days and no evidence of blending. We have assumed a distance

to Large Magellanic Cloud of µLMC = 18.50±0.10 mag; if µLMC = 18.30±0.10 mag,

as suggested by both DEBs and red clump stars, then the distance modulus to

M33 would be µM33 = 24.45± 0.12 mag, corresponding to DM33 = 780± 40 kpc.

The full uncertainty in our distance modulus reflects several sources of error,

as follows: i) a statistical uncertainty of ±0.03 mag (§2.6.3); ii) a photometric

calibration uncertainty of ±0.05 mag (§2.3.6); iii) a metallicity correction

uncertainty of ±0.04 mag (§2.6.4); and iv) an uncertainty in the distance to the

LMC of ±0.10 mag (§2.6.5). Note that the first three sources of error add up to an

uncertainty of only ±0.07 mag. An accurate determination of the distance to the

LMC is required before we achieve a significant reduction in the overall uncertainty

of the extragalactic distance scale.


Chapter 3

A Cepheid distance to NGC 2841

Abstract

This chapter presents the discovery of Cepheids in the spiral galaxy NGC 2841,

based on observations made with the Wide Field and Planetary Camera 2 on

board the Hubble Space Telescope. NGC 2841 was observed over 12 epochs using

the F555W filter, and over 5 epochs using the F814W filter. Photometry was

performed using the DAOPHOT/ALLFRAME package.

We discovered a total of 29 variables, including 18 high-quality Cepheids

with periods ranging from 15 to 40 days. Period-luminosity relations in the V

and I bands, based on the high-quality Cepheids, yield an extinction-corrected

distance modulus of 30.74 ± 0.23 mag, which corresponds to a distance of

14.1 ± 1.5 Mpc. Our distance is based on an assumed LMC distance modulus of

µ0 = 18.50 ± 0.10 mag (D = 50 ± 2.5 kpc) and a metallicity dependence of the

Cepheid P-L relation of γV I = −0.2± 0.2 mag/dex.

Contains material from The Astrophysical Journal, volume 559, pages 243-259, “The Discoveryof Cepheids and a New Distance to NGC 2841 Using the Hubble Space Telescope”, byL.M. Macri, P.B. Stetson, G.D. Bothun, W.L. Freedman, P.M. Garnavich, S. Jha, B.F. Madore &M.W. Richmond.

101


3.1 Introduction

This chapter presents the discovery of 26 Cepheids and a distance determination

to NGC 2841. NGC 2841 is an isolated, flocculent spiral galaxy, classified as Sb(r):

I (de Vaucouleurs et al. 1991) or Sb I (Sandage & Tammann 1981), and located

at α = 9h 22m 03s, δ = +50◦ 58′ 36′′ (J2000.0). It exhibits a heliocentric redshift

of +683 km/s, and has a major axis diameter of 8.′3. Tully (1988) places it in the

northwestern-most association of the Leo Spur (Group 15+10).

The inclination angle of NGC 2841 is 64◦ (de Vaucouleurs et al. 1991), making

it a suitable calibrator of the Tully-Fisher relation. Furthermore, the large observed

21-cm line-width of NGC 2841 (614 ± 4 km/s, Rothberg et al. 2000) significantly

extends the range in rotation velocity over which the Tully-Fisher relation has been

calibrated using Cepheid distances.

NGC 2841 has been the host of four supernovae in the last century: SN 1912A,

SN 1957A, SN 1972R and SN 1999by. The last one is a well-observed type Ia SN

which has been classified as a fast decliner (hence sub-luminous). Thus, it is of

special importance for the calibration of the type Ia SNe distance indicator.

§3.2 describes the observations and preliminary reductions of the images. §3.3

contains the details of photometry and calibration of the instrumental magnitudes.

§3.4 presents the sample of variables and their properties. §3.5 describes the

fiducial Cepheid Period-Luminosity relations used in our analysis, derives a distance

modulus, and lists the sources of uncertainty. §3.6 discusses some implications of

our distance measurement, and §3.7 presents our conclusions.

3.2 Observations and Data Reduction

NGC 2841 was observed by the Wide Field and Planetary Camera 2 (WFPC2)

(Biretta et al. 2000) on board HST on twelve epochs between 2000 February 29

and April 19. The observations were performed using the F555W (approximately

Johnson V) and the F814W (approximately Kron-Cousins I) filters. All twelve


epochs contained a pair of CR-split images in the F555W band, while five epochs

contained an additional pair of CR-split images in the F814W. Each individual

image had an exposure time of 1100s. All observations were made with the

telescope guiding in fine lock with a stability of approximately 3 mas. The gain

and readout noise were 7 e−/DN and 7 e−, respectively. The CCD was operated at

a temperature of –88◦C for all observations. A log of the observations is presented

in Table 3.1. The sampling strategy followed in these observations was similar to

the one employed by the HST Key Project on the Extragalactic Distance Scale

(Freedman et al. 2001), It followed a power-law distribution in time, which provides

an optimum sampling of the light curves of Cepheids in the period range between

10 and 50 days.

The images were calibrated using the pipeline processing at the Space

Telescope Institute (STScI). The full reduction procedure (Holtzman et al. 1995a)

consisted of: a correction for A/D conversion errors, the subtraction of a bias level

for each chip, the subtraction of a superbias frame, the subtraction of a dark frame,

a correction for shutter shading, and a division by a flat field. Furthermore, the

images were corrected for vignetting and geometrical distortions in the WFPC2

optics (the latter correction was done using files kindly provided by J. Holtzman).

Lastly, the images were multiplied by four and converted to two-byte integers, to

reduce disk usage and allow image compression. This conversion led to an effective

readout noise of 4 DN and a gain of 1.75e−/DN.

Figure 3.1 displays a ground-based image of NGC 2841, obtained at the

Whipple Observatory 1.2-m telescope, with a super-imposed mosaic of the WFPC2

field of view. The mosaic is shown in greater detail in Figure 3.2.

3.3 Photometry and Calibration

Photometry of NGC 2841 was performed using the DAOPHOT/ALLFRAME

package. Stetson (1994); Stetson et al. (1998) contain comprehensive overviews of

the package and the reduction strategy, which we briefly summarize here.


Table 3.1. HST Observations of NGC 2841

Date JD Exp. time Filter

2000 Feb 29 2451603.35 2× 1100s F555W

2451603.41 2× 1100s F814W

2000 Mar 02 2451605.29 2× 1100s F555W

2000 Mar 04 2451607.24 2× 1100s F555W

2000 Mar 06 2451609.66 2× 1100s F555W

2451609.72 2× 1100s F814W

2000 Mar 09 2451612.54 2× 1100s F555W

2000 Mar 12 2451615.49 2× 1100s F555W

2000 Mar 16 2451619.38 2× 1100s F555W

2451619.44 2× 1100s F814W

2000 Mar 20 2451623.60 2× 1100s F555W

2000 Mar 26 2451629.30 2× 1100s F555W

2451629.36 2× 1100s F814W

2000 Apr 02 2451636.27 2× 1100s F555W

2000 Apr 09 2451643.24 2× 1100s F555W

2451643.31 2× 1100s F814W

2000 Apr 19 2451653.56 2× 1100s F555W


Fig. 3.1.— Ground-based image of NGC 2841, obtained at the FLWO 1.2-m tele-

scope, with a super-imposed mosaic of the WFPC2 field of view (see Figure 3.2).

North is up and east is to the left.


Fig. 3.2.— Mosaic of the WFPC2 field of view of NGC 2841. Individual images of

each chip, showing the location of the variables, can be found in Figure 3.3


As in the case of previous ALLFRAME reductions of WFPC2 data, we used

external point-spread functions (PSFs), determined by P.B.S. for each chip and

filter combination from high S/N , uncrowded observations of Galactic globular

cluster fields. These external PSFs take into account the variation in the PSF

across the field of view of each WFPC2 chip.

The photometric reduction started with a preliminary detection of sources

in each individual image. DAOMATCH and DAOMASTER were used to derive

offsets and rotations between frames, relative to the first F555W frame. In the

case of these observations, the shifts were < 1 pixel for 31 frames, and ∼ 2 pixels

for the other two. Once the transformations were established, MONTAGE was

used to create a medianed image, free of cosmic rays and chip defects. The FIND

routine in DAOPHOT was used to detect the sources present in that image, and

their positions were refined by running ALLSTAR. The resulting list of objects was

used by ALLFRAME to perform the photometry of each object in every frame.

The conversion from PSF to standard (Holtzman et al. 1995b) 0.5′′-radius

aperture magnitudes involved the determination of growth curves. First, we

selected bright and isolated stars (hereafter, “secondary standards”) that were

located in areas with low and slowly-varying backgrounds. Next, all other objects

were removed from the frames and aperture photometry was carried out at a

variety of radii. DAOGROW (Stetson 1990) was used to derive growth curves

and to obtain 0.5′′-radius aperture magnitudes for the secondary standards in each

frame. Lastly, we used COLLECT to calculate the “aperture correction” coefficient

for each frame from the difference between PSF and aperture magnitudes of the

secondary standards.

The conversion from F555W and F814W magnitudes to Johnson V and

Kron-Cousins I bandpasses followed the precepts of Holtzman et al. (1995b):

V = F555W − 0.052(V −I) + 0.027(V −I)2 + Zi,F555W (3.1)

I = F814W − 0.062(V −I) + 0.025(V −I)2 + Zi,F814W (3.2)


Table 3.2. WFPC2 Zeropoints

Chip Zeropoints

F555W F814W

PC1 0.9510± 0.0028 1.9201± 0.0017

WF2 0.9584± 0.0016 1.8478± 0.0011

WF3 0.9513± 0.0014 1.8724± 0.0010

WF4 0.9697± 0.0015 1.9007± 0.0010

where F555W and F814W equal −2.5 log(DN s−1). The color terms come from

Table 7 of Holtzman et al. (1995b), while the zeropoint terms (Zi) are listed in

Table 3.2 and were determined by P.B.S. and reflect evolution in the understanding

of the WFPC2 calibration since the publication of Stetson (1998) (cf. Table 5 of

that paper). For those epochs without F814W data, the transformation of the

F555W magnitudes into the standard V bandpass was carried out using the mean

V −I color of each object. Lastly, the magnitudes of each object were corrected

for the effects of charge transfer inefficiency following the prescription of Stetson

(1998).

In order to facilitate the comparison of our magnitude system with future

studies, we list in Table 3.3 the mean V and I magnitudes of bright, isolated stars

present in each of the CCDs.


Table 3.3. Secondary standard stars in NGC 2841

ID Chip x y R.A. (J2000.0) Dec. V (mag) I (mag)

S01 1 132.2 467.7 09:22:10.649 50:56:12.66 25.40± 0.02 24.55± 0.04S02 1 141.4 530.3 09:22:10.725 50:56:09.88 25.26± 0.02 25.17± 0.07S03 1 238.3 600.8 09:22:11.223 50:56:07.16 26.47± 0.04 24.00± 0.02S04 1 540.2 144.5 09:22:12.433 50:56:29.20 25.18± 0.02 25.14± 0.10S05 1 508.3 685.9 09:22:12.556 50:56:04.64 25.22± 0.02 25.23± 0.07S06 1 591.2 687.4 09:22:12.952 50:56:04.99 25.84± 0.04 24.29± 0.03S07 1 659.5 98.5 09:22:12.976 50:56:31.81 25.27± 0.02 25.30± 0.07S08 1 715.8 262.0 09:22:13.329 50:56:24.75 24.76± 0.01 24.54± 0.06S09 2 117.0 744.0 09:22:02.603 50:56:16.07 24.92± 0.02 23.20± 0.02S10 2 390.5 543.7 09:22:05.010 50:55:51.50 25.28± 0.02 23.26± 0.01S11 2 272.8 410.5 09:22:06.260 50:56:04.66 24.65± 0.01 23.92± 0.02S12 2 193.1 396.0 09:22:06.315 50:56:12.69 24.22± 0.01 24.06± 0.02S13 2 68.9 371.7 09:22:06.418 50:56:25.17 24.78± 0.01 24.07± 0.03S14 2 464.0 355.9 09:22:07.063 50:55:46.39 24.52± 0.01 24.66± 0.03S15 2 349.2 308.1 09:22:07.424 50:55:58.29 24.65± 0.01 24.66± 0.05S16 2 189.2 271.2 09:22:07.615 50:56:14.49 24.86± 0.01 24.30± 0.03S17 2 208.3 181.5 09:22:08.574 50:56:13.62 24.86± 0.02 24.20± 0.04S18 2 225.7 160.3 09:22:08.816 50:56:12.14 24.50± 0.01 23.69± 0.02S19 2 332.0 64.2 09:22:09.944 50:56:02.75 24.69± 0.02 24.14± 0.03S20 3 730.9 495.3 09:22:02.202 50:57:07.63 24.47± 0.01 24.31± 0.04S21 3 723.7 457.7 09:22:02.319 50:57:04.01 26.69± 0.06 24.08± 0.03S22 3 705.2 400.4 09:22:02.576 50:56:58.57 25.38± 0.03 25.10± 0.09S23 3 716.0 214.2 09:22:02.682 50:56:40.13 25.19± 0.02 24.92± 0.07S24 3 689.1 373.8 09:22:02.774 50:56:56.12 26.39± 0.07 24.26± 0.04S25 3 702.8 156.2 09:22:02.888 50:56:34.59 26.83± 0.07 24.14± 0.03S26 3 631.8 364.0 09:22:03.382 50:56:55.77 23.78± 0.01 22.80± 0.02S27 3 634.1 284.6 09:22:03.450 50:56:47.92 24.44± 0.01 24.11± 0.03S28 3 607.5 139.7 09:22:03.897 50:56:33.96 25.09± 0.01 22.40± 0.02S29 3 509.6 207.4 09:22:04.840 50:56:41.64 26.46± 0.06 24.30± 0.03S30 3 473.9 177.8 09:22:05.247 50:56:39.12 23.22± 0.01 22.34± 0.01S31 3 462.7 101.3 09:22:05.452 50:56:31.73 24.77± 0.02 24.83± 0.06S32 3 434.2 248.7 09:22:05.580 50:56:46.53 27.02± 0.07 23.91± 0.02S33 3 425.0 225.3 09:22:05.704 50:56:44.32 26.31± 0.04 24.42± 0.04S34 3 385.3 100.9 09:22:06.261 50:56:32.52 24.48± 0.01 24.24± 0.03S35 3 360.1 82.5 09:22:06.545 50:56:31.00 26.07± 0.03 23.60± 0.02S36 3 282.6 110.9 09:22:07.322 50:56:34.63 26.55± 0.06 23.91± 0.02



ID Chip x y R.A. (J2000.0) Dec. V (mag) I (mag)

S37 3 280.5 93.6 09:22:07.363 50:56:32.96 25.19± 0.02 24.77± 0.05S38 3 249.9 78.8 09:22:07.698 50:56:31.85 25.15± 0.02 24.64± 0.05S39 3 220.4 141.7 09:22:07.936 50:56:38.34 24.75± 0.01 24.45± 0.04S40 3 163.9 162.4 09:22:08.500 50:56:41.01 24.85± 0.02 24.32± 0.03S41 4 85.5 262.1 09:22:12.214 50:56:37.22 23.26± 0.01 22.95± 0.02S42 4 588.9 323.0 09:22:12.322 50:57:27.53 24.52± 0.01 24.49± 0.03S43 4 296.7 300.6 09:22:12.392 50:56:58.40 23.90± 0.01 23.80± 0.01S44 4 132.5 309.9 09:22:12.663 50:56:42.30 25.08± 0.02 24.58± 0.04S45 4 202.5 371.4 09:22:13.233 50:56:49.80 24.41± 0.01 23.06± 0.01S46 4 502.3 421.4 09:22:13.443 50:57:19.95 23.95± 0.01 23.58± 0.02S47 4 154.1 389.7 09:22:13.476 50:56:45.21 24.79± 0.01 24.72± 0.03S48 4 257.2 420.9 09:22:13.695 50:56:55.69 22.80± 0.01 21.97± 0.01S49 4 229.0 439.2 09:22:13.916 50:56:53.09 24.83± 0.02 24.37± 0.03S50 4 684.1 510.6 09:22:14.185 50:57:38.74 24.76± 0.01 24.65± 0.03S51 4 738.3 543.7 09:22:14.473 50:57:44.37 24.76± 0.01 24.31± 0.03S52 4 595.7 535.8 09:22:14.543 50:57:30.30 26.11± 0.05 23.25± 0.01S53 4 507.6 545.1 09:22:14.733 50:57:21.69 24.94± 0.02 24.06± 0.05S54 4 595.3 562.4 09:22:14.821 50:57:30.52 24.66± 0.01 24.06± 0.02S55 4 722.2 577.1 09:22:14.838 50:57:43.11 24.57± 0.01 23.54± 0.02S56 4 752.0 587.9 09:22:14.919 50:57:46.12 24.44± 0.01 24.10± 0.02S57 4 157.4 539.7 09:22:15.042 50:56:47.04 23.71± 0.01 23.39± 0.02S58 4 131.8 652.5 09:22:16.243 50:56:45.68 25.90± 0.03 23.45± 0.01S59 4 662.6 737.1 09:22:16.565 50:57:38.77 23.54± 0.01 22.82± 0.01S60 4 481.2 718.5 09:22:16.569 50:57:20.77 24.85± 0.01 23.93± 0.02S61 4 459.2 747.9 09:22:16.897 50:57:18.89 23.49± 0.01 22.94± 0.01


3.4 The Cepheids found in NGC 2841

The initial search for variables was carried out using TRIAL, a program that

calculated the value of the J statistic for each star, based on the V-band data.

The J statistic is a robust index of variability developed by Stetson (1996), and it

is designed so that objects with constant magnitudes yield values near zero. The

mean value and r.m.s. deviation of this index for all stars present in our database

was 0.01 ± 0.29. We flagged 79 objects with J > 0.8 as possible variables and

extracted their individual light curves from the photometry database for further

analysis, using programs developed by the DIRECT team (Kaluzny et al. 1998).

We calculated periods for the candidate variables using a modified version of

the Lafler-Kinman technique (Stetson 1996); we restricted the range of possible

periods to the range between 10 and 50 days. Next, template Cepheid light curves

(derived by Stetson 1996) were simultaneously fitted to the phased V- and I-band

photometry of each candidate. The use of templates allows a robust classification

of a candidate variable as a Cepheid, refines the period of the variable, and yields

reliable mean magnitudes through numerical integration of the best-fit template. If

the candidate object was classified as a Cepheid, an iterative 3σ rejection algorithm

was applied to the data to reject anomalous photometric measurements, most of

them associated with cosmic-ray hits, and the light curve was analyzed again.

About 5% of the individual data points were rejected in this manner.

The automated classification software rejected 50 candidates and classified

26 objects as Cepheids. An additional 3 objects are clearly variables, and most

likely Cepheids, but their periods are longer that our observing window and we

cannot obtain accurate values for their mean magnitudes. Table 3.4 lists the

following properties of the 29 variables which passed the analysis: identification

number (C01-C26 in order of descending period, for the Cepheids, and V01-V03 in

order of increasing R.A., for the other variables); chip where the object is located;

(J2000.0) coordinates; best-fit period and uncertainty (Cepheids only); V and I

mean magnitudes, derived from the best-fit template light curves; and a selection

flag (see §3.5.2 for details).


Table 3.4. Variables discovered in NGC 2841

ID Chip R.A. (J2000.0) Dec. P (d) V (mag) I (mag)

C01 4 09:22:13.556 +50:56:35.13 13.9± 0.6 26.61± 0.05 25.64± 0.11C02 3 09:22:07.430 +50:56:43.10 16.1± 0.5 25.96± 0.03 25.05± 0.06C03 4 09:22:10.055 +50:57:32.45 16.5± 0.2 26.30± 0.04 25.06± 0.07C04 4 09:22:12.669 +50:56:57.42 18.5± 0.5 26.35± 0.04 25.19± 0.05C05 3 09:22:09.441 +50:57:01.23 18.9± 0.6 24.84± 0.02 23.95± 0.05C06 2 09:22:09.112 +50:56:23.87 20.0± 0.3 25.67± 0.04 24.92± 0.04 *C07 3 09:22:05.636 +50:56:38.26 21.0± 0.4 25.96± 0.03 24.59± 0.11C08 2 09:22:09.298 +50:56:22.28 21.1± 1.1 25.39± 0.03 24.38± 0.04C09 4 09:22:12.416 +50:57:06.63 21.5± 0.5 25.96± 0.03 24.73± 0.09C10 3 09:22:01.632 +50:57:29.27 21.7± 1.0 26.06± 0.06 25.15± 0.05 *C11 3 09:22:02.530 +50:57:29.84 21.8± 0.7 26.09± 0.05 24.96± 0.14 *C12 4 09:22:12.161 +50:57:12.21 22.5± 0.3 25.71± 0.02 24.77± 0.03 *C13 1 09:22:11.681 +50:56:28.38 23.0± 0.8 26.79± 0.05 25.43± 0.08 *C14 4 09:22:12.536 +50:56:34.94 23.2± 0.4 26.42± 0.03 25.32± 0.05 *C15 4 09:22:12.363 +50:56:53.81 23.2± 0.3 25.94± 0.03 24.89± 0.08 *C16 3 09:22:02.836 +50:57:11.58 26.5± 0.8 25.88± 0.05 24.89± 0.06 *C17 4 09:22:12.449 +50:57:31.34 27.3± 1.0 25.96± 0.04 24.97± 0.05 *C18 3 09:22:06.896 +50:56:29.77 27.8± 0.6 25.73± 0.05 24.70± 0.05 *C19 4 09:22:09.914 +50:56:59.89 29.0± 0.9 25.99± 0.03 24.93± 0.05 *C20 2 09:22:09.735 +50:56:10.33 30.2± 0.5 25.88± 0.05 24.90± 0.05 *C21 4 09:22:10.985 +50:57:22.56 32.2± 0.7 25.04± 0.01 24.01± 0.03 *C22 1 09:22:13.295 +50:56:16.80 33.2± 0.8 25.38± 0.03 24.24± 0.02 *C23 3 09:22:05.051 +50:56:43.88 34.6± 1.4 25.17± 0.03 24.31± 0.04 *C24 4 09:22:12.412 +50:56:37.74 36.6± 1.8 25.84± 0.04 24.66± 0.03 *C25 2 09:22:09.587 +50:56:06.44 39.5± 0.8 25.31± 0.02 24.26± 0.05 *C26 4 09:22:12.264 +50:57:21.81 40.9± 0.5 25.15± 0.02 24.06± 0.05 *V01 2 09:22:06.469 +50:56:10.35 . . . 24.75± 0.04 23.62± 0.04V02 3 09:22:06.573 +50:56:38.48 . . . 24.80± 0.05 23.49± 0.04V03 1 09:22:12.073 +50:56:26.84 . . . 25.24± 0.04 24.02± 0.05

Note. — (*): Variable was used to construct the P-L relations shown in Figures 3.8and 3.9.


Figure 3.3 contains chip-wide images of each of the WFPC2 CCDs, indicating

the locations of the variables. Finding charts for each of the stars are displayed in

Figure 3.4; the charts encompass a 50 by 50 pixel area around each variable (i.e.,

2′′.15 × 2′′.15 for the PC and 5′′ × 5′′ for the WF). The individual V and I band

photometric measurements are listed in Tables 3.5 and 3.6, respectively, and shown

as phase-magnitude plots (for the Cepheids) and as time series (for the other

variables) in Figure 3.5. That figure also shows the V and I best-fit template light

curves for each Cepheid, which were used to determine their mean magnitudes.

Figure 3.6 shows a color-magnitude diagram of the ∼ 9000 stars detected in

our images. As expected, the Cepheids occupy a region of the diagram that is

consistent with the location of the instability strip. Figure 3.7 shows the observed

differential luminosity functions for the V and I data, which indicate that our

completeness limits are V∼ 26.5 mag and I∼ 25.5 mag. Additionally, the I band

luminosity function does not exhibit the signature associated with the Tip of the

Red Giant Branch (c.f. Figure 2 of Sakai, Zaritsky & Kennicutt 2000), yielding a

lower limit for the distance to NGC 2841 of ∼ 29.5 mag or ∼ 8 Mpc.

3.5 Period-Luminosity Relations and Distance

Moduli

3.5.1 Methodology

The method used to derive V- and I-band apparent distance moduli is the

one adopted by the HST Key Project on the Extragalactic Distance Scale,

which is described in detail by Freedman et al. (2001). It relies on fiducial

Period-Luminosity relations of LMC Cepheids, corrected for reddening and scaled

based on an assumed true distance modulus of µ0,LMC = 18.50±0.10 mag. The P-L

relations used are those from (Udalski et al. 1999), based on a sample of ∼ 650

OGLE Cepheids with periods ranging from 2.5 to 28 days:


Fig. 3.3a.— Medianed images of the four WFPC2 chips. The circles indicate the

position of each of the variables, labeled as in Table 3.4. Each of the images is

oriented such that the bottom left corner has the pixel coordinates (0,0) in each

image.


Fig. 3.3b.— continued.


Fig. 3.3c.— continued.


Fig. 3.3d.— continued.


Fig. 3.4.— Individual finding charts for the variables. The position of each object is

shown by the circle. The charts are 50 pixels on a side, i.e., 2′′.15× 2′′.15 for objects

in the PC chip and 5′′ × 5′′ for objects in the the WF chips.


Fig. 3.5a.— V and I light curves for the variables, plotted as magnitude vs. phase

for the Cepheids and as magnitude vs. date for the other variables. In the case of

the Cepheids, two complete cycles are plotted to facilitate ease of interpretation.

Filled and open symbols are used to represent the V and I magnitudes listed in

Tables 3.5-3.6, respectively. The uncertainties associated with each measurement,

also listed in that Table, are plotted using error bars. The solid and dashed lines

overplotted on each panel indicate the best-fit V and I band template light curves,

respectively.








Fig. 3.5e.— continued.


Fig. 3.6.— Color- magnitude diagram of the ∼ 9000 stars detected in our images

of NGC 2841. Filled and open circles are used to plot the Cepheids and the other

variables, respectively.


Fig. 3.7.— Observed differential luminosity functions for the stars detected in our

images of NGC 2841. Solid and dashed lines are used to plot the V and I histograms,

respectively. Based on these distributions, we determine completeness limits of

V∼ 26.5 mag and I∼ 25.5 mag.


Table 3.5. Individual V band photometric measurements

MJD

C01 C02 C03 C04 C05603.36 26.28± 0.16 25.48± 0.21 25.74± 0.12 26.33± 0.13 24.55± 0.04603.38 26.50± 0.28 25.53± 0.14 25.66± 0.16 26.09± 0.16 24.60± 0.06605.30 26.91± 0.34 25.69± 0.14 26.06± 0.20 26.59± 0.38 24.66± 0.13605.32 26.98± 0.23 25.64± 0.16 26.07± 0.17 26.63± 0.21 24.60± 0.09607.25 . . . 26.13± 0.20 26.25± 0.18 26.60± 0.24 24.67± 0.05607.26 27.21± 0.28 26.02± 0.25 26.40± 0.24 26.74± 0.24 24.79± 0.08609.67 27.21± 0.36 26.20± 0.20 26.78± 0.22 26.43± 0.22 24.95± 0.06609.68 27.88± 0.68 25.85± 0.18 26.90± 0.52 27.11± 0.30 24.93± 0.13612.55 26.61± 0.24 . . . 26.80± 0.27 . . . 24.92± 0.06612.56 26.95± 0.27 26.16± 0.22 27.18± 0.55 26.84± 0.19 24.85± 0.11615.50 26.00± 0.16 26.34± 0.26 26.73± 0.22 26.27± 0.23 25.18± 0.09615.51 26.01± 0.19 . . . 27.16± 0.46 26.16± 0.24 25.06± 0.15619.39 26.64± 0.22 25.57± 0.14 25.57± 0.11 26.27± 0.25 24.94± 0.06619.40 26.78± 0.24 25.63± 0.08 25.77± 0.19 25.98± 0.12 25.10± 0.13623.61 27.49± 0.38 25.97± 0.15 26.36± 0.16 26.25± 0.15 24.55± 0.05623.62 26.76± 0.24 26.14± 0.15 26.48± 0.31 26.45± 0.25 24.77± 0.06629.31 26.18± 0.22 . . . 26.49± 0.31 26.54± 0.26 24.74± 0.08629.32 26.14± 0.19 26.14± 0.23 26.93± 0.30 26.93± 0.31 24.96± 0.09636.28 27.21± 0.37 25.69± 0.13 25.79± 0.17 26.16± 0.18 24.87± 0.09636.29 27.78± 0.84 . . . 25.77± 0.15 25.95± 0.15 25.00± 0.08643.25 26.27± 0.13 26.16± 0.17 27.08± 0.35 26.32± 0.26 24.68± 0.10643.27 26.03± 0.12 25.92± 0.22 27.14± 0.36 27.04± 0.41 24.65± 0.11653.57 27.16± 0.52 25.75± 0.17 25.86± 0.11 26.09± 0.19 25.01± 0.12653.59 27.23± 0.66 25.62± 0.23 25.76± 0.20 25.77± 0.10 25.09± 0.17

C06 C07 C08 C09 C10603.36 26.27± 0.22 25.81± 0.15 25.32± 0.10 . . . 27.21± 0.52603.38 26.19± 0.17 25.48± 0.12 25.19± 0.14 26.14± 0.17 27.24± 0.39605.30 26.44± 0.35 25.64± 0.10 25.39± 0.14 26.42± 0.23 26.30± 0.23605.32 26.29± 0.16 25.53± 0.11 25.28± 0.07 26.16± 0.15 26.34± 0.43607.25 25.18± 0.10 25.82± 0.09 25.33± 0.12 26.57± 0.22 25.65± 0.16607.26 25.20± 0.11 25.81± 0.15 25.37± 0.07 26.64± 0.20 25.50± 0.20609.67 25.25± 0.06 26.02± 0.24 25.31± 0.16 26.34± 0.13 25.86± 0.15609.68 25.24± 0.10 25.98± 0.15 . . . 26.18± 0.17 26.09± 0.32612.55 25.36± 0.11 26.12± 0.25 25.43± 0.12 25.86± 0.13 25.74± 0.21612.56 25.39± 0.11 26.33± 0.24 25.46± 0.07 26.12± 0.12 26.08± 0.35



MJD

615.50 25.82± 0.14 26.39± 0.26 25.77± 0.16 25.38± 0.09 26.07± 0.17615.51 25.89± 0.15 26.32± 0.23 25.65± 0.27 25.59± 0.11 26.12± 0.28619.39 25.76± 0.13 26.49± 0.25 25.42± 0.11 25.83± 0.12 26.73± 0.46619.40 26.00± 0.17 26.64± 0.24 25.83± 0.13 25.98± 0.10 26.88± 0.47623.61 26.18± 0.21 25.71± 0.10 24.95± 0.19 26.01± 0.12 26.53± 0.24623.62 25.91± 0.15 25.84± 0.14 24.95± 0.12 26.00± 0.14 26.94± 0.33629.31 25.27± 0.09 25.55± 0.12 25.53± 0.16 26.46± 0.25 25.55± 0.18629.32 25.40± 0.13 25.72± 0.16 25.62± 0.15 26.44± 0.18 25.44± 0.18636.28 25.58± 0.13 26.27± 0.20 25.69± 0.20 25.40± 0.10 25.79± 0.14636.29 25.80± 0.10 26.00± 0.13 25.69± 0.23 25.38± 0.08 25.77± 0.13643.25 26.13± 0.20 26.09± 0.20 25.08± 0.07 25.86± 0.16 26.32± 0.23643.27 26.07± 0.12 26.40± 0.58 25.06± 0.12 25.84± 0.14 26.30± 0.23653.57 25.52± 0.18 25.96± 0.13 25.45± 0.15 26.65± 0.36 26.00± 0.17653.59 . . . 26.23± 0.20 . . . 26.43± 0.23 . . .

C11 C12 C13 C14 C15603.36 . . . 25.87± 0.15 26.15± 0.18 25.95± 0.13 26.19± 0.19603.38 26.72± 0.39 26.07± 0.20 26.10± 0.12 25.92± 0.10 26.44± 0.21605.30 26.36± 0.26 25.90± 0.12 26.59± 0.26 26.17± 0.21 25.40± 0.15605.32 . . . 25.65± 0.14 26.40± 0.17 26.05± 0.18 25.42± 0.16607.25 25.33± 0.11 25.34± 0.08 26.43± 0.22 26.50± 0.20 25.30± 0.08607.26 25.48± 0.20 25.38± 0.07 26.61± 0.19 26.44± 0.26 25.30± 0.08609.67 25.68± 0.16 25.39± 0.08 26.71± 0.26 26.54± 0.22 25.56± 0.10609.68 25.85± 0.28 25.32± 0.08 26.97± 0.37 26.64± 0.25 25.64± 0.15612.55 25.93± 0.14 25.70± 0.11 27.12± 0.23 26.90± 0.29 25.95± 0.13612.56 26.25± 0.27 25.55± 0.13 27.20± 0.34 26.66± 0.20 25.94± 0.15615.50 26.33± 0.23 25.64± 0.20 27.08± 0.45 . . . 25.87± 0.16615.51 . . . 25.65± 0.14 26.83± 0.26 27.34± 0.35 26.20± 0.16619.39 26.60± 0.31 25.82± 0.13 . . . 26.91± 0.20 . . .619.40 . . . 25.72± 0.41 . . . . . . 26.15± 0.17623.61 26.95± 0.34 26.04± 0.12 26.70± 0.24 25.97± 0.19 26.80± 0.34623.62 26.77± 0.38 26.11± 0.14 27.26± 0.48 25.65± 0.15 26.33± 0.12629.31 25.23± 0.13 25.47± 0.07 26.30± 0.23 26.22± 0.12 25.42± 0.14629.32 25.57± 0.14 25.60± 0.19 26.61± 0.27 26.24± 0.14 25.41± 0.06636.28 25.89± 0.19 25.77± 0.09 27.49± 0.40 27.19± 0.50 25.55± 0.22636.29 26.48± 0.35 25.71± 0.12 27.05± 0.44 27.17± 0.29 25.94± 0.12643.25 26.75± 0.27 26.08± 0.17 27.40± 0.46 27.16± 0.51 26.30± 0.22



MJD

643.27 26.22± 0.27 25.80± 0.12 27.22± 0.34 26.84± 0.22 26.53± 0.22653.57 25.66± 0.28 25.23± 0.10 26.34± 0.24 26.15± 0.19 25.31± 0.10653.59 25.77± 0.18 25.36± 0.09 26.82± 0.23 26.25± 0.17 25.51± 0.11

C16 C17 C18 C19 C20603.36 26.22± 0.16 26.14± 0.23 25.68± 0.38 25.58± 0.12 25.84± 0.15603.38 26.05± 0.23 26.37± 0.29 25.63± 0.14 25.76± 0.19 25.78± 0.11605.30 26.67± 0.35 26.25± 0.28 26.19± 0.17 25.66± 0.14 26.00± 0.10605.32 26.28± 0.32 26.22± 0.15 26.05± 0.31 25.74± 0.18 26.05± 0.20607.25 26.30± 0.19 26.39± 0.30 26.36± 0.23 25.60± 0.06 26.40± 0.18607.26 26.91± 0.39 26.34± 0.29 25.95± 0.25 25.98± 0.16 25.99± 0.11609.67 26.43± 0.27 26.46± 0.18 26.36± 0.16 . . . 26.06± 0.25609.68 25.96± 0.15 26.58± 0.23 26.46± 0.23 26.05± 0.35 26.05± 0.18612.55 25.47± 0.10 26.04± 0.11 26.27± 0.13 26.12± 0.34 26.59± 0.22612.56 25.50± 0.18 26.02± 0.16 26.67± 0.34 26.09± 0.14 26.17± 0.10615.50 25.52± 0.13 . . . 25.77± 0.24 . . . 26.72± 0.23615.51 25.48± 0.15 26.31± 0.27 25.78± 0.15 26.46± 0.39 26.09± 0.14619.39 25.70± 0.20 25.28± 0.18 25.00± 0.07 26.59± 0.30 26.53± 0.23619.40 25.62± 0.09 25.52± 0.11 25.16± 0.12 26.48± 0.21 26.84± 0.28623.61 25.79± 0.17 25.88± 0.10 25.55± 0.14 26.62± 0.21 25.46± 0.07623.62 26.00± 0.15 . . . 25.52± 0.09 26.58± 0.29 25.50± 0.12629.31 26.68± 0.32 26.24± 0.22 26.09± 0.18 25.50± 0.12 25.45± 0.11629.32 26.91± 0.47 26.19± 0.32 25.80± 0.21 25.57± 0.11 . . .636.28 26.20± 0.15 26.43± 0.27 26.80± 0.41 . . . 25.86± 0.11636.29 26.13± 0.18 26.49± 0.27 26.11± 0.13 25.88± 0.10 26.29± 0.19643.25 . . . 25.77± 0.15 26.65± 0.45 26.49± 0.17 26.45± 0.22643.27 . . . 26.00± 0.25 26.10± 0.18 26.08± 0.16 26.18± 0.21653.57 26.22± 0.17 26.07± 0.18 25.61± 0.13 26.30± 0.25 25.45± 0.14653.59 26.57± 0.26 26.43± 0.42 . . . 26.65± 0.34 . . .

C21 C22 C23 C24 C25603.36 25.29± 0.09 25.02± 0.07 24.62± 0.09 25.82± 0.16 25.65± 0.12603.38 25.29± 0.15 24.71± 0.09 24.48± 0.22 25.61± 0.17 25.36± 0.14605.30 25.19± 0.10 24.74± 0.34 24.76± 0.07 25.94± 0.13 25.69± 0.09605.32 25.02± 0.12 25.13± 0.09 . . . 25.89± 0.14 25.87± 0.22607.25 24.97± 0.08 25.10± 0.09 25.15± 0.08 26.01± 0.17 25.83± 0.18607.26 24.70± 0.11 25.14± 0.09 24.73± 0.08 25.82± 0.19 25.74± 0.13609.67 24.72± 0.06 25.32± 0.08 25.13± 0.08 26.28± 0.13 . . .



MJD

609.68 24.69± 0.08 25.32± 0.10 . . . 25.82± 0.19 25.66± 0.13612.55 24.81± 0.07 25.26± 0.09 25.05± 0.09 26.00± 0.13 25.72± 0.12612.56 24.75± 0.06 25.18± 0.08 25.03± 0.11 25.83± 0.11 25.58± 0.13615.50 24.81± 0.08 25.79± 0.14 25.22± 0.09 26.01± 0.16 25.32± 0.13615.51 24.88± 0.11 25.85± 0.22 25.39± 0.12 26.48± 0.24 25.32± 0.10619.39 . . . . . . 25.74± 0.17 26.31± 0.12 24.89± 0.07619.40 25.00± 0.07 26.01± 0.19 25.58± 0.13 26.00± 0.19 24.78± 0.11623.61 25.10± 0.07 25.97± 0.16 25.54± 0.09 26.40± 0.15 25.03± 0.09623.62 25.17± 0.10 25.60± 0.13 25.30± 0.06 26.50± 0.25 24.95± 0.08629.31 25.39± 0.15 . . . 25.78± 0.22 25.39± 0.09 25.19± 0.10629.32 25.34± 0.12 25.66± 0.14 25.75± 0.18 25.29± 0.11 25.13± 0.09636.28 25.31± 0.15 24.81± 0.10 24.66± 0.08 25.51± 0.11 25.55± 0.08636.29 25.25± 0.10 24.83± 0.08 . . . 25.70± 0.17 25.42± 0.09643.25 24.75± 0.09 25.30± 0.10 25.05± 0.13 25.96± 0.14 25.62± 0.11643.27 24.68± 0.07 25.29± 0.09 24.91± 0.07 25.98± 0.14 25.46± 0.17653.57 25.07± 0.10 25.76± 0.14 . . . 26.60± 0.34 25.61± 0.12653.59 . . . 25.73± 0.13 25.45± 0.12 26.13± 0.21 . . .

C26 V01 V02 V03603.36 25.73± 0.09 24.87± 0.08 24.84± 0.05 25.49± 0.09603.38 . . . 24.86± 0.06 24.77± 0.11 25.41± 0.13605.30 25.51± 0.10 24.87± 0.05 24.70± 0.04 25.34± 0.11605.32 25.67± 0.10 24.87± 0.05 24.68± 0.07 25.38± 0.12607.25 . . . . . . 24.50± 0.06 25.45± 0.13607.26 25.60± 0.14 24.86± 0.07 24.56± 0.07 25.40± 0.13609.67 25.48± 0.09 24.93± 0.10 24.58± 0.07 25.35± 0.11609.68 25.42± 0.09 24.89± 0.08 24.59± 0.07 25.39± 0.08612.55 24.80± 0.05 24.92± 0.05 24.51± 0.05 25.44± 0.09612.56 24.94± 0.05 . . . 24.58± 0.06 25.28± 0.10615.50 24.61± 0.08 24.98± 0.08 24.62± 0.06 25.40± 0.16615.51 24.71± 0.04 25.01± 0.10 24.55± 0.09 25.36± 0.10619.39 24.75± 0.04 24.85± 0.06 24.71± 0.10 . . .619.40 24.88± 0.05 24.92± 0.07 24.80± 0.10 25.15± 0.10623.61 25.00± 0.07 24.78± 0.05 24.84± 0.09 24.98± 0.10623.62 25.03± 0.06 24.82± 0.07 24.86± 0.12 . . .629.31 25.23± 0.12 24.69± 0.04 24.84± 0.06 24.83± 0.09629.32 25.07± 0.08 24.74± 0.10 . . . 24.87± 0.09



MJD

636.28 25.48± 0.06 24.55± 0.06 25.06± 0.07 25.08± 0.07636.29 25.39± 0.07 24.44± 0.04 25.02± 0.08 24.98± 0.10643.25 25.70± 0.18 24.43± 0.05 25.23± 0.10 24.79± 0.17643.27 25.55± 0.05 24.34± 0.06 24.93± 0.08 25.21± 0.10653.57 24.86± 0.06 24.41± 0.09 25.36± 0.08 25.38± 0.11653.59 . . . . . . 25.20± 0.06 25.32± 0.11


Table 3.6. Individual I band photometric measurements

MJD

C01 C02 C03 C04 C05603.42 25.91± 0.35 24.90± 0.19 24.97± 0.34 25.35± 0.23 23.88± 0.13603.43 25.82± 0.27 24.73± 0.12 25.11± 0.31 25.39± 0.20 23.87± 0.14609.73 25.54± 0.25 24.95± 0.31 25.14± 0.21 25.50± 0.26 23.86± 0.09609.74 26.00± 0.60 25.04± 0.21 25.04± 0.19 25.51± 0.22 24.07± 0.14619.45 26.16± 0.48 24.80± 0.46 24.84± 0.22 25.12± 0.17 24.35± 0.14619.47 . . . . . . 24.69± 0.16 25.00± 0.14 24.07± 0.16629.37 25.54± 0.31 25.61± 0.43 25.31± 0.29 25.27± 0.16 23.96± 0.13629.39 25.10± 0.14 25.52± 0.28 . . . 25.32± 0.30 24.16± 0.15643.32 25.50± 0.24 25.13± 0.36 25.02± 0.16 25.09± 0.12 23.61± 0.09643.33 25.38± 0.20 25.43± 0.34 25.44± 0.41 25.19± 0.21 23.75± 0.10

C06 C07 C08 C09 C10603.42 25.41± 0.24 24.59± 0.15 24.29± 0.38 25.34± 0.26 25.58± 0.26603.43 25.09± 0.24 . . . 24.39± 0.16 24.89± 0.16 25.49± 0.37609.73 24.59± 0.12 24.73± 0.28 24.22± 0.15 24.95± 0.18 25.13± 0.31609.74 24.69± 0.17 24.45± 0.12 24.35± 0.12 24.78± 0.08 24.97± 0.19619.45 25.08± 0.21 25.21± 0.36 24.50± 0.22 24.75± 0.15 25.23± 0.25619.47 25.22± 0.34 24.66± 0.15 24.64± 0.19 24.77± 0.14 25.13± 0.28629.37 24.57± 0.09 24.32± 0.14 24.28± 0.11 24.94± 1.04 24.85± 0.18629.39 24.64± 0.15 24.83± 0.15 24.56± 0.24 25.57± 0.49 24.99± 0.22643.32 25.42± 0.23 24.55± 0.12 24.23± 0.14 25.05± 0.19 25.23± 0.21643.33 25.32± 0.23 24.06± 0.47 24.23± 0.16 24.59± 0.09 . . .

C11 C12 C13 C14 C15603.42 . . . 24.99± 0.15 25.13± 0.20 24.87± 0.18 25.52± 0.28603.43 . . . 24.91± 0.15 25.23± 0.22 25.03± 0.13 25.50± 0.40609.73 25.12± 0.37 . . . 25.05± 0.18 25.30± 0.20 24.64± 0.15609.74 24.81± 0.23 24.80± 0.19 25.54± 0.24 25.12± 0.18 24.78± 0.16619.45 . . . 25.00± 0.16 . . . . . . 24.90± 0.18619.47 . . . 24.83± 0.12 . . . . . . 25.55± 0.28629.37 24.57± 0.19 24.60± 0.11 25.26± 0.24 . . . 24.43± 0.10629.39 24.72± 0.12 24.72± 0.14 . . . 25.27± 0.18 24.70± 0.12643.32 24.73± 0.27 25.02± 0.30 . . . 25.80± 0.35 25.54± 0.25643.33 25.21± 0.25 24.83± 0.13 . . . . . . 25.18± 0.21

C16 C17 C18 C19 C20603.42 25.25± 0.48 25.21± 0.24 24.87± 0.21 24.78± 0.10 24.56± 0.15603.43 25.34± 0.31 25.13± 0.27 24.58± 0.13 24.66± 0.15 24.67± 0.16



MJD

609.73 25.54± 0.39 25.44± 0.21 25.17± 0.41 24.68± 0.24 25.26± 0.16609.74 25.27± 0.43 25.33± 0.33 24.98± 0.18 24.58± 0.17 25.23± 0.13619.45 24.95± 0.21 24.67± 0.12 24.70± 0.15 25.13± 0.33 25.15± 0.21619.47 24.72± 0.17 24.99± 0.28 24.28± 0.10 25.52± 0.29 . . .629.37 . . . 25.02± 0.21 24.84± 0.16 24.52± 0.14 24.72± 0.20629.39 24.99± 0.19 24.76± 0.17 24.67± 0.10 24.80± 0.14 24.60± 0.10643.32 24.60± 0.19 25.05± 0.34 24.79± 0.21 24.93± 0.14 . . .643.33 24.53± 0.17 24.76± 0.22 24.78± 0.16 25.11± 0.26 25.09± 0.17

C21 C22 C23 C24 C25603.42 . . . 24.05± 0.10 24.08± 0.10 24.47± 0.14 . . .603.43 24.18± 0.10 23.94± 0.12 24.10± 0.10 24.55± 0.20 24.54± 0.17609.73 23.72± 0.07 24.05± 0.08 24.20± 0.21 24.57± 0.12 24.66± 0.16609.74 23.75± 0.06 24.11± 0.12 24.26± 0.10 24.73± 0.21 24.59± 0.12619.45 24.00± 0.11 24.34± 0.11 24.59± 0.17 24.87± 0.20 24.02± 0.07619.47 24.07± 0.09 24.29± 0.11 24.59± 0.19 25.04± 0.21 23.99± 0.10629.37 24.19± 0.11 24.48± 0.15 24.64± 0.19 24.68± 0.14 24.12± 0.10629.39 24.34± 0.18 24.56± 0.14 24.72± 0.15 24.37± 0.11 23.98± 0.08643.32 23.91± 0.07 . . . 23.97± 0.07 24.78± 0.14 24.77± 0.20643.33 23.87± 0.09 24.01± 0.08 24.15± 0.14 24.60± 0.14 24.66± 0.18

C26 V01 V02 V03603.42 24.50± 0.16 23.60± 0.06 23.43± 0.06 24.19± 0.14603.43 24.78± 0.21 23.73± 0.09 23.49± 0.04 24.03± 0.09609.73 24.12± 0.08 23.75± 0.27 23.29± 0.23 24.14± 0.13609.74 24.35± 0.18 23.77± 0.05 23.42± 0.08 24.03± 0.13619.45 23.89± 0.09 23.72± 0.06 23.37± 0.04 24.16± 0.09619.47 23.88± 0.10 23.70± 0.09 23.48± 0.06 24.15± 0.11629.37 24.01± 0.10 23.56± 0.06 23.53± 0.07 23.77± 0.09629.39 23.92± 0.09 23.48± 0.06 23.58± 0.08 23.83± 0.08643.32 24.26± 0.11 23.49± 0.04 23.69± 0.07 . . .643.33 24.43± 0.11 23.44± 0.09 23.65± 0.06 23.84± 0.09


MV = −2.76(±0.03) [log P− 1]− 4.22(±0.02), (3.3)

MI = −2.96(±0.02) [log P− 1]− 4.90(±0.01), (3.4)

(3.5)

These relations can be combined to obtain an equation for the reddening-

corrected distance modulus of a Cepheid (Freedman et al. 2001):

µ0 = W + 3.26(±0.01) [log P− 1] + 5.90(±0.01), (3.6)

where W = V − 2.45(V − I) is the reddening-free Wesenheit magnitude (Madore

1982).

3.5.2 Distance moduli

Before determining distance moduli from Equations 3.3-3.5, we must impose a

cut in period at the short end to avoid an incompleteness bias (see Appendix A

of Freedman et al. 2001). The completeness limits determined at the end of §3.4

imply that this cut must be applied around P = 20 d, resulting in the rejection of

Cepheids C01-C05. We also rejected Cepheids C07-C09 due to their rather poor

quality I band light curves. Thus, the final sample of Cepheids used for distance

determination consists of 18 variables, identified with an asterisk in the last column

of Table 3.4.

Figures 3.8 and 3.9 show the V and I band P-L relations of the final sample

of Cepheids. By fitting the P-L relations described in Equations 3.3-3.4, we

obtain apparent V and I band distance moduli of µV = 31.23 ± 0.08 mag

and µI = 30.96 ± 0.06 mag (internal errors only), and a mean color excess of

EV−I = 0.27± 0.03 mag. The application of Equation 3.5 results in an extinction-

corrected distance modulus of µ0 = 30.58 ± 0.06 mag (random uncertainty

only).


Fig. 3.8.— V-band Period-Luminosity relation for the selected Cepheids in our

sample (see Table 3.4 and §3.5.2). The solid line is the best fit to the fiducial

LMC P-L relation listed in Equation 3.3 and the dotted lines correspond to the

r.m.s. dispersion of the fit. The apparent distance modulus obtained from the fit is

31.23± 0.08 mag.


Fig. 3.9.— I-band Period-Luminosity relation for the selected Cepheids in our

sample (see Table 3.4 and §3.5.2). The solid line is the best fit to the fiducial

LMC P-L relation listed in Equation 3.4 and the dotted lines correspond to the

r.m.s. dispersion of the fit. The apparent distance modulus obtained from the fit is

30.96± 0.06 mag.


3.5.3 Metallicity correction

The measured value of µ0 must be corrected for the metallicity dependence of the

Cepheid P-L relation, using the following equation:

δµZ = γV I ([O/H]N2841 − [O/H]LMC), (3.7)

where γV I is the metallicity dependence index for the V and I filters, and

[O/H]gal = log(O/H)gal/ log(O/H)�. We adopt γV I = −0.2 ± 0.2 mag/dex, for

consistency with Freedman et al. (2001), although that value is lower than most

recent determinations of the effect (Kochanek 1997; Sasselov et al. 1997; Kennicutt

et al. 1998). The [O/H] value for the LMC is −0.4 dex (Kennicutt et al. 1998).

The [O/H] value for our field in NGC 2841 can be calculated using the ([O II]

λλ 3727)/Hβ and [O III] λλ 4959,5007)/Hβ line flux ratios listed in Table 3 of

Bresolin et al. (1999) for four HII regions located at galactocentric radii similar to

those spanned by our Cepheids. The sum of these two line flux ratios (known as

R23) can be turned into a value of [O/H] by using the appropriate equation from

Zaritsky et al. (1994). We find [O/H]N2841 = 0.4 ± 0.15 dex, which reflects the

scatter in the abundances of the four HII regions (±0.07) and the uncertainty in

the calibration of the metallicity-R23 relation for high abundances.

In conclusion, Equation 3.6 results in an overall correction of δµZ =

+0.16 ± 0.15 mag to our distance modulus, making it µ0,Z = 30.74 ± 0.23 mag.

This uncertainty includes several sources of error, which we list in the following

sub-section.

3.5.4 Error Budget

The error budget for our distance determination is listed in Table 3.7, and explained

in greater detail here. The internal error due to the dispersion in individual values

of µ0 is a small contribution to the total error, which is heavily dominated by

external sources of error. These are, in decreasing order of importance: the


Table 3.7. Error Budget for the Cepheid Distance to NGC 2841

Item Value (mag)

Dispersion in µ0 ±0.06

Metallicity correction ±0.15

LMC distance ±0.10

WFPC2 calibration ±0.07

Blending +0.10

Total +0.23,−0.20

metallicity dependence of the Cepheid P-L relation, the distance to the LMC, the

absolute calibration of WFPC2, contamination of the Cepheid magnitudes due to

unresolved blends, and the uncertainty in the reddening law of NGC 2841.

i. Metallicity correction: As stated in §3.5.3, the uncertainty in the adopted value

of the metallicity correction index γV I is ±0.2 mag/dex, and the uncertainty in

the difference in abundances between the LMC and NGC 2841 is ±0.15 dex. The

combination of these two uncertainties results in a contribution to the error budget

of ±0.15 mag.

ii. LMC Distance: The uncertainty in the distance to the LMC has been

recently summarized by Freedman et al. (2001). We have adopted µ0(LMC) =

18.50 ± 0.10 mag in order to maintain consistency with the Cepheid distances

presented in that paper. However, different distance indicators yield widely

different (and non-overlapping) estimates of the LMC distance modulus, ranging

from 18.3 to 18.65 mag (see Table 13 of Freedman et al. 2001).

iii. Blending: An additional source of uncertainty is the possible contamination

of our Cepheid magnitudes by nearby stars, physically unrelated to the variables,

but located at distances smaller than the resolution provided by the telescope and

detector. Mochejska et al. (2001) have studied this contamination by comparing


ground-based and HST images of long-period (P > 10d) Cepheids in M33. They

conclude that the median value of this effect on HST data for galaxies at 10–15 Mpc

is ∼ 7% in V and ∼ 12% in I. If these numbers were to apply to our Cepheids, our

W magnitudes would be biased by 5%, or 0.1 mag. We take this value to represent

a 1σ uncertainty due to the possible effects of blending.

iv. WFPC2 calibration: Freedman et al. (2001) have estimated the size of the

uncertainty related to the absolute photometric calibration of WFPC2 to be

±0.07 mag; this includes the uncertainties in the characterization of the zeropoints,

the color transformations, the camera gain ratios, and the effects of CTE.

v. Reddening law: The reddening-free Wesenheit magnitudes used in Equation

(5) were calculated using an assumed value of total-to-selective extinction

R ≡ AV /EB−V = 3.1 ≡ AV /EV−I = 2.45. If the interstellar medium of NGC 2841

were to follow a different extinction law than the ISM of the Milky Way, the

adoption of the standard value of R would introduce an additional systematic error

to our distance estimate. This issue is addressed in Chapter 4, where NICMOS H

band observations of extragalactic Cepheids in a dozen galaxies are used to show

that extinction corrections determined from either V and I data or from V and H

data, using the standard extinction law, are consistent with each other. Thus, the

assumption of a standard reddening law is a valid one, and does not introduce a

significant source of error.

The aforementioned sources of error (i-iv) can be combined in quadrature to

arrive at a total external uncertainty in our metallicity-corrected true distance

modulus of +0.22,−0.19 mag. The addition of the internal error term (±0.06 mag)

increases the total uncertainty to +0.23,−0.20 mag, which we simplify as

±0.23 mag.

3.6 Discussion

NGC 2841 is one of eight galaxies with Cepheid distances associated with the Leo

Cloud & Spur, out of a total of 65 members listed in Tully (1988). Table 3.8 lists


Table 3.8. Galaxies with Cepheid Distances in the Leo Cloud & Spur

Name Cepheid R.A. Dec. Helioc. Super-galactic coord.

distance (J2000.0) cz X Y Z

(Mpc) (km/s) (Mpc)

NGC 2541 11.2 08:14:40.2 +49:03:42 559± 1 7.8 6.7 -4.4

NGC 2841 14.1 09:22:02.7 +50:58:36 638± 3 8.7 10.3 -3.9

NGC 3198 13.8 10:19:54.9 +45:32:59 663± 4 6.6 11.7 -3.2

NGC 3319 13.3 10:39:08.8 +41:41:16 739± 1 5.3 11.8 -2.9

NGC 3351 10.0 10:43:57.8 +11:42:14 778± 4 -0.6 8.9 -4.6

NGC 3368 10.5 10:46:45.7 +11:49:12 897± 4 -0.7 9.4 -4.7

NGC 3621 6.6 11:18:16.0 −32:48:42 727± 5 -4.8 3.3 -3.2

NGC 3627 10.1 11:20;15.0 +12:59:30 727± 3 -1.1 9.5 -3.2

some properties of those eight galaxies. All distances (except for the one derived

in this paper) are from Freedman et al. (2001). The mean velocity and dispersion

of the previously observed galaxies is 727 ± 96 km/s, while the average distance

(excluding the nearby NGC 3621) is 11.5± 0.6 Mpc. The small velocity dispersion

for this relatively spread out structure is somewhat surprising, but consistent

with bulk motion of the Leo Cloud. Kinematically, at a redshift of 638± 3 km/s,

NGC 2841 is clearly a member of the Leo Spur, and our derived distance of

14.1 ± 1.5 Mpc places it on the far side of this structure. Figure 3.10 shows the

location in super-galactic coordinates of NGC 2841 and other galaxies in the Leo

Cloud & Spur.

Given the Cepheid distance of 14.1 ± 1.5 Mpc derived in the previous

section, and the surface brightness profiles shown in Figure 5.1, we determine a

B = 25 mag/ut′′ isophotal radius of ∼ 40 kpc. Thus, NGC 2841 is an impressively

large disk galaxy, with a disk scale length about twice as large as that of

M31, a galaxy which shares many other properties. Furthermore, the values of


extinction-corrected effective radius, rie ∼ 6 kpc, and extinction-corrected effective

surface brightness, 〈µ〉ie ∼ 19.5 I mag/ut′′, place NGC 2841 in a relatively unique

position in the surface brightness – radius plane (see Figure 2 of de Jong & Lacey

2000).

3.7 Conclusions

We have discovered a total of 26 Cepheids and 3 other variables in the Sb spiral

galaxy NGC 2841, a member of the Leo Spur. We have applied fiducial OGLE

LMC V- and I-band Cepheid Period-Luminosity relations to a sub-sample of

18 Cepheids. We adopted an LMC distance of µ0(LMC)= 18.50 ± 0.10 mag,

and a metallicity dependence of γV I = −0.2 ± 0.2 mag/dex. Based on these

assumptions, we obtain a distance modulus of 30.74± 0.23 mag, corresponding to a

distance of 14.1± 1.5 Mpc. Our distance estimate is consistent with an association

of this galaxy to the Leo Spur. The mean reddening of the Cepheid sample is

EV−I = 0.27± 0.03 mag.


Fig. 3.10.— Distribution of Leo Cloud & Spur galaxies in super-galactic coordinates,

after Figure 5 of Tully & Fisher (1987). The star indicates the location of NGC 2841,

while filled symbols indicate the location of other galaxies with Cepheid distances.

Open circles indicate the location of other members of this structure, using data

from Tully (1988) suitably rescaled to agree with the Cepheid distances.


Chapter 4

Infrared observations of

extragalactic Cepheids

Abstract

This chapter presents near-infrared observations of extragalactic Cepheids obtained

with the Near Infrared Camera and Multi-Object Spectrometer on board the Hubble

Space Telescope. The variables are located in the galaxies IC 1613, IC 4182, M31,

M81, M101, NGC 925, NGC 1365, NGC 2090, NGC 3198, NGC 3621, NGC 4496A

and NGC 4536. All fields were observed in the F160W bandpass; additional images

were obtained in the F110W and F205W filters. Photometry was performed using

the DAOPHOT/ALLSTAR package.

Self-consistent distance moduli and color excesses were obtained by fitting

Period-Luminosity relations in the H, I and V bands. Our results support the

assumption of a standard reddening law adopted by the HST Key Project on the

Extragalactic Distance Scale.

Contains material from The Astrophysical Journal, volume 549, pages 721-744, “NICMOSObservations of Extragalactic Cepheids. I. Photometry Database and a Test of the StandardExtinction Law”, by L.M. Macri, D. Calzetti, W.L. Freedman, B.K. Gibson, J.A. Graham,J.P. Huchra, S.M.G. Hughes, B.F. Madore, J.R. Mould, S.E. Persson & P.B. Stetson.

143


4.1 Introduction

One of the most important legacies of the Hubble Space Telescope (HST) will

undoubtedly be its revolutionary increase in the number of Cepheid-based distances

to nearby galaxies. Two major projects, the HST Key Project on the Extragalactic

Distance Scale (Freedman et al. 2001) and the HST SN Ia Calibration Project

(Saha et al. 1999), as well as smaller collaborations have resulted in the discovery

of over 700 Cepheid variables and the determination of distances to 27 galaxies.

This number will continue to grow as the community continues to take advantage

of HST’s unparalleled ability to deliver high-resolution images of the crowded

spiral arms where Cepheids are located. The next generation of instruments to be

installed on board HST will increase its sensitivity and resolution and will extend

these observations to larger distances.

Most HST Cepheid observations have concentrated on obtaining data in the

V band (typically in eight to thirteen non-aliasing epochs) with some additional

I-band data, usually four to eight epochs. Although sparsely sampled, the I-band

light curves are important for several reasons. First, they provide confirmation of

the variables as Cepheids, since the V and I light curves should track each other,

with the latter displaying an amplitude of about half of that of the former. Second,

the V −I colors should be consistent with those of Cepheids in the instability strip.

Third, and most important, the I-band data provide the only means of correcting

the observed distance modulus µV for extinction through the relation

µ0 = µV −RV−IEV−I (4.1)

where RV−I = 2.45 is the adopted ratio of total-to-selective extinction for the

V -band (Cardelli et al. 1989) and EV−I is the mean color excess of the Cepheid

sample (§4.6 contains a calculation of the value of RV−I). This approach makes the

true distance modulus quite sensitive to both RV−I and EV−I . A better procedure

(Freedman & Madore 1990) involves fitting a standard extinction curve through

observed distance moduli at several wavelengths (usually B, V , R and I) and


extrapolating the fit to λ−1 = 0. This approach is less susceptible to uncertainties

in the individual observed distance moduli, and can also be used to test the

assumed reddening law.

As the HST Key Project on the Extragalactic Distance Scale started its final

cycle of observations, a subset of the team joined forces with colleagues outside

the group to extend the work further into the infrared. Our aim was to perform

random-phase near-IR photometry of a sample of Cepheids in fourteen galaxies and

to combine the new and existing observed distance moduli. Such a data set would

allow us to improve the derivation of true distance moduli, check the assumptions

behind Equation 4.1, and perhaps explore the effects of metallicity on the Cepheid

distance scale.

This chapter is organized as follows: §4.2 describes the observations and

the data reduction pipeline; §4.3 delineates the steps followed to obtain accurate

and precise photometry in our fields; §4.4 presents the Cepheid sample, period-

luminosity relations, and observed distance moduli; §4.5 discusses the possible

effects of blending in an inner field of M101; and §4.6 studies the correlation

between color excesses and its relation to the extinction law.

4.2 Observations and Data Reduction

4.2.1 Observations

The HST Near Infrared Camera and Multi-Object Spectrograph (NICMOS)

instrument (Thompson 1993), with its high spatial resolution and low thermal

background, was uniquely suited to carry out the observations required by our

program. NICMOS contains three cameras (named 1, 2 and 3) which illuminate

Rockwell 256 × 256 HgCdTe arrays. The cameras have different pixel scales

(0.′′043, 0.′′076 and 0.′′2, respectively), resulting in fields-of-view of 11′′, 19′′ and 51′′,

respectively. Since Cepheids are scattered throughout the spiral arms of the target

galaxies, we chose Camera 2 (hereafter NIC2) as it provided the best trade-off


between resolution and coverage.

The fourteen galaxies selected for this study are listed in Table 4.1. The

selection of specific fields within each galaxy was based on known positions and

periods of Cepheids, in order to maximize the number of variables and our coverage

of the Period-Luminosity plane. We observed two fields in M101, matching those

observed by Stetson et al. (1998) and Kelson et al. (1996). These will be hereafter

referred to as “M101-Inner” and “M101-Outer.”

The observations followed the standard SPIRAL-DITH pattern, with two to

four pointings depending on the field and filter used. Exposure times for each

pointing ranged from 16s for M31 to 640s for the most distant galaxies. Some

of the latter fields were imaged multiple times in order to increase measurement

precision.

4.2.2 Data reduction

Once NICMOS had been installed on board HST, several instrument characteristics

were discovered. One is a variable additive bias (called “pedestal”) introduced

during array reset, which has a different amplitude in each of the four quadrants

that make up the array. Because HgCdTe arrays do not have overscan regions, it

is impossible to automatically remove this effect in the STScI pipeline. Therefore,

the bias offset is modulated by the flat field and appears as an inverse flat-field

pattern in the final image. A second characteristic of the detectors is a noiseless

signal gradient (called “shading”), which is a temperature- and pixel- dependent

bias that changes in the direction of pixel clocking during read-out. This presented

a problem because the original implementation of the STScI processing pipeline

did not use temperature-dependent darks. The combination of “pedestal” and

“shading,” resulted in images with prominent spurious features. The level of

photometric precision required by our program made it necessary to remove these

instrumental effects. We did so by retrieving the raw frames from the STScI

Archive and reprocessing them as described below.


Table 4.1. Log of observations

Galaxy Number Filter Exp. time

name of fields /field (s)

IC1613 6 F110W 32

F160W 128

IC4182 4 F160W 1152

M31 18 F110W 46

F160W 89

F205W 285

M81 2 F160W 1280

M101 8 F110W 512

F160W 2048

N0925 2 F160W 2560

N1365 2 F160W 5120

N2090 2 F160W 2560

N2403 2 F160W 1280

N3198 2 F160W 2560

N3621 1 F160W 5120

N4496A 1 F160W 10240

N4536 1 F160W 10240

N5253 5 F160W 973


The reprocessing of the data was performed using the NICMOS pipeline

present in IRAF/STSDAS with some modifications. First, temperature-dependent

dark frames were generated and used when running the first part of the pipeline (a

program called calnicA). This removed the “shading” effect.

The “pedestal” effect was corrected using a program outside of the standard

pipeline, courtesy of R. van der Marel (STScI). The program read in an image

created by calnicA, removed the flat-fielding imposed by it, and executed a loop to

identify the pedestal. The pedestal is in fact measured by exploiting the property

that a flat-fielded bias imparts fluctuations on the background of the final image.

The fluctuations reach a minimum when the pedestal is removed completely. Once

a robust minimum was found in each of the quadrants, the best-fit pedestals were

removed. Lastly, the image was flat-fielded and written to disk.

Having obtained images with proper zero, dark and flat-field corrections, the

second part of the pipeline (calnicB) was run to combine the dithered pointings

of each target field and produce a final mosaic. In addition, we used the dither

package to produce higher-resolution mosaics of the M101 fields in the F160W

band. This was possible thanks to the existence of four pointings per field in that

galaxy.

4.3 Photometry

4.3.1 Technique

The mosaics were analyzed with the DAOPHOT II/ ALLSTAR software package

(Stetson 1994). Objects were detected with the FIND routine set to a threshold of

3σ above sky, and aperture photometry was carried out with the PHOT routine,

using different apertures and sky annuli for each filter (see below for details).

Point-spread functions were determined by the PSF routine for each field using

bright, isolated stars present in the frame. After an initial ALLSTAR run, the

star-subtracted frame was put through the FIND algorithm once more to pick up


any additional 3σ objects. Object lists were merged and ALLSTAR was run one

last time on the original image.

PSF magnitudes were brought onto a consistent aperture magnitude system

using DAOGROW (see Stetson 1990 for details; only a short summary is presented

here). Aperture photometry was obtained for PSF stars in each field (∼ 450 in

total) using a monotonically increasing set of radii. DAOGROW then solved for a

function representing the “growth curve”, i.e., the change in aperture magnitude

as a function of radius. The cumulative growth curves for the F110W, F160W and

F205W bands are shown in Figure 4.1. Other programs in the DAOPHOT suite

used this information to transform PSF magnitudes to aperture magnitudes for

objects of interest in each frame.

4.3.2 Absolute photometric calibrations

The NICMOS primary standards are G191-B2B, a white dwarf, and P330-E, a

solar analog. These two stars provide absolute calibration in the white dwarf and

solar analog scales, respectively. Since Cepheids have colors similar to those of

solar analog stars, we used P330-E for the determination of magnitude zeropoints.

We used NICMOS observations of G191-B2B, P330-E, and P117-D (another

solar analog standard) for the determination of color terms. Ground-based JHK

photometry for NICMOS standards comes from Persson et al. (1998).

Magnitude zeropoints

Our definition of J , H and K zeropoints is based on different apertures and sky

annuli for each band, to match the noticeable increase in FWHM as a function of

wavelength. Table 4.2 lists our choices of aperture radius and inner and outer sky

annuli for each of the three bandpasses. In the case of the drizzled M101 F160W

images, which have twice the spatial resolution, all radii were increased by a factor

of two in pixel units so they would subtend the same angular size.

Marcia Rieke kindly provided us with synthetic (TinyTim) stellar images as


Fig. 4.1.— Cumulative growth curves for the F110W, F160W and F205W bands

derived by DAOGROW. Aperture and inner and outer sky radii are listed in each

panel and in Table 4.2. One pixel equals 0.′′075.

Table 4.2. Photometry apertures

Filter Aperture Sky annulus Magnitude

pix ′′ pix ′′ zeropoint

F110W 7 0.53 14–20 1.05–1.50 22.141 (008)

F160W 10 0.75 20–30 1.50–2.25 21.617 (006)

F205W 14 1.05 30–40 2.25–3.00 21.831 (008)


well as NICMOS observations of P330-E, which we used to derive the magnitude

zeropoints for our choices of aperture and sky annuli. First, we computed the ratio

of TinyTim counts to observed NICMOS count rates for P330-E as a function of

aperture radius. We found this ratio to be constant, at the 0.05%, 0.03%, and

1.77% levels for F110W, F160W and F205W, respectively, over a large range

in radius (5–25 pixels). This confirmed that the TinyTim image was a good

representation of the actual system PSF.

We then re-scaled the TinyTim image (in arbitrary units) to match the actual

mean observed count rate of P330-E; this produced a synthetic image of P330-E

that could be used to perform aperture measurements on a “perfect” image free

of defects, cosmic rays, or any other source of scatter found in real images. Next,

we ran DAOPHOT’s PHOT routine on the synthetic P330-E images using the

same aperture and sky annuli as for the Cepheid photometry. DAOPHOT quoted

measurement errors of 0.004 mag for these magnitudes. Lastly, we combined

the Persson et al. (1998) standard magnitudes and the DAOPHOT NICMOS

instrumental magnitudes for P330-E to arrive at our magnitude zeropoints, listed

in Table 4.2.

Color terms

Since the NICMOS filters are not exact matches to the standard filters, color term

corrections had to be determined. Synthetic spectra of the NICMOS standards

were created based on Kurucz’ latest solar-abundance models. These model spectra

were convolved with two sets of transmission curves: one contained the NICMOS

filter responses plus the quantum efficiency of camera 2, while the other was based

on standard filter responses plus an atmospheric transmission curve. This allowed

us to predict F110W, F160W, F205W, J , H and K magnitudes for the NICMOS

standards. We then compared our results with published values (Persson et al.

1998) and found negligible offsets of 0.002 ± 0.003 mag for J and H and a small

offset of 0.022± 0.001 mag for K.

We used the same model atmospheres and transmission curves described


above to generate synthetic spectra for a variety of spectral types (F, G and

K) and luminosity classes (I and V). We compared the values of 〈F110W − J〉and 〈F160W − H〉 as a function of 〈F110W − F160W 〉 as well as the values of

〈F205W −K〉 as a function of 〈F160W − F205W 〉. We found

〈F110W − J〉 = 0.013(±0.006) + 0.315(±0.011) 〈F110W − F160W 〉 (4.2)

〈F160W −H〉 = 0.003(±0.002) + 0.071(±0.005) 〈F110W − F160W 〉 (4.3)

〈F205W −K〉 = 0.053(±0.008)− 0.556(±0.085) 〈F160W − F205W 〉 (4.4)

where 〈F110W − F160W 〉 and 〈F160W − F205W 〉 are the mean instrumental

colors of the star to be corrected. These formulae are suitable for correcting our

data since our F110W, F160W and F205W observations were taken within minutes

of each other.

The mean values of the corrections were 0.23 ± 0.11 mag for 〈F110W − J〉,0.05± 0.02 mag for 〈F160W −H〉 and −0.04± 0.08 mag for 〈F205W −K〉. Note

that an exact correction for 〈F160W − H〉 was only applied to the stars in the

IC 1613, M31, M101-Inner and M101-Outer fields. The other fields were observed

only in F160W and therefore only an average H-band correction of 0.03 mag could

be applied, based on a mean Cepheid 〈F110W − F160W 〉 color of 0.46 mag.

4.3.3 Photometric recovery tests

The dense nature of most of our fields makes it difficult to obtain accurate

values of the local sky around each object and to perform unbiased magnitude

measurements. This effect is commonly referred to as “crowding”. In order to

characterize its impact on our measurements, we injected artificial stars into each

field and compared their input magnitudes with the recovered values. We used

the point-spread functions derived for each field to generate the artificial stars,

which were placed randomly across each field. The objects spanned a magnitude

range including that encompassed by the variables. In the case of the M101


fields, we injected artificial stars into the original-resolution mosaics as well as the

higher-resolution ones created by drizzling. We re-ran our photometry programs on

the new images and searched the new star lists to locate the artificial stars.

The results of the tests are presented in Figure 4.2 and summarized in

Table 4.3. Figure 4.2a contains plots of the difference between input and recovered

magnitudes as a function of magnitude for each field. The bottom panel of

Figure 4.2b shows the strong correlation that exists between the crowding bias

and the stellar density of each field. The effect ranges from 0.01 mag for the least

crowded fields to 0.09 mag for the denser ones. All magnitudes were corrected for

this effect.

In addition to these “crowding” tests, we also undertook simulations to

estimate the contamination of Cepheid magnitudes by unresolved nearby stars.

These “blending” tests are presented in §4.5.

4.3.4 Photometry checks

We performed several internal and external photometry checks to ensure the

accuracy and precision of our magnitudes. We tested our aperture correction

technique by comparing our corrected magnitudes against “standard” aperture

magnitudes for stars in the IC 1613 fields. We found no significant difference

(< 0.01 mag) between the two sets. We also tested the repeatability of our PSF

photometry by comparing magnitudes of objects that appeared twice in our data

set, due to some overlap between different fields in M81 and M101. We found that

the magnitude differences were consistent with the reported uncertainties.

We also performed an external photometry check by comparing HST and

ground-based photometry of bright, isolated stars in our IC 1613 fields. The

ground-based photometry was obtained at the Las Campanas 2.5-m du Pont

telescope using its infrared camera (Persson et al. 1992) over fourteen nights

between November 1993 and November 1996. Photometry was conducted using

DAOPHOT II/ALLSTAR and DAOGROW (as described in §4.3.1) on 19 stars


Fig. 4.2a.— Results of the photometric recovery tests described in §4.3.3. Each

panel represents one of the field/filter combinations which yielded useful data. In-

put magnitudes are plotted on the ordinate, while the abscissa shows differences

between the input and the recovered magnitudes. Averages over 0.25 mag are plot-

ted using filled circles. The dashed vertical lines mark the faint end of the Cepheid

distribution.


Fig. 4.2b.— Results of the photometric recovery tests described in §4.3.3. Corre-

lation between stellar density and crowding bias; filled circles represent the data

found in Table 4.3. The solid line is derived from a linear least-squares fit to the

data.


Table 4.3. Results of the photometric recovery tests

Field Offset Log (N/

(mag) sq pix)

IC 1613 0.007±0.005 -2.93

IC 4182 0.013±0.006 -2.28

M31 0.009±0.007 -2.19

M81 0.085±0.043 -1.49

M101-Inner (o) 0.069±0.033 -1.55

M101-Inner (d) 0.030±0.033 -2.16

M101-Outer (o) 0.026±0.019 -2.37

M101-Outer (d) 0.022±0.028 -2.97

NGC 925 0.084±0.032 -1.54

NGC 1365 0.093±0.043 -1.49

NGC 2090 0.024±0.029 -2.05

NGC 3198 0.073±0.017 -1.56

NGC 3621 0.111±0.034 -1.55

NGC 4496A 0.077±0.039 -1.60

NGC 4536 0.083±0.031 -1.57

Note:(d): drizzled; (o): original


common to our ground-based and HST images. Table 4.4 lists their magnitudes

and Figure 4.3 shows a comparison of the two systems; the mean offset is

0.011± 0.061 mag, in the sense that the HST magnitudes are marginally brighter.

Unfortunately, there was no published J- or K-band photometry available for stars

in any of our fields, so we were unable to check our transformation of NICMOS

F110W and F205W magnitudes.

4.4 The Cepheid sample

4.4.1 Sample selection and identification

As described in §4.2.1, we targeted specific fields within each galaxy in order to

maximize the number of variables and our coverage of the Period-Luminosity plane.

We selected the variables in each galaxy based on published catalogs, applying

the following selection criteria: i) existence of both V and I photometry; ii) range

in color of 0.5 < V −I < 1.75; iii) periods between 10 days and the width of

the observing window (applicable to Cepheids discovered with HST). Our fields

contained 93 variables that met these criteria.

Cepheids in M31 and IC1613 were identified by visual inspection, using finding

charts created from ground-based images. These fields are sparse enough that

identifications did not present a problem, and twelve variables were located. In the

case of the other galaxies, identifications followed a more rigorous process. First,

the FITS header coordinates for the center of the mosaic were used to obtain a

rough alignment and rotation relative to an optical image (from WFPC2 in most

cases). Next, bright stars present in both the optical and the near-IR images were

identified and used as input to the IRAF task geomap to determine the geometric

transformations between the images. Lastly, the task geoxytran was used to predict

the coordinates of 81 variables.

The DAOPHOT star lists generated in §4.3.1 were used to locate the object

nearest to the predicted position of the variables. In general, counterparts were


Table 4.4. Secondary standards in the IC 1613 field

Star R.A. Dec. HST LCO

(2000.0) J H H

01 01:04:43.101 +02:05:18.31 18.43± 0.14 17.67± 0.02 17.67± 0.06

02 01:04:43.775 +02:05:21.84 19.82± 0.19 19.14± 0.08 19.23± 0.07

03 01:04:43.898 +02:05:25.48 · · · 18.85± 0.05 18.84± 0.03

04 01:04:43.997 +02:05:23.95 18.05± 0.05 17.23± 0.02 17.31± 0.10

05 01:04:44.095 +02:05:25.68 · · · 19.21± 0.08 19.23± 0.06

06 01:04:44.330 +02:05:33.52 · · · 18.97± 0.05 18.92± 0.04

07 01:04:44.492 +02:05:25.27 · · · 18.78± 0.04 18.71± 0.05

08 01:04:44.599 +02:05:18.94 · · · 18.91± 0.10 19.00± 0.08

19 01:04:47.897 +02:05:09.59 19.35± 0.17 18.55± 0.08 18.56± 0.04

10 01:04:48.192 +02:05:08.14 19.27± 0.17 18.53± 0.04 18.62± 0.01

11 01:04:48.273 +02:05:06.92 18.29± 0.10 17.46± 0.02 17.38± 0.03

12 01:04:50.808 +02:04:41.49 · · · 19.91± 0.11 19.98± 0.03

13 01:04:51.006 +02:04:47.48 20.41± 0.32 19.64± 0.10 19.59± 0.01

14 01:04:51.142 +02:05:28.80 19.90± 0.23 19.37± 0.07 19.36± 0.08

15 01:04:51.368 +02:05:29.27 · · · 19.74± 0.07 19.78± 0.07

16 01:04:51.478 +02:05:32.47 19.75± 0.23 19.01± 0.05 18.99± 0.16

17 01:04:51.553 +02:05:19.08 · · · 19.01± 0.07 18.98± 0.08

18 01:04:51.728 +02:05:36.74 19.83± 0.25 19.11± 0.06 19.05± 0.09

19 01:04:51.732 +02:05:21.78 · · · 19.45± 0.06 19.55± 0.07

Mean ∆H (LCO-HST): +0.011±0.061


Fig. 4.3.— Comparison of ground-based and HST H-band photometry for bright,

isolated stars in the IC 1613 field listed in Table 4.4. A mean offset of 0.011 ±0.061 mag is indicated by solid and dashed lines.


found within one pixel of their predicted location. Figure 4.4 shows the distribution

of differences between the predicted and actual positions. Based on this figure,

we decided to reject any candidate located more than 1.5 pixels (0.′′11) away

from its predicted position. This process resulted in the rejection of 11 possible

counterparts.

In order to further discriminate between real counterparts and field

contaminants, we plotted V −H vs. V −I colors for all remaining candidates.

Cepheids follow a vector that is a combination of two closely degenerate quantities:

the reddening trajectory and the color-color relation for these bands. Several

objects deviate significantly from the rest of the sample; we suspect these are

variables which are blended with unresolved red or blue companions. We performed

a least-squares fit to the sample, using a fixed slope of V −H/V −I= 1.71 (the

average of the reddening and color-color slopes). The color-color diagram is shown

in Figure 4.5a; the solid line indicates the fixed-slope color-color relation fitted

to the points, and the dashed lines correspond to twice the r.m.s. deviation, or

0.46 mag. We rejected twelve possible counterparts that fell outside of the dashed

boundaries.

Figure 4.5b shows a histogram of the deviations from the best-fit line. The

asymmetric distribution of the outliers is to be expected, since we are more likely

to detect a Cepheid that is blended with a red (i.e., IR-bright) field star than with

a blue (i.e., IR-faint) one. Note that this color-color rejection process is insensitive

to blends of Cepheids with stars of similar colors, a point to which we will return

later.

In conclusion, our final sample consists of 70 variables (93 original candidates

– 11 astrometric rejections – 12 color-color rejections). Finding charts for fields

containing at least one variable are shown in Figures 4.6a-4.6f, while Figures 4.7a-

4.7b contain close-up views of each object. Table 4.5 presents periods and

magnitudes for the final Cepheid sample. We include in this Table the previously-

published optical magnitudes of the variables. There are minor variations in the V

and I zeropoints used in the different sources of optical photometry, reflecting the


Fig. 4.4.— Histogram of radial distances between predicted positions of our variables

and the location of the nearest object in the frame. We rejected 11 candidates whose

distance between these two positions was larger than 1.5 pixels.


Fig. 4.5a.— Color-color diagram for the 82 candidates which passed the astrometry

test. Filled and open symbols indicate the candidates that passed and failed this

test, respectively. The solid line is a least-squares fit to a color/color relation with

a slope of 1.71 (see text for details).


Fig. 4.5b.— Histogram of the deviations from the best-fit line of Figure 4.5a. We

rejected 12 candidates with deviations larger than twice the rms.


Fig. 4.6a.— Images of all fields that contain at least one variable. The imagesare full-frame F160W mosaics, spanning ∼ 24′′. The galaxy name and the STScI-assigned mosaic identification are displayed in each image. Small circles indicatethe location of the Cepheids used in this work. The variable names match those ofTable 4.5.










Fig. 4.6f.— continued.


Fig. 4.7a.— Individual finding charts for all Cepheids used in this work. Each box is

38 pixels or ∼ 3′′ on a side. Cepheids are marked by a small circle. The designation

of each star is shown in the upper-left corner of each box.




Table 4.5. Cepheid magnitudes

Field Var. P H J K V I

IC 1613 V01 5.6 19.66 (11) 20.25 (24) · · · 20.79 20.14 [1]V14 5.1 19.49 (07) 19.81 (19) · · · 20.89 20.12 [1]V34 8.5 19.01 (06) 19.54 (14) · · · 20.74 20.03 [1]V37 12.4 18.60 (04) 18.88 (08) · · · 20.27 19.42 [1]

IC 4182 C3V12 36.3 20.51 (05) · · · · · · 22.36 21.57 [2]C4V11 42.0 20.44 (11) · · · · · · 22.33 21.40 [2]

M31-F1 H17 18.8 18.01 (06) 19.19 (09) 17.89 (04) 19.80 (10) 19.00 (10) [3]V120 44.9 16.83 (05) 17.13 (06) 16.75 (03) 19.50 (10) 18.20 (10) [3]

-F3 H29 19.5 17.93 (05) 18.29 (08) 17.87 (03) 20.60 (10) 19.45 (10) [3]V404 17.4 18.13 (07) 18.63 (12) 18.11 (06) 20.80 (10) 19.60 (10) [3]V427 11.3 18.88 (06) 19.18 (11) 18.81 (04) 21.00 (10) 20.05 (10) [3]V423 14.4 17.90 (07) 18.74 (12) 17.82 (04) 21.00 (10) 19.65 (10) [3]

-F4 V08 9.6 18.82 (05) 19.24 (07) 18.80 (06) 20.40 (10) 19.70 (10) [3]V09 8.5 19.42 (08) 20.19 (22) 19.33 (06) 20.60 (10) 20.00 (10) [3]

M81 C06 40.8 20.33 (08) · · · · · · 22.26 21.36 [4]C07 27.2 20.77 (09) · · · · · · 22.60 21.69 [4]C10 12.8 21.69 (08) · · · · · · 22.91 22.29 [4]C11 47.2 20.05 (10) · · · · · · 22.46 21.30 [4]C13 18.6 21.73 (08) · · · · · · 23.56 22.75 [4]C15 11.2 21.99 (12) · · · · · · 23.84 22.96 [4]

M101- C051 13.0 22.78 (15) 23.39 (32) · · · 24.89 (03) 23.96 (05) [5]Inner C161 23.9 21.78 (05) 22.49 (20) · · · 24.36 (02) 23.33 (03) [5]

C172 15.4 22.93 (09) 23.46 (42) · · · 24.92 (02) 23.84 (04) [5]C186 27.8 21.87 (05) 22.55 (22) · · · 25.14 (03) 23.55 (04) [5]C192 73.8 20.89 (03) 21.19 (12) · · · 23.00 (02) 21.89 (02) [5]C194 44.8 21.47 (04) 22.27 (16) · · · 24.26 (02) 22.93 (03) [5]C205 26.1 22.02 (05) 22.33 (24) · · · 23.56 (01) 22.80 (03) [5]C212 29.4 21.91 (05) 22.18 (19) · · · 24.09 (01) 23.04 (01) [5]

M101- C01 58.5 21.14 (04) 21.55 (09) · · · 23.83 (07) 22.42 (09) [6]Outer C06 45.8 21.37 (06) 21.81 (13) · · · 23.47 (07) 22.62 (13) [6]

C07 43.0 22.04 (07) 22.42 (18) · · · 23.75 (08) 22.84 (08) [6]C08 41.0 21.69 (07) 22.45 (41) · · · 23.88 (08) 23.00 (09) [6]C10 37.6 22.18 (05) 22.65 (12) · · · 24.01 (08) 22.94 (16) [6]C20 42.5 21.91 (06) 22.61 (16) · · · 24.11 (07) 22.93 (08) [6]C24 23.5 22.46 (09) 22.72 (15) · · · 24.25 (09) 23.55 (09) [6]C26 17.7 23.03 (19) 23.33 (18) · · · 24.66 (09) 23.82 (09) [6]

NGC 925 C06 43.2 22.48 (09) · · · · · · 24.55 (10) 23.47 (10) [7]C08 37.3 22.23 (07) · · · · · · 24.65 (10) 23.63 (10) [7]C09 35.1 22.36 (09) · · · · · · 24.79 (10) 23.74 (10) [7]C13 30.4 22.60 (15) · · · · · · 24.64 (10) 23.55 (10) [7]C17 28.5 23.14 (10) · · · · · · 25.14 (10) 23.94 (10) [7]C24 25.3 22.52 (09) · · · · · · 25.11 (10) 23.94 (10) [7]C26 23.7 22.83 (10) · · · · · · 25.02 (10) 23.98 (10) [7]C33 21.5 22.86 (11) · · · · · · 24.54 (10) 23.92 (10) [7]



Field Var. P H J K V I

C41 18.3 23.47 (26) · · · · · · 25.55 (10) 24.59 (10) [7]C50 16.4 23.45 (14) · · · · · · 25.01 (10) 24.41 (10) [7]

NGC 1365 C01 60.0 23.40 (24) · · · · · · 25.66 (07) 24.40 (07) [8]C04 55.0 22.77 (11) · · · · · · 25.52 (06) 24.29 (06) [8]C06 47.0 23.84 (31) · · · · · · 26.08 (09) 25.19 (09) [8]

NGC 2090 C03 48.8 23.25 (16) · · · · · · 25.07 24.07 [9]C18 23.7 23.70 (21) · · · · · · 25.61 24.69 [9]C21 18.5 23.81 (20) · · · · · · 25.60 24.78 [9]C23 17.3 23.82 (22) · · · · · · 25.51 24.84 [9]

NGC 3198 C03 26.4 23.03 (12) · · · · · · 25.32 (12) 24.44 (09) [10]C06 18.7 23.71 (22) · · · · · · 25.82 (09) 25.05 (12) [10]C10 45.1 22.68 (10) · · · · · · 24.97 (10) 23.98 (11) [10]

NGC 3621 C16 31.2 21.99 (12) · · · · · · 24.50 (03) 23.28 (04) [11]C17 28.3 21.86 (07) · · · · · · 23.89 (03) 22.84 (04) [11]C32 23.5 22.00 (14) · · · · · · 24.11 (04) 23.26 (08) [11]C35 22.8 22.78 (10) · · · · · · 24.77 (03) 23.60 (05) [11]C66 11.9 22.87 (10) · · · · · · 25.57 (06) 24.23 (08) [11]

NGC 4496A C44 36.1 23.89 (15) · · · · · · 25.65 (03) 24.61 (05) [12]C46 25.1 24.36 (31) · · · · · · 25.72 (02) 24.97 (05) [12]C47 38.5 23.54 (11) · · · · · · 25.50 (02) 24.67 (05) [12]C50 46.2 23.13 (07) · · · · · · 25.41 (02) 24.28 (03) [12]C59 22.2 24.20 (19) · · · · · · 25.98 (03) 24.95 (08) [12]C60 33.8 23.56 (16) · · · · · · 25.04 (02) 24.37 (04) [12]C67 39.3 23.68 (12) · · · · · · 26.02 (03) 24.82 (05) [12]

NGC 4536 C2-V4 28.7 24.18 (18) · · · · · · 25.81 (18) 25.06 (15) [13]C2-V9 58.0 23.50 (11) · · · · · · 25.39 (12) 24.45 (11) [13]

References. — [1]: Freedman (1988); [2]: Saha et al. (1994); [3]: Madore (priv. comm.);[4]: Freedman et al. (1994) [5]: Stetson et al. (1998); [6]: Kelson et al. (1996); [7]:Silbermann et al. (1996); [8]: Silbermann et al. (1999); [9]: Phelps et al. (1998); [10]:Kelson et al. (1999); [11]: Rawson et al. (1997); [12]: Gibson et al. (2000); [13]: Saha etal. (1996)


evolution in our knowledge of the HST calibration from 1994 to the present (see

Mould et al. 2000 for details). For our target galaxies, the mean difference between

the various calibrations used in the published papers and the current calibration

(Stetson 1998) amounts to −0.03 ± 0.03 mag in V, −0.05 ± 0.04 mag in I and

+0.02± 0.02 mag in V −I.

4.4.2 Period-Luminosity relations

The method used to derive observed distance moduli is the same as that used by

the HST Key Project on the Extragalactic Distance Scale (see Freedman et al.

2001, for details). It is based on the Period-Luminosity relations of individually

de-reddened LMC Cepheids from Udalski et al. (1999) (V and I) and Persson et

al. (2001) (J , H and K), scaled to an assumed true distance modulus of µ0,LMC =

18.50±0.10 mag (total uncertainty). The relations are:

MV = −2.76(±0.03) [log P− 1]− 4.22(±0.02), (4.5)

MI = −2.96(±0.02) [log P− 1]− 4.90(±0.01), (4.6)

MH = −3.23(±0.04) [log P− 1]− 5.66(±0.05), (4.7)

MJ = −3.15(±0.05) [log P− 1]− 5.32(±0.06), (4.8)

MK = −3.26(±0.04) [log P− 1]− 5.73(±0.05). (4.9)

In fitting the data from each field and filter, we fix the slope to the one

given in the corresponding equation and obtain a magnitude shift by minimizing

the unweighted rms dispersion. The resulting magnitude shifts are converted to

observed distance moduli by subtracting the relevant magnitude zeropoint.

4.4.3 Observed distance moduli

Period-Luminosity relations were constructed for each field and filter using the

data listed in Table 4.5 and fitted using Equations 4.5-4.9. Figures 4.8a-4.8f show


our near-IR P-L relations, while Figures 4.9a-4.9e present the optical ones. In

each panel, the solid line represents the results of the fitting process described in

§4.4.2 while the dashed lines indicate the rms uncertainty of the fit. Fit results are

displayed in each panel and listed in Tables 4.6 and 4.7.

We also tabulate in Table 4.6 the published distance moduli for these galaxies

(mostly from Table 4 of Freedman et al. 2001), determined from substantially

larger samples of variables and using the Stetson (1998) zeropoints. The optical

distance moduli determined from our smaller samples should not take precedence

over the above values.

4.5 Blending effects in M101 Inner

As mentioned in the introduction, one of the motivations of this project was

to further study the metallicity dependence of the Cepheid Period-Luminosity

relation. Our data can contribute to these studies on two ways: first, a global test

of the metallicity dependence can be performed by analyzing the apparent distance

moduli of all galaxies; second, a differential test of the effect can be performed by

analyzing the distance moduli to two regions of the same galaxy, provided they

differ significantly in abundance. The first approach was undertaken by Kochanek

(1997), while the second one was followed by Freedman & Madore (1990) in M31

and by Kennicutt et al. (1998) in M101. The differential test is a challenging one,

because the Inner field of M101 deviates substantially from other Key Project fields

in terms of surface brightness and stellar density.

Our near-infrared distance moduli to the inner and outer fields in M101

exhibit large differences: ∆µH = 0.46 ± 0.12 mag and ∆µJ = 0.37 ± 0.12 mag. If

taken at face value, they imply a very large metallicity dependence, of the order

of 0.6 mag/dex. However, other observational effects could be contributing to

the observed differences in distance moduli. One of them is “blending”, or the

contamination of Cepheid fluxes by nearby stars, not physically associated with the

variables, that fall within the NICMOS seeing disk and cannot be resolved. This


Fig. 4.8a.— Near-infrared Period-Luminosity relations for all field/filter combina-

tions. Field name, observed distance modulus and its uncertainty appear in the

top-left corner of each panel. Solid lines indicate fitting results while dashed ones

indicate the rms uncertainties.










Fig. 4.8f.— continued.


Fig. 4.9a.— Optical Period-Luminosity relations for all field/filter combinations.

Field name, observed distance modulus and its uncertainty appear in the top-left

corner of each panel. Solid lines indicate fitting results while dashed ones indicate

the rms uncertainties.










Tab

le4.

6.O

bse

rved

H,I

andV

dis

tance

moduli

Fie

ldT

his

wor

kP

ublish

ed

µH

µI

µV

NµI

µV

NR

ef.

IC16

1324

.43

(08)

24.4

4(1

3)24

.53

(13)

424

.39

(09)

24.5

0(0

9)9

[1]

IC41

8228

.05

(07)

28.1

4(0

1)28

.20

(07)

228

.33

(06)

28.3

7(0

7)27

[2]

M31

24.5

4(0

8)24

.94

(09)

25.2

3(1

7)9

24.7

6(0

5)25

.01

(07)

37[2

]

M81

27.9

1(0

8)28

.02

(13)

28.1

5(1

7)6

28.0

3(0

7)28

.22

(09)

17[2

]

M10

1-In

ner

29.0

4(0

8)29

.37

(10)

29.7

1(1

8)8

29.3

1(0

6)29

.49

(08)

61[3

]

M10

1-O

ute

r29

.45

(08)

29.5

8(0

9)29

.77

(09)

829

.33

(05)

29.4

6(0

7)25

[2]

NG

C09

2529

.84

(08)

30.0

8(0

5)30

.30

(10)

1030

.12

(03)

30.3

3(0

4)72

[2]

NG

C13

6531

.36

(27)

31.6

9(2

1)31

.99

(11)

331

.49

(04)

31.6

9(0

5)47

[2]

NG

C20

9030

.57

(20)

30.6

6(1

3)30

.75

(18)

430

.54

(04)

30.7

1(0

5)30

[2]

NG

C31

9830

.25

(12)

30.7

2(0

7)30

.83

(09)

330

.89

(04)

31.0

4(0

5)36

[2]

NG

C36

2129

.09

(15)

29.3

8(1

0)29

.75

(16)

529

.61

(05)

29.9

7(0

7)59

[2]

NG

C44

96A

31.1

2(0

7)31

.12

(09)

31.2

9(1

4)7

31.0

0(0

3)31

.14

(03)

94[2

]

NG

C45

3631

.47

(15)

31.4

6(1

5)31

.51

(21)

231

.06

(04)

31.2

4(0

4)35

[2]

Ref

eren

ces.

—[1

]:F

reed

man

(198

8);

[2]:F

reed

man

etal

.(2

001)

;[3

]:Ste

tson

etal

.(1

998)

.


Table 4.7. Observed J and K distance moduli

Field Filter µ N

IC 1613 J 24.53 (12) 4

M31 J 24.77 (13) 9

M31 K 24.55 (08) 9

M101-Inner J 29.19 (08) 8

M101-Outer J 29.53 (03) 8

Fig. 4.10.— Simulated M101 Inner fields, based on our observations of M31 (right)

and M81 (left) fields. These were used to study the effects of blending in our M101

Inner Cepheids.


effect has been the subject of a recent investigation in the optical by Mochejska et

al. (2000).

One way to characterize the effect of blending on our distance determination

to M101-Inner is to move nearby, well-resolved fields to the distance of M101,

re-observe Cepheids in these fields, and compare the resulting magnitudes with the

ones obtained from the original images. Our program contains observations of two

suitable galaxies: M31 and M81. The fields observed in these galaxies show similar

stellar densities and mean nearest-neighbor distances between Cepheids when

compared to our M101-Inner fields. We used our two M81 fields as well as fourteen

of our M31 fields, which were located in Fields I and III of Baade & Swope (1965).

We started by collecting the positions and magnitudes reported by ALLSTAR

for all objects in our input fields. The separation between stars were reduced

by the ratio of distances between the input galaxies and the M101-Outer field

(D(M101/M31) = 10.1 and D(M101/M81) = 2.2). The input magnitudes were

corrected for the exposure time of the original frames and distance to the input

galaxies, and then modified to reflect the distance of M101 and the exposure time

of the M101 frames. The stars were added to blank frames using the ADDSTAR

routine found in DAOPHOT, which takes into account the properties of the

detector and the PSF, as well as photon statistics. The artificial fields are shown

in Figure 4.10 and compare favorably with the actual M101-Inner images shown in

Figures 4.6c and 4.6d.

Once the artificial fields had been generated, they were photometered in

exactly the same way as our real data. To identify the variables in our artificial

frames, we used the input positions as the equivalent of the astrometric information

available for the real data, and searched for the objects nearest to those positions,

subject to the same 1.5-pixel rejection criterion from §4.4.1. All Cepheids that were

recovered were located at distances smaller than the rejection limit.

Figure 4.11 shows the P-L relations obtained from the simulation, compared

with the original input data. Seven long period Cepheids (P > 20 d) exhibit

changes in magnitude of order 0.1-0.2 mag, most of them being in the expected


Fig. 4.11.— Period-Luminosity relations of our simulated M101 Inner fields shown

in Figure 4.10. Filled triangles indicate the input magnitudes of the Cepheids (as

observed in our original M31 and M81 fields). Circles represent the recovered mag-

nitudes for the same variables. Filled and open circles are used to indicate whether

the recovered Cepheids would have passed or failed the color-color test of §4.4.1.

Dashed and solid lines denote the P-L fits of the input and recovered magnitudes,

respectively.


direction (i.e., towards brighter magnitudes). In the case of the eight Cepheids with

short periods (P < 20 d), one was not recovered, four exhibited large variations

(which would have resulted in their rejection based on color-color criteria), and

three had very modest changes in magnitude.

The resulting distance moduli are smaller than the input ones by 0-0.2 mag,

depending on the period cutoff applied to these small samples. The rms scatter

of the relations do not increase significantly, once the short-period outliers are

removed from the fits. We therefore conclude that a substantial fraction of the

difference in distance moduli between M101-Inner and M101-Outer could be due

to blending, preventing us from performing a differential determination of the

metallicity effect.

4.6 Consistency of reddening determinations

Another goal of this project is to test whether the mean V −I color excess, EV−I ,

is an appropriate indicator of total extinction and whether it can be used to obtain

true distance moduli. One could claim that the range in wavelength between these

two bands is too small to allow a good extrapolation to λ−1 = 0. There is also no

guarantee that a “standard” value of RV−I is applicable to other galaxies. If EV−I

is indeed a good indicator of reddening, and if a standard reddening law (Cardelli

et al. 1989) applies to other galaxies, then one would expect EV−I and EV−H to

be strongly correlated and to follow the slope predicted by the standard reddening

law.

4.6.1 Predicted relation between E(V–I) and E(V–H)

The mean V −I and V −H color excesses of a Cepheid sample are related by

EV−H =RV−I

RV−HEV−I . (4.10)


Furthermore, the value of RV−λ (λ denotes the bandpass of interest) can be

calculated using the following relation:

1

RV−λ= 1− Aλ

AV, (4.11)

where the ratio Aλ/AV is defined in Equation (1) of Cardelli et al. (1989) as

Aλ/AV = a(x) + b(x)/RV . (4.12)

In turn, a(x) and b(x) can be calculated using Equation (2) of Cardelli et al.

(1989); x is the inverse of the central wavelength of the band of choice. The value

of RV ≡ AV /EB−V suitable for Cepheids and stars of similar colors is 3.3. Lastly,

Figure 3 of Cardelli et al. (1989) can be used to estimate the size of the uncertainty

in Aλ/AV .

In our case, we want to calculate the values of RV−I and RV−H . The Cousins

I filter has x = 1.23µm−1, so a(x) = 0.77 and b(x) = −0.59 (Kelson et al. 1996).

Thus, AI = 0.59± 0.03 and RV−I = 2.45± 0.10. The H filter has x = 0.63µm−1,

so a(x) = 0.27 and b(x) = −0.25 (Cardelli et al. 1989). Thus, AH = 0.19 ± 0.03

and RV−H = 1.24± 0.20. Therefore, the predicted ratio of EV−H to EV−I is

EV−H =2.45± 0.10

1.24± 0.20EV−I

= 1.98± 0.16 EV−I . (4.13)

4.6.2 Observed relation

Mean V −I and V −H color excesses were calculated following the methodology of

the HST Key Project on the Extragalactic Distance Scale (Freedman et al. 2001).

We used Period-Color relations based on the Period-Luminosity relations from

Equations 4.5-4.7:


V − I = −0.20(±0.04) [log P− 1] + 0.68(±0.02), (4.14)

V −H = −0.47(±0.05) [log P− 1] + 1.44(±0.05). (4.15)

The mean color excess of a field was calculated by averaging over the individual

color excesses of the variables in that field. The total scatter about the average

value of the color excess in each field was used to determine the quoted uncertainty

on the mean. The values of EV−I for IC 4182, M101 (Inner & Outer), NGC 925,

NGC 1365, NGC 2090, NGC 3621, NGC 4496A and NGC 4536 were corrected by

+0.02 mag to bring them into the Stetson (1998) photometric system (the other

galaxies have ground-based or WF/PC V and I values and need not be corrected).

The mean values of EV−I and EV−H are listed in Table 4.8 and plotted in

Figure 4.12. A least-squares fit to the data yields

EV−H = 2.02± 0.22EV−I − 0.05± 0.05. (4.16)

The agreement between the predicted and observed ratio of EV−H to EV−I ,

and the fact that the fit to the data goes through (0, 0) within the errors, supports

the assumption of a standard reddening law in the fields we have studied.

One data point, corresponding to NGC 3198 and plotted with an open circle,

was excluded from the fit because it lies 4σ away from the relation defined by all

other points. This field contains only three Cepheids, two of which barely passed

the color-color rejection test and are probably contaminated by red companions,

therefore yielding an abnormally high value of EV−H .

It is interesting to note that the Cepheids present in the M101-Inner field

exhibit the same correlation between EV−I and EV−H as the other fields. This

could imply that, on average, the contamination due to “blending” in that field has

not introduced a significant change in the color of the Cepheids. Mochejska et al.

(2001) have found a similar effect among Cepheids in the inner regions of M33.


Table 4.8. Mean color excesses

Field EV−I EV−H

IC 1613 0.09 (03) 0.10 (09)

IC 4182 0.06 (05) 0.15 (00)

M31 0.29 (08) 0.69 (20)

M81 0.13 (05) 0.24 (11)

M101-Inner 0.36 (08) 0.67 (17)

M101-Outer 0.21 (07) 0.31 (10)

NGC 0925 0.24 (06) 0.47 (09)

NGC 1365 0.32 (09) 0.63 (13)

NGC 2090 0.11 (05) 0.18 (04)

NGC 3198† 0.13 (03) 0.58 (03)

NGC 3621 0.40 (08) 0.66 (15)

NGC 4496A 0.19 (07) 0.17 (12)

NGC 4536 0.06 (05) 0.03 (04)

Mean ratio: 2.02±0.22

Zeropoint: -0.05±0.05

Note. — †: 4σ outlier, rejected from fit.


Fig. 4.12.— The correlation between EV−H and EV−I for our fields. Filled circles

represent the crowding-corrected color excesses for our fields. The open circle corre-

sponds to NGC 3198, which was rejected from the fit. The solid line is a least-squares

fit to the data, while the dashed lines indicate the rms uncertainty of the fit.


4.7 Summary

We have obtained near-infrared photometry for a sample of 70 extragalactic

Cepheid variables located in thirteen galaxies ranging in distance from the Local

Group to the Virgo and Fornax Clusters. We have combined our magnitudes with

existing optical data to derive self-consistent Period-Luminosity relations.

Cepheids in the inner field of M101 appear to be severely contaminated by

unresolved blends with nearby stars, thereby affecting our ability to perform a

differential test of the dependence on metallicity of the Cepheid Period-Luminosity

relation.

An analysis of mean color excesses of our sample supports the assumption of

a standard reddening law by the HST Key Project on the Extragalactic Distance

Scale in their derivation of true distance moduli.

Chapter 5

Optical and infrared observations

of Tully-Fisher calibrators

Abstract

This chapter presents BVRIHK observations, surface photometry measurements,

and the derivation of total magnitudes for a sample of spiral galaxies suitable

for the absolute calibration of the Tully-Fisher relation. It also contains new

derivations of 20% and 50% 21-cm linewidths for most of these galaxies, based on

previously existing profiles.

Special care has been taken to perform these measurements in a manner that

is consistent with the analysis of “distant” samples of Tully-Fisher galaxies by

other teams. The motivation for this approach is the desire to minimize the effects

of any systematic error in the photometry that would induce corresponding errors

in the determination of the Hubble Constant.

Contains material from The Astrophysical Journal Supplement Series, volume 128, pages 461-468,“A database of Tully-Fisher calibrator galaxies”, by L.M. Macri, J.P. Huchra, S. Sakai, J.R. Mould& S.M.G. Hughes.

197


5.1 Introduction

This chapter presents optical and near-infrared observations, the resulting surface

photometry measurements, and the derivation of total magnitudes for a sample of

nearby (D ∼< 20 Mpc) spiral galaxies suitable for the absolute calibration of the

Tully-Fisher relation. Additionally, it includes re-derivations of the 20% and 50%

21-cm linewidths for these objects, based on pre-existing observations.

In the early to mid-1990s, as observations with the Hubble Space Telescope

started to yield accurate Cepheids distances to galaxies in the Local Supercluster,

large-format (1024× 1024 or greater) CCD cameras were becoming common in 1-

to 2-m class ground-based telescopes. These instruments provided fields of view

of about 10′ on a side, allowing complete views of most nearby galaxies. The

initial motivation for this project was to obtain a complete set of BVRI images of

every galaxy targeted for an HST-based Cepheid search that could be used for the

absolute calibration of the Tully-Fisher relation. In the late 1990s, as panoramic

infrared detectors became available, the project was expanded to include the HK

bands.

The optical magnitudes and linewidth measurements presented here became

the main source of data used by Sakai et al. (2000) to obtain the absolute calibration

of the Tully-Fisher relation in the BVRI bands. The infrared magnitudes also

contained in this work will be used in Chapter 6 of this Thesis to derive the

absolute calibration of the Tully-Fisher relation in the HK bands.

This chapter is organized as follows: §5.2 presents the details of data

acquisition, reduction and calibration for our optical images, while §5.3 describes

the corresponding steps for the infrared data; §5.4 describes the common

methodology of our optical and infrared surface photometry measurements, the

derivation of total magnitudes, and a comparison with other observations of some

of our objects; §5.5 presents the derivation of 20% and 50% linewidths; and §5.6

summarizes our results.


5.2 Optical observations and data reduction

The optical observations were obtained at three sites. The Fred L. Whipple

Observatory 1.2-m telescope was used to observe most of the objects. The Mount

Stromlo and Siding Spring Observatories 1-m telescope provided images of the

southernmost objects as well as some equatorial objects to provide an overlap

with the northern observations. The Cerro Tololo Interamerican Observatory

1.5-m telescope also provided a few images of southern objects as well as data

on galaxies from the Giovanelli et al. (1997a) sample, to check the consistency

between different surface photometry procedures.

The observing runs took place between 1994 March and 1999 August.

Furthermore, S. Jha kindly provided images of NGC 2841 obtained at the FLWO

1.2-m telescope between 1999 May and 2000 February. The large time span of the

observations and the multiple sources of data resulted in the use of seven different

optical cameras, whose properties are listed in Table 5.1.

The typical night in an optical observing run started with the acquisition of

bias frames and dome and twilight flats. Standard star fields were observed several

times during each night at a large range of airmasses. Most standard star fields

were from Landolt (1992), although the E-regions (Graham 1982) were sometimes

observed from the south. At FLWO, galaxies were typically observed for 600

seconds in B, V , R and I. At MSSSO, exposure times ranged between 160 and 320

seconds, and the filters of choice were V and I. At CTIO, exposure times were 300

seconds in B, V , R and I.

The reduction of the optical images was performed in the standard way, using

the IRAF CCDRED package. Mean bias and dome flat frames were created by

median-combining the calibration frames obtained each night. The data images

went through the steps of overscan fitting, trimming, bias subtraction, and division

by the flat field frame. Dark current was negligible in all CCDs, so that step of the

processing was omitted.


Table 5.1. Cameras used in the observations

Camera Chip Size Pixel Gain Readout

scale (′′) (e−/DN) noise (e−)

Optical cameras

MSSSO Tek 20482 0.61 1.0 10

CCD#1 thick (binned)

MSSSO EEV 2186× 0.58 1.0 6

CCD#6 thick 1152

MSSSO Tek 20482 0.60 1.0 9

CCD#12 thin

FLWO Loral 20482 0.66 2.3 15

CCD thick (binned)

FLWO Loral 20482 0.63 2.5 9.5

Andycam thin (binned)

FLWO Loral 4× (20482) 0.67 2.0 7

4-shooter thin (binned)

CTIO Tek (20482) 0.48 2.7 5

T2K6 thin (binned)

Infrared cameras

FLWO SBRC 2× (2562) 1.21 9.5 60

SIRCAM InSb

MSSSO SBRC 2562 0.49 9.5 60

CASPIR InSb


The photometric calibration of the frames was based on aperture magnitude

measurements of standard stars using the IRAF wphot task. The aperture radius

was set to 10′′ and the sky annulus extended from 10 to 15′′. The photometric

solutions for each band were calculated by solving simultaneously for a magnitude

zeropoint and an extinction coefficient for each night, and a color term for each

run. Typically, our photometric solutions had rms values of 0.02-0.05 mag.

The internal consistency of the photometric solutions was checked via

secondary standard stars located in every galaxy field. Typically, aperture

magnitudes were obtained for 6–12 stars around each object and transformed

into the standard system using the derived photometric solutions. The resulting

magnitudes were compared across different runs in which the same field had been

observed. Run-to-run offsets were usually less than 0.05 mag.

5.3 Infrared observations and data reduction

Infrared observations were carried out between 1997 December and 2000 April,

mostly at the FLWO 1.2-m telescope, with one additional run at the MSSSO 2.3-m

telescope. Table 5.1 summarizes the properties of the infrared cameras used in the

project. They are based on the same type of detector, but the FLWO camera has

dual beams which allow simultaneous observations in a “blue” (i.e. H) and a “red”

(i.e. K) band.

The typical night of an infrared run started with the acquisition of dark frames

for each combination of number of coadds and exposure time to be used during the

night. Dome flats were not acquired, since the pattern that must be followed during

infrared observations provides a plentiful amount of sky flats. Standard stars from

Hawarden et al. (2001) and Persson et al. (1998) were observed frequently and at

a large range of airmasses.

At both FLWO and MSSSO, the fundamental unit of observing time was

60 seconds (6 coadds of 10 seconds for SIRCAM and 5 coadds of 12 seconds for

CASPIR). Unlike the case of the optical observations, the field of view of the


infrared cameras (∼ 5′ for SIRCAM and ∼ 2′ for CASPIR) was smaller than the

target galaxies, and therefore the objects were observed following a mosaic pattern,

with overlaps between neighboring positions of ∼ 10% of the array size. Following

standard practice for infrared observations, each “on-source” position was followed

by a “sky” position typically offset by 10 − 20′. Mosaic sizes ranged in every

combination between a single pointing (for standard star fields and small galaxies

such as NGC 4639) to a 3 × 3 pointing for NGC 2403. In order to build up S/N ,

the mosaic pattern was repeated several times (typically between 3 and 9) with a

small offset (∼ 10′′) in the starting position.

The dark-current and linearization corrections of the SIRCAM data were

carried out under IDL, using procedures developed by the author, while the

CASPIR data were corrected using the IRAF package of the same name, developed

by the camera team. Master dark frames for each sequence of coadds and exposure

time were created by median-combining the calibration frames obtained each

night. Science frames had this mean dark frame subtracted first, after which a

linearization matrix was applied to correct small non-linearities present in each

camera. The “on-source” images of each observation sequence were flatfielded

under IDL using their own sky flat, created by median-combining the “sky” frames

of that observation sequence, once they had been brought to the same mean value.

Repeated observations of the same area of a target object within a sequence

were combined into a single image as follows. First, the pointing information

found in the FITS headers of the frames was used to derive the approximate offset

between them. The frames were shifted by an integer number of pixels, flatfielded,

brought to the same mean level, and median combined. An IDL version of the

FIND routine of DAOPHOT was used to detect stars present in the median image,

which were then located in the individual frames. The stellar positions provided a

refined determination of the offsets between frames, which were used to obtain an

improved median image. This procedure was iterated until convergence. Typically,

five iterations were required until all individual frames were properly shifted.

Lastly, aperture photometry was carried out on the stars detected in the median

image, using an IDL version of the PHOT routine of DAOPHOT. Aperture radii


were set to 10 pixels (∼ 12′′ in SIRCAM and ∼ 5′′ in CASPIR), with inner and

outer sky annuli of 15 and 25 pixels (∼ 18− 30′′ in SIRCAM and ∼ 7.5− 12.5′′ in

CASPIR). These values were motivated by typical stellar FWHM values of 1 − 2

pixels.

The plate solution for each median image was obtained using IMWCS (Mink

1999) by combining the previously-determined star list with the 2 Micron All Sky

Survey (2MASS) Working Point Source Catalog (v2.0). Accurate values of the pixel

scale and rotation angle of the instruments for each observing run were obtained

from the plate solutions of fields with large numbers of stars; these quantities were

held fixed when determining the plate solution of sparsely populated fields. This

step was required in order to be able to assemble the different portions of a galaxy

mosaic into a properly registered image. At the time of assembly, the different

portions of the mosaic were brought to the same background value in order to

deliver a seamless montage.

Analysis of the aperture photometry of infrared standard stars revealed very

stable (±0.05 mag) H and K magnitude zeropoints for FLWO+SIRCAM over the

three years during which the observations were carried out. No significant extinction

coefficient nor color term could be determined from the data. Additionally, we

matched the aperture photometry measurements of all stars present in the standard

fields with their corresponding entries in the 2MASS Working Point Source Catalog

(v2.0) and found magnitude zeropoints that were entirely consistent (±0.02 mag)

with the previously-determined ones. Based on this satisfactory agreement, we

decided to use those stars present in the field of each galaxy to determine the

magnitude zeropoint of each image.


5.4 Galaxy photometry

5.4.1 Surface photometry measurements

The surface photometry measurements were carried out using the SFOTO program

of Han (1991), which operates under Figaro (Shortridge et al. 1995). Several steps

must be carried out to obtain a total extrapolated magnitude for a galaxy. First,

foreground stars and array defects are removed by interpolation. Second, certain

parameters pertaining to each frame are calculated, such as the sky value, the

position of the galaxy nucleus, and the maximum possible radius out to which

ellipses can be fitted. Third, ellipses are fitted to the galaxy profile. These steps

can be repeated several times, for example, to increase or decrease the maximum

fitting radius, until satisfactory results are obtained. Fourth, the ellipse-fitting

results are used to perform the surface photometry of the galaxy, and lastly, these

measurements are used to determine the total magnitudes of the object.

The first step in the process, interpolating over foreground stars and array

defects, was carried out using SFOTO’s “image repair mode”. The position and

size of the interpolated areas were recorded in a “mask” file for later use by

the ellipse-fitting program. The second step, the characterization of the image

properties, was also carried out using SFOTO. The sky value was determined from

blank areas in the frame. The position of the galaxy center was determined by

computing the intensity-weighted centroid of a box of 6 pixels on a side, centered

by eye on the galaxy nucleus. The maximum semi-major axis ellipse to be fitted

was estimated based on the location of the nucleus within the frame, the extent of

the galaxy and its position angle. These parameters were written to disk for later

use by the ellipse-fitting program.

The third step, the actual fitting of the ellipses, was carried out using the

Figaro EFIT routine. That program uses an iterative procedure described by Kent

(1983) to solve for the eccentricity and position angle of, and mean intensity within,

ellipses of increasing radii. The resulting ellipses were visually inspected using

SFOTO, and –if necessary– any leftover point sources enclosed by the outermost


ellipses were removed to ensure convergence of the eccentricity and position angle

of the outermost ellipses. In some cases, the radius of the outermost ellipse was

revised upward when galaxian flux could be seen to extend further out than our

original estimate, or downward when the original estimate had been too optimistic.

The ellipse-fitting results for all images of a given galaxy were combined

to obtain robust estimates of the mean optical, infrared, and band-by-band

eccentricity and position angle of its outer disk. Table 5.3 lists the inclination

angles derived from the mean eccentricities. There is excellent agreement between

our mean inclinations (determined from all optical data) and the values listed in

de Vaucouleurs et al. (1991). The mean eccentricity and position angle of each

galaxy in the optical and infrared were used to generate “self-similar” ellipses for

use during the corresponding surface photometry measurements.

The fourth step, the surface photometry measurement, was carried out using

SFOTO’s “surface photometry mode.” The program used the previously-generated

ellipses to add the signal within each annulus, and applied the appropriate

photometric solution to obtain the mean mag/ut′′ value inside each annulus, and

the cumulative magnitude out to that radius.

The author developed software to interactively fit an exponential disk to the

outer parts of the surface brightness profile. The derived disk scale length and

central surface brightness were used to extrapolate the total magnitude of the

galaxy, following the prescriptions of Han (1992).

Figure 5.1 shows representative B, V , R and I profiles for each of the galaxies

observed in the optical, while Figure 5.2 shows the mean H and K profiles for

those galaxies observed in the infrared. Figures 5.3 through 5.5 show some overall

properties of the data set, through histograms of: the number of disk scale lengths

covered by the profiles, the magnitude extrapolations required to obtain total

magnitudes, and the sky surface brightness of the images, respectively. As these

figures show, most of the data is of high quality, i.e., the profiles extend more than

4 disk scale lengths, the magnitude extrapolations are small (< 0.15 mag), and the

sky surface brightness was low.


Table 5.3. Inclination data

Galaxy Band Mean RC3

(NGC) B V R I H K opt.

0925 57 (1) 55 (1) 57 (1) 57 (1) 55 (4) 54 (6) 56 (1) 57 (1)

1365 57 (2) 55 (1) 56 (1) 55 (2) 47 (2) · · · 55 (2) 57 (1)

1425 64 (1) 64 (1) 64 (1) 62 (1) 63 (1) · · · 63 (1) 64 (2)

2090 66 (3) 65 (2) 67 (2) 65 (3) 68 (1) 67 (1) 65 (3) 62 (2)

2403 · · · · · · · · · · · · 57 (1) 55 (2) · · · 57 (1)

2541 63 (1) 62 (1) 63 (1) 62 (1) 62 (2) 66 (4) 62 (1) 62 (2)

2841 66 (1) 65 (1) 65 (1) 65 (1) 66 (1) 66 (1) 66 (1) 65 (1)

3198 71 (4) 72 (2) 71 (3) 71 (3) 74 (1) 74 (2) 71 (3) 70 (1)

3319 58 (1) 58 (1) 58 (1) 57 (1) 75 (1) 74 (3) 58 (1) 58 (1)

3351 45 (1) 46 (1) 45 (1) 45 (1) 40 (3) 41 (3) 45 (1) 47 (2)

3368 49 (1) 49 (1) 49 (1) 49 (1) 48 (2) 49 (2) 49 (1) 46 (2)

3521 · · · · · · · · · · · · 49 (1) 48 (1) · · · 64 (1)

3621 66 (1) 66 (1) 66 (1) 66 (1) 65 (2) 65 (2) 66 (1) 56 (1)

3627 64 (1) 65 (1) 65 (1) 65 (1) 64 (1) 65 (1) 65 (1) 63 (1)

4414 47 (1) 47 (1) 46 (1) 46 (1) 45 (2) 44 (3) 46 (1) 57 (2)

4535 51 (1) 51 (1) 50 (1) 51 (1) 47 (4) 41 (3) 51 (1) 46 (2)

4536 69 (1) 68 (1) 69 (1) 69 (1) 75 (1) 72 (1) 69 (1) 67 (1)

4548 39 (1) 39 (1) 39 (1) 38 (1) 38 (4) 39 (4) 39 (1) 37 (3)

4565 · · · · · · · · · · · · 90 (0) 90 (0) · · · 87 (4)

4603 51 (1) 52 (1) 51 (1) 51 (1) · · · · · · 51 (1) 44 (5)

4639 55 (1) 49 (1) 47 (1) 44 (2) 53 (1) 51 (1) 48 (3) 48 (3)

4651 55 (2) 53 (1) 53 (2) 52 (2) 48 (1) 53 (2) 53 (2) 50 (2)

4654 58 (1) 58 (1) 58 (1) 58 (1) 57 (1) 56 (1) 58 (1) 56 (1)

4725 62 (1) 61 (1) 62 (1) 61 (1) 54 (3) 51 (1) 62 (1) 45 (2)

7331 70 (2) 69 (2) 68 (2) 68 (1) 70 (1) 70 (1) 69 (2) 70 (1)


Fig. 5.1.— Representative surface brightness profiles for those galaxies with optical

data (BVRI, bottom to top).


Fig. 5.2.— Mean surface brightness profiles for those galaxies with infrared data.

Open and filled circles are K- and H-band measurements, respectively.


Fig. 5.3.— Histograms of disk scale lengths reached by the surface brightness pro-

files.


Fig. 5.4.— Histograms of extrapolation values from the last isophote to total mag-

nitudes. Mean values are 0.09 mag for B and V , and 0.07 mag for R, I, H and

K.


Fig. 5.5.— Histograms of sky surface brightness levels in the images.


5.4.2 Photometry results and external comparisons

Tables 5.4 and 5.5 present the optical and infrared photometry data, respectively.

The magnitudes listed are the observed values, uncorrected for galactic or internal

extinction. Table 5.4 lists total extrapolated BV RI magnitudes and major-axis

diameters at the B = 25 and I = 23.5 mag/ut′′ isophotes. Table 5.5 lists total

extrapolated and isophotal HK magnitudes at the 21 mag/ut′′ level, as well as the

major-axis diameters at that isophote.

Several external comparisons were carried out to ensure the photometric

quality of the data. First, the surface photometry techniques used in this work were

tested against those of Giovanelli et al. (1997a), whose data on distant clusters and

groups is used by Sakai et al. (2000) for the determination of H0. A comparison of

derived properties for twenty-six galaxies in the MDL cluster 59 (Maia, da Costa &

Latham 1989) showed mean offsets of 0.03± 0.12 mag for I-band magnitudes and

2± 5 degrees for galaxy inclinations.

A comparison of BRI magnitudes for 18 galaxies in common with Tully

& Pierce (2000) revealed offsets (this work - their work) of: = +0.07 ±0.14 mag,−0.08 ± 0.08 mag, and − 0.02 ± 0.09 mag in B, R and I, respectively.

The B and R offsets are dominated by four objects with large (> 0.15 mag)

disagreements: NGC 925, NGC 2090, NGC 2541 and NGC 3198, for the B band;

and NGC 925, NGC 1425, NGC 3627 and NGC 4535, for the R band. A direct

comparison of those profiles and the magnitudes of local standards should resolve

these discrepancies.

A comparison of H = 21mag/ut′′ isophotal diameters and integrated

magnitudes for eleven galaxies in common with Watanabe et al. (2001) revealed

excellent agreement for seven objects, with an offset (this work - their work)

of −0.03 ± 0.06 mag and a ratio of D21 values (this work / their work) of

1.02 ± 0.07. However, there was significant discrepancy in the derived isophotal

diameters for four objects: NGC 925, NGC 2541, NGC 4639, and NGC 4725, and

the corresponding integrated magnitudes. These discrepancies might be due the

different procedures followed for the surface brightness measurements. The


Table 5.4. Photometric data

Galaxy BT VT RT IT DB=25 DI=23.5

0925 10.59 (13) 10.15 (09) 9.80 (11) 9.39 (17) 531 461

1365 10.11 (10) 9.50 (06) 9.05 (04) 8.24 (04) 672 603

1425 11.47 (14) 10.91 (02) 10.43 (03) 9.73 (02) 337 347

2090 11.20 (03) 10.76 (08) 10.25 (08) 9.45 (07) 449 396

2541 12.10 (03) 11.65 (04) 11.37 (03) 10.86 (10) 294 263

2841 10.09 (02) 9.30 (02) 8.73 (03) 8.14 (04) 552 458

3198 11.09 (05) 10.55 (02) 10.14 (02) 9.59 (05) 415 388

3319 11.77 (10) 11.35 (18) 11.07 (11) 10.63 (11) 360 312

3351 10.45 (09) 9.75 (15) 9.18 (02) 8.53 (06) 424 453

3368 10.08 (08) 9.25 (05) 8.73 (03) 8.12 (03) 491 509

3621 10.07 (12) 9.52 (07) 9.00 (08) 8.50 (08) 494 554

3627 9.57 (04) 8.87 (04) 8.38 (03) 7.78 (04) 625 651

4414 10.85 (05) 10.14 (04) 9.66 (03) 9.01 (04) 281 292

4535 10.67 (06) 10.01 (02) 9.73 (09) 9.04 (04) 427 424

4536 11.08 (05) 10.45 (02) 9.95 (07) 9.38 (05) 460 459

4548 10.83 (12) 10.13 (04) 9.66 (06) 8.92 (12) 338 357

4603 12.29 (08) 11.49 (10) 10.90 (05) 10.18 (09) 235 250

4639 12.21 (08) 11.52 (06) 11.07 (03) 10.45 (04) 171 171

4651 11.66 (09) 10.93 (06) 10.43 (04) 9.64 (07) 239 300

4654 11.12 (07) 9.54 (04) 9.53 (06) 11.11 (03) 324 318

4725 9.98 (11) 9.23 (01) 8.77 (10) 8.17 (06) 656 651

7331 10.25 (02) 9.40 (04) 8.81 (05) 8.08 (01) 583 641


Table 5.5. Photometric data

Galaxy H21 K21 HT KT DH=21 DK=21

0925 8.34 (04) 7.85 (10) 7.95 (15) 7.47 (15) 303 341

1365 6.71 (07) 6.65 (18) · · · · · · 406 · · ·1425 8.57 (13) 8.48 (15) · · · · · · 218 · · ·2090 8.24 (00) 8.22 (01) 8.02 (10) 8.01 (10) 195 211

2403 6.46 (13) 6.36 (17) 6.07 (12) 5.97 (16) 529 609

2541 10.00 (04) 9.29 (05) · · · · · · 184 · · ·2841 6.35 (13) 6.32 (16) 6.13 (15) 6.10 (17) 463 477

3198 8.10 (06) 7.98 (07) 7.81 (01) 7.66 (01) 334 357

3319 10.04 (07) 9.55 (20) · · · · · · 234 · · ·3351 6.97 (02) 6.90 (02) 6.69 (02) 6.60 (02) 328 345

3368 6.52 (04) 6.45 (06) 6.25 (06) 6.20 (11) 363 390

3521 5.98 (06) 5.94 (06) 5.71 (08) 5.69 (09) 436 457

3621 6.96 (04) 6.91 (04) 6.69 (03) 6.66 (03) 399 452

3627 6.05 (09) 6.02 (09) 5.95 (00) 5.92 (01) 512 502

4414 7.19 (01) 7.07 (01) 6.77 (03) 6.73 (03) 227 298

4535 7.47 (04) 7.31 (04) 7.17 (08) 7.01 (12) 336 365

4536 7.83 (04) 7.63 (05) 7.47 (03) 7.32 (06) 384 408

4548 7.41 (04) 7.27 (07) 7.12 (01) 7.01 (02) 294 315

4565 6.28 (08) 6.25 (08) 5.90 (08) 5.88 (08) 781 834

4639 9.01 (06) 8.83 (07) 8.59 (01) 8.49 (05) 140 193

4651 8.05 (06) 7.95 (07) 7.90 (03) 7.82 (04) 213 233

4654 8.09 (10) 7.98 (10) 7.67 (03) 7.59 (03) 234 254

4725 6.74 (03) 6.65 (11) 6.41 (04) 6.33 (08) 434 430

7331 6.30 (02) 6.23 (01) 5.96 (04) 5.90 (05) 512 551


procedure used in this work, i.e., the use of self-similar ellipses and the determination

of a mean isophotal level inside each ellipse, should be more robust than the direct

measurements performed on the images by Watanabe et al. (2001) (c.f. their

Figure 1), especially given the low S/N at that isophotal level.

These comparisons show that our measurements are in fairly good agreement

with previous studies. Given additional telescope time, it would be desirable to

re-observe galaxies with data from only one observing run, with inadequate scale

length coverage, or with large discrepancies with other published work.

5.5 21-cm linewidths

Having obtained a consistent set of galaxian magnitudes, we undertook a similar

approach for 21-cm data and decided to re-measure 20% and 50% widths in a

consistent way for as many objects as possible.

Linewidths were determined following three different methodologies: i)

Aaronson et al. (1982b), where linewidths are measured at the 20% level of the

mean of the two-horned flux maxima; ii) Pierce & Tully (1992), where linewidths

are measured at the 20% level of the flux maximum; iii) Giovanelli et al. (1997a),

where linewidths are measured at the 50% level of each of the two-horned flux

maxima. In this latter methodology, the 50% level is defined separately for

each horn as the interpolated value between the 15% and the 85% levels. In all

methodologies, the determination of the locations of these various intensity levels

is done by searching from the mid-point of the profile to the extreme velocities

for the 15% and 20% levels, and in the opposite way for the 85% levels. In all

cases, the measured linewidths were corrected for instrumental broadening using

the prescription of Bottinelli et al. (1990). The slight difference in methodology

between the Aaronson et al. (1982b) and the Pierce & Tully (1992) 20% linewidth

measurement has no discernible effect, and therefore only one set of 20% linewidths

is quoted below. Some representative 21-cm profiles are shown in Figure 5.6,

indicating the different flux levels involved in the linewidth measurement.


21-cm profiles for most objects were kindly provided by Martha Haynes

from the Giovanelli & Haynes’ digital archive (Haynes, private communication).

Several objects were not present in that archive, so scanned profiles from published

data were kindly provided by Barry Madore, from an upcoming addition to the

NASA/IPAC Extragalactic Database (NED). One profile was kindly provided by

the HIPASS team before their survey was complete. Some objects had no profiles

in either the G&H or the NED archive, so we used linewidth measurements from

the literature. In a few cases, either the 20% or the 50% level linewidths were

available in the literature, so we transformed the available linewidth by using a

mean 50%-to-20% ratio of 0.91 (based on ∼ 80 profiles). Linewidth errors were

calculated from the data when we had access to the profiles; in all other cases, the

errors come from the literature.

Table 5.6 lists the raw 20% and 50% linewidth measurements, their

uncertainties and their sources. A comparison between previously published

linewidth determinations and our re-measurements reveals agreement to better

than 2% rms. Furthermore, when profiles of the same galaxy were available from

both the Giovanelli & Haynes’ digital archive and the NED database, linewidths

measured from one set agreed with the other to better than 3% rms.

5.6 Conclusions

Total galaxian magnitudes in the BVRIHK bands and 20% and 50% 21-cm

linewidth measurements have been determined for most of the calibrators of the

Tully-Fisher relation. The surface photometry and linewidth measurements were

performed in a consistent way for all objects, following the prescriptions used in the

reduction of “distant” T-F samples. There is good agreement between the present

and previous determinations of total galaxian magnitudes and 21-cm linewidths.

The infrared data is used in Chapter 6 to obtain the absolute calibration of

the Tully-Fisher relations in the HK bands, while the optical data was used by

Sakai et al. (2000) for the corresponding calibration in the BVRI bands.


Fig. 5.6.— Typical 21-cm profiles, showing the different flux levels used in the

determination of 20% and 50% linewidths.


Table 5.6. Linewidth data

Galaxy W20 W50 Galaxy W20 W50

NGC meas. ref. meas. ref. NGC meas. ref. meas. ref.

0925 220 (1) [1] 203 (7) [1] 1365 398 (1) [2] 376 (2) [2]

1425 375 (7) [1] 360 (10) [1] 2090 293 (2) [1] 282 (2) [1]

2541 209 (1) [1] 197 (1) [1] 3198 317 (1) [1] 305 (1) [1]

3319 216 (2) [1] 201 (3) [1] 3351 276 (1) [1] 268 (1) [1]

3368 358 (3) [1] 336 (9) [1] 3621 296 (2) [3] 245 (3) [3]

3627 383 (14) [1] 337 (15) [1] 4414 404 (10) [1] 358 (8) [1]

4535 300 (9) [4] 278 (9) [5] 4536 341 (7) [6] 323 (7) [6]

4548 261 (8) [7] 237 (8) [5] 4603 406 (13) [8] 370 (13) [9]

4639 313 (20) [10] 284 (20) [5] 4651 392 (1) [8] 357 (1) [11]

4654 315 (3) [12] 291 (4) [12] 4725 414 (3) [1] 390 (2) [1]

7331 521 (2) [1] 500 (2) [1]

224 543 (5) [13] 495 (5) [5] 598 204 (5) [13] 186 (5) [5]

2403 262 (2) [14] 243 (2) [14] 3031 434 (10) [14] 382 (10) [14]

Note. — [1]: measured from Giovanelli & Haynes’ digital archive (Haynes, priv. comm.). [2]:

measured from scanned NED profile from Bureau et al. (1996). [3]: Measured from HIPASS profile.

[4]: as published in Aaronson et al. (1982b). [5]: computed from matching W20. [6]: measured from

scanned NED profile from Dickel & Rood (1978). [7]: as published in Pierce & Tully (1988). [8]:

computed from matching W50. [9]: as published in Giovanelli et al. (1997a). [10]: as published in

Fisher & Tully (1981). [11]: as published in Haynes et al. (1999b). [12]: measured from scanned

NED profile from Shostak (1975). [13]: as published in Pierce & Tully (1992). [14]: measured from

scanned NED profile from Rots (1980).

Chapter 6

The absolute calibration of the

luminosity–linewidth relation

Abstract

This chapter presents the absolute calibration of the luminosity–linewidth relation,

commonly referred to as the Tully–Fisher relation, in the near-infrared H and K

bands as well as in the optical R and I bands.

The absolute calibration is performed using Cepheid distances such as those

derived in Chapters 2 and 3 of this Thesis, and it is based on the surface photometry

and linewidth measurements of spiral galaxies presented in Chapter 5 of this

Thesis.

Relations are derived for both total extrapolated magnitudes and isophotal

magnitudes, using 20% linewidths. All relations exhibit linear slopes and a scatter

of ∼ 0.2 mag. Shallower isophotal magnitude relations in the H and K bands,

based on 2MASS data, yield distance moduli that are consistent with those

determined from total-magnitude I-band relations.

219


6.1 Introduction

The recent determination of Cepheid-based distances to spiral galaxies in the Local

Supercluster, made possible by the angular resolution of the Hubble Space Telescope,

has ushered a new era for the absolute calibration of the luminosity–linewidth

relation. As part of the HST Key Project on the Extragalactic Distance Scale,

Sakai et al. (2000) used distances to twenty-one galaxies to derive a new calibration

of the luminosity–linewidth relation in the BV RI bands, as well as in the H−0.5

system. The scatter of the relation in the latter was 0.36 mag. Sakai et al.

(2000) found discrepant values of H0 as determined from the I-band and the H−0.5

relations, which were ascribed to differences in the I −H−0.5 color of the calibrator

and “distant cluster” samples.

At the same time, a calibration of the BRIK relations was undertaken by

Tully & Pierce (2000). They used twenty-four calibrators for the optical bands, but

only had K data for four galaxies (M81, NGC 3198, NGC 3627 and NGC 4258). In

their analysis, they used slopes derived from template relations based on galaxies

located in several nearby clusters, and reported a scatter of 0.24 mag in the R and

I bands, and a larger scatter of 0.44 mag for the K band template relation.

Recently, Watanabe et al. (2001) performed a calibration of the H-band

relation, using surface photometry measurements for twelve galaxies. They reported

a “break” in the slope of the relation, at logW c20 ∼ 2.45, although the evidence

is rather meager, based on only two objects (NGC 2541 and NGC 3319). Their

relation, based on nine objects with logW c20 > 2.45, had a scatter of 0.28 mag.

Watanabe et al. (2001) confirmed the finding of Sakai et al. (2000) regarding a

I −H color difference between the calibrators and cluster samples.

Lastly, Verheijen (2001) derived a K-band relation based on a volume-limited

complete sample of all suitable spiral galaxies that are members of the Ursa Major

cluster. The sample contains forty-nine objects, all with detailed radio synthesis

data that allow a better determination of the rotational velocity of the galaxy. The

scatter of his relation was 0.32 mag.


This Chapter presents the absolute calibration of the luminosity–linewidth

relation in the RIHK bands, based on a sample of nineteen galaxies. §6.2

presents the calibrator sample, and lists the corrections required to obtain absolute

magnitudes from the original data; §6.3 derives the absolute calibration of the

relations; and §6.4 discusses the application of 2MASS data to the determination

of H0.

6.2 The calibrator sample

The calibrator sample used in this work consists of nineteen galaxies with

Cepheid-based distances that were measured in a consistent manner. The Cepheids

were discovered by several teams, most notably the HST Key Project on the

Extragalactic Distance Scale and the Type Ia Supernovae Distance Scale teams,

between 1996 and 1999. At the time of the observations, distances were determined

using LMC Period-Luminosity relations derived in the early 1990s (Madore &

Freedman 1991). However, during this period new insight was gained into the

V − I Cepheid Period-Color Relation of LMC Cepheids (Udalski et al. 1999),

and the community grew more aware of the possible metallicity dependence of

the Cepheid Period-Luminosity Relation (Kochanek 1997; Sasselov et al. 1997;

Kennicutt et al. 1998). This prompted a re-evaluation of the original distances by

Freedman et al. (2001), which is the source of all but one of our distance moduli.

The exception is NGC 2841, whose distance moduli was determined following the

updated methodology in Chapter 3 of this Thesis.

The galaxian magnitudes (both total extrapolated and isophotal), as well as

their linewidth measurements, come from Chapter 5 of this Thesis. This work will

only calibrate the RIHK relations, since the BV ones are of little use for current

extragalactic work. Magnitudes were corrected for Galactic extinction using the

reddening map of Schlegel, Finkbeiner & Davis (1998) and the extinction law of

Cardelli et al. (1989), for an assumed value of RV = 3.1. Linewidth measurements

were corrected for inclination using the standard 1/ sin i factor. Inclinations and


axis ratios were taken from Tully & Pierce (2000). Additionally, galaxian surface

brightness profiles and integrated magnitudes were corrected for internal extinction

following the precepts of Tully et al. (1998):

Aiλ = γλ log(a/b), (6.1)

γλ = c1 + c2(logW iR − 2.5), (6.2)

where a/b is the major-to-minor axis ratio. The values of (c1, c2) for RIK

come from Tully et al. (1998), while the values for H were calculated through

extrapolation of the published values; they were found to be (0.46, 0.80).

Table 6.1 lists the designation, distance modulus, Galactic extinction, corrected

linewidth measurements, and absolute magnitudes of the galaxies in the calibrator

sample. It lists both extrapolated magnitudes and isophotal magnitudes, at the

R = 24, I = 23.5, H = 21 and K = 21 mag/ut′′ isophotes.

6.3 Analysis

The near-infrared luminosity–linewidth relations are shown on four panels in

Figure 6.1. The top and bottom left panels show the H and K-band total

magnitude relations, respectively, while the corresponding right panels show the

isophotal (21 mag/ut′′) magnitude relations. Figure 6.2 shows similar relations

for the R and I bands. In both figures, solid, dashed and dotted lines indicate

the result of bivariate, direct and inverse least-squares fits, respectively, to the

functional form

M = a+ b (logW c20 − 2.5) (6.3)

Table 6.2 lists the results of the fits. In all cases, the data point corresponding

to NGC 2841, located at logW c20 = 2.827, was excluded from the fit, since it is a

clear outlier. This galaxy has an extremely large rotational velocity, and no similar

objects are present in the sample used by Tully et al. (1998) to derive the internal


Tab

le6.

1.C

alib

rato

rdat

a

NG

Cµ

0E

logW

c 20

Hc T

Kc T

Rc T

Ic T

Hc 21

Kc 21

Rc 24

Ic 23.5

0925

29.8

1(0

4)76

2.45

8(1

5)-2

2.08

(11)

-22.

40(1

6)-2

0.38

(11)

-20.

69(1

7)-2

1.65

(05)

-21.

95(1

6)-2

0.22

(09)

-20.

49(1

4)

1365

31.2

7(0

5)20

2.73

6(1

5)-2

4.76

(19)

···

-22.

60(0

7)-2

3.33

(06)

-24.

71(0

9)···

-22.

64(0

7)-2

3.25

(06)

1425

31.7

0(0

5)13

2.61

7(1

5)-2

3.42

(16)

···

-21.

76(0

6)-2

2.36

(05)

-23.

35(1

4)···

-21.

70(0

6)-2

2.31

(05)

2090

30.3

5(0

4)40

2.49

7(0

9)-2

2.33

(04)

-22.

44(1

1)-2

0.64

(09)

-21.

32(0

8)-2

2.31

(04)

-22.

43(1

1)-2

0.55

(09)

-21.

18(0

8)

2541

30.2

5(0

5)50

2.37

0(1

0)-2

1.10

(07)

···

-19.

29(0

6)-1

9.70

(11)

-20.

51(0

6)···

-19.

11(0

5)-1

9.48

(09)

2841

30.7

4(0

6)16

2.82

7(1

0)-2

4.68

(17)

-24.

77(1

9)-2

2.66

(07)

-23.

13(0

7)-2

4.65

(14)

-24.

75(1

6)-2

2.65

(07)

-23.

10(0

8)

3198

30.7

0(0

8)12

2.53

4(0

7)-2

2.91

(10)

-23.

13(0

8)-2

1.04

(08)

-21.

49(0

9)-2

2.81

(10)

-23.

00(0

8)-2

1.00

(08)

-21.

44(0

9)

3319

30.6

2(0

9)15

2.41

1(1

4)-2

1.18

(22)

···

-19.

82(1

5)-2

0.20

(14)

-20.

76(1

2)···

-19.

65(0

9)-1

9.98

(10)

3351

30.0

0(0

9)28

2.57

0(1

5)-2

3.20

(09)

-23.

45(0

9)-2

1.10

(09)

-21.

68(1

1)-2

3.14

(09)

-23.

36(0

9)-2

1.04

(09)

-21.

63(1

0)

3368

30.1

1(0

6)25

2.67

6(1

7)-2

3.78

(08)

-23.

97(1

2)-2

1.69

(07)

-22.

24(0

7)-2

3.72

(07)

-23.

92(0

9)-2

1.65

(07)

-22.

20(0

7)

3621

29.1

1(0

6)80

2.52

1(1

1)-2

2.40

(07)

-22.

55(0

7)-2

0.66

(10)

-21.

03(1

0)-2

2.35

(07)

-22.

52(0

7)-2

0.64

(09)

-21.

00(0

9)

3627

30.0

1(0

8)32

2.67

5(2

7)-2

4.14

(12)

-24.

16(0

8)-2

2.02

(09)

-22.

54(0

9)-2

4.11

(12)

-24.

14(0

8)-2

2.01

(09)

-22.

53(0

9)

4414

31.2

4(0

5)19

2.68

3(2

1)-2

4.33

(05)

-24.

59(0

6)-2

2.00

(06)

-22.

57(0

6)-2

4.23

(05)

-24.

54(0

6)-2

1.97

(05)

-22.

54(0

5)

4535

30.9

9(0

5)19

2.64

3(2

9)-2

3.77

(06)

-24.

02(1

3)-2

1.49

(10)

-22.

13(0

6)-2

3.62

(06)

-23.

87(1

0)-2

1.41

(10)

-22.

05(0

6)

4536

30.8

7(0

4)18

2.56

6(1

5)-2

3.44

(07)

-23.

65(0

7)-2

1.44

(08)

-21.

90(0

6)-2

3.29

(06)

-23.

52(0

5)-2

1.41

(07)

-21.

87(0

6)

4548

31.0

5(0

5)38

2.62

7(3

3)-2

3.86

(09)

-24.

08(0

5)-2

1.62

(08)

-22.

30(1

3)-2

3.73

(06)

-23.

98(0

5)-2

1.53

(05)

-22.

19(0

8)

4639

31.7

1(0

8)26

2.58

8(3

9)-2

3.01

(10)

-23.

29(0

9)-2

0.98

(08)

-21.

53(0

9)-2

2.84

(10)

-23.

19(0

8)-2

0.93

(08)

-21.

46(0

9)

4725

30.4

6(0

6)12

2.66

3(1

1)-2

4.01

(13)

-24.

22(1

0)-2

2.19

(12)

-22.

70(0

9)-2

3.94

(07)

-24.

16(0

7)-2

2.15

(12)

-22.

66(0

9)

7331

30.8

4(0

9)91

2.75

3(0

8)-2

4.91

(09)

-25.

09(1

0)-2

2.83

(10)

-23.

38(0

9)-2

4.86

(09)

-25.

05(1

0)-2

2.81

(10)

-23.

36(0

9)

Not

e.—

EisEB−V

,lis

ted

in10−

3m

ag;

all

mag

nitu

deer

rors

are

expr

esse

din

10−

2m

ag;

erro

rsin

logW

c 20

are

expr

esse

din

10−

3un

its.


Fig. 6.1.— Luminosity–linewidth relations for galaxies with Cepheid distances. The

top and bottom left panels show the H and K-band total magnitude relations,

respectively, while the corresponding right panels show the isophotal (21 mag/ut′′)magnitude relations. Solid, dashed and dotted lines indicate the result of bivariate,

direct and inverse least-squares fits. The open symbol indicates the location of

NGC 2841, which was excluded from the fits.



top and bottom left panels show the R and I-band total magnitude relations, respec-

tively, while the corresponding right panels show the isophotal (24 and 23.5 mag/ut′′,respectively) magnitude relations. Solid, dashed and dotted lines indicate the result

of bivariate, direct and inverse least-squares fits. The open symbol indicates the

location of NGC 2841, which was excluded from the fits.


Table 6.2. Fit results

Mag. Type a b σ N

HT dir. −22.40± 0.02 −10.0± 0.2 0.19 18

inv. −22.38± 0.04 −10.2± 0.3 0.19

biv. −22.39± 0.05 −10.0± 0.3 0.19

H21 dir. −22.19± 0.02 −11.0± 0.2 0.22

inv. −22.15± 0.04 −11.3± 0.3 0.22

biv. −22.16± 0.05 −11.1± 0.3 0.22

KT dir. −22.66± 0.04 −9.9± 0.3 0.22 14

inv. −22.61± 0.06 −10.1± 0.4 0.22

biv. −22.65± 0.07 −9.7± 0.5 0.21

K21 dir. −22.59± 0.04 −9.8± 0.3 0.20

inv. −22.50± 0.06 −10.3± 0.4 0.19

biv. −22.53± 0.07 −10.0± 0.5 0.19

RT dir. −20.54± 0.03 −8.5± 0.2 0.20 18

inv. −20.59± 0.04 −9.0± 0.2 0.22

biv. −20.58± 0.04 −8.7± 0.3 0.20

R24 dir. −20.44± 0.02 −8.9± 0.2 0.20

inv. −20.50± 0.04 −9.4± 0.2 0.23

biv. −20.49± 0.04 −9.2± 0.4 0.21

IT dir. −21.10± 0.03 −8.7± 0.2 0.20 18

inv. −21.06± 0.04 −9.5± 0.2 0.22

biv. −21.09± 0.05 −9.1± 0.3 0.21

I23.5 dir. −20.97± 0.03 −9.2± 0.2 0.21

inv. −20.95± 0.04 −10.0± 0.3 0.22

biv. −20.96± 0.05 −9.7± 0.3 0.21


extinction corrections used in this work. The HST/WFPC2 image of this galaxy

(Figure 3.2) shows prominent dust lanes embedded in its disk, which introduce

additional internal extinction that may not be compensated for in the formulation

of Tully et al. (1998). The Cepheid distance to NGC 2841 is not likely to blame

for the offset, since that distance provided an absolute calibration for the type Ia

supernova 1998by Garnavich et al. (2001) that is in excellent agreement with the

existing calibration for the type Ia SNe distance indicator.

The scatter in all the relations, σ = 0.19 − 0.22 mag, is comparable to

those of the R and I-band calibrator samples of Tully & Pierce (2000) and the

K-band Ursa Major cluster sample of Verheijen (2001). Figure 6.3 shows the

RIK relations for this cluster, along with fits to the bivariate results presented in

Table 6.2. The resulting distance moduli are 31.32± 0.08 mag, 31.35± 0.08 mag,

and 31.36± 0.08 mag, respectively (internal errors only).

6.4 An application to 2MASS data

The Two-Micron All Sky Survey will soon release a catalog of JHK photometry

for ∼ 106 galaxies across the sky. The combination of these magnitudes with

the output of ongoing redshift and 21-cm surveys will result in an unprecedented

database for Tully-Fisher studies. The short integration times of 2MASS (7.6s)

results in shallower isophotal magnitudes, measured at the HK = 20 mag/ut′′

level. Recent studies by Bouche & Schneider (2000) and Pahre, Kochanek & Falco

(2001) have determined template relations for this isophote at K.

In order to provide an absolute calibration for 2MASS Tully-Fisher studies, the

calibrator data presented in Chapter 5 was used to determine magnitudes at the

quoted isophotal level. The luminosity–linewidth relations, shown in Figure 6.4,

are best fit (using a bivariate weighting scheme) by:

H20 = −22.01± 0.02− 10.5± 0.4(logW c20) (6.4)

K20 = −22.34± 0.07− 10.4± 0.5(logW c20) (6.5)


Fig. 6.3.— Luminosity–linewidth relations in the RIK bands for galaxies in the Ursa

Major cluster. Photometry and linewidth data are from Tully & Pierce (2000). The

solid lines represent the best fits to the relations listed in Table 6.2, yielding distance

moduli of 31.32± 0.08 mag, 31.35± 0.08 mag, and 31.36± 0.08 mag, respectively.



left and right panels show the H and K-band 20 mag/ut′′ isophotal magnitude

relations, respectively. Solid lines indicate the result of bivariate least-squares fits.

The open symbol indicates the location of NGC 2841, while the starred symbols (in

the H relation) indicate the location of NGC 2541 and NGC 3319; all were excluded

from the fits.


The r.m.s. scatter of these relations is 0.24 mag and 0.22 mag, similar to the

deeper isophotal and the total magnitude relations. However, two low linewidth

galaxies (NGC 2541 and NGC 3319) were rejected from the fit to the H-band data.

Their location in the diagram could be interpreted as a “break” in the slope of

the relation; however, it would be preferable to characterize such a change using a

template relation based on a much larger sample of cluster galaxies.

The 2MASS-based relations were tested against the I-band total magnitude

relation using a sample of 25 galaxies from the Coma cluster and 14 galaxies in

the Abell 1367 cluster. Linewidth, inclinations, and total I band magnitudes were

obtained from Tully & Pierce (2000), while 2MASS magnitudes were provided by

J. Huchra. The relations are shown in Figure 6.5; as before, solid lines indicate

best-fit results based on a bivariate error weighting scheme.

The best-fit distance moduli are as follows: Coma, µI = 34.81 ± 0.07 mag,

µH = 34.85 ± 0.08 mag, µK = 34.85 ± 0.08 mag, for a mean value of

µ = 34.83± 0.03 mag; Abell 1367, µI = 34.79± 0.09 mag, µH = 34.85± 0.09 mag,

µK = 34.88±0.10 mag, for a mean value of µ = 34.84±0.04 mag. All quoted errors

are internal only. This limited analysis seems to indicate that the HK 20 mag/ut′′

relations can provide distance estimates with a precision similar to the total I-band

relations.

The mean distance moduli derived above imply distances to these clusters

of DComa = 92.6 ± 1.1 Mpc and DA1367 = 92.8 ± 1.9 Mpc. When combined

with mean recession velocities (in the CMB frame) of VComa = 7185 km/s and

VA1367 = 6735 km/s Tully & Pierce (2000), they yield a mean value of the Hubble

constant of 75± 4 km is−1 Mpc−1 (internal errors only). The external error for the

Cepheid distance scale, as derived by Freedman et al. (2001), is ±7 km s−1 Mpc−1.

6.5 Conclusion

This Chapter has presented the absolute calibration of the luminosity–linewidth

relation in the RIHK bands, based on the photometry data presented in Chapter 5.


Fig. 6.5.— Luminosity–linewidth relations for galaxies in the Coma and Abell 1367

clusters. The left panels show the relations based on total I-band magnitudes from

Tully & Pierce (2000). The center and right panels show H and K-band rela-

tions based on 2MASS isophotal magnitudes (defined at the 20 mag/ut′′ isophotes).

Linewidth and inclination data were obtained from Tully & Pierce (2000). The

solid lines represent bivariate fits to relations determined from the calibrator sam-

ple (Table 6.2 Equations 6.4-6.5). The average distance modulus for each cluster is

listed on top of its panels.


The total magnitude and deep isophotal magnitude relations exhibit linear slopes

and have a scatter of ∼ 0.2 mag. Relations based on shallower H and K isophotal

magnitudes, such as those to be provided by 2MASS, yield distances that are

comparable to those obtained with total I-band magnitudes. As an example,

2MASS data for galaxies in the Coma and Abell 1367 clusters were used to derive

a value of the Hubble constant of H0 = 75± 4i ± 7e km s−1 Mpc−1.

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