Morphological Classification of Nearby Galaxies Based on Asymmetry and Luminosity Concentration

8/13/2019 Morphological Classification of Nearby Galaxies Based on Asymmetry and Luminosity Concentration

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Morphological classification of nearby galaxies basedon asymmetry and luminosity concentration

1. M. Yagi1*2. Y. Nakamura23. M. Doi34. K. Shimasaku24and5. S. Okamura24

+Author Affiliations

1. 1Optical and Infrared Astronomy Division, National Astronomical Observatory of Japan,2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

2. 2Department of Astronomy, School of Science, University of Tokyo, 7-3-1 Hongo,Bunkyo-ku, Tokyo 113-0033, Japan

3. 3Institute of Astronomy, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015,Japan

4. 4Research Centre for the Early Universe, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

1. *E-mail:[email protected] original form 2006 January 26.

Accepted 2006 January 30.

Next Section

AbstractWe investigate the behaviour of the asymmetry parameter Aas a morphological parameter using a

volume-limited sample of 349 galaxies (distance 25 Mpc, MV18.5 mag) and a larger

magnitude-limited sample of 707 nearby galaxies. We confirm the correlation of Awith

morphological type. The late-type galaxies (Sdm, Sm and Im) have larger Athan early-type galaxies,

and they tend to have larger Athan spiral galaxies. We investigate the usefulness of the Aversus

concentration index Cindiagram as a tool for the regularirregular and earlylate classification. The

diagram is not very useful to the regular versus late-type irregular classification, as inferred

previously, but it is found to be useful to the earlylate classification.

Key words

methods: data analysis

galaxies: fundamental parameters

galaxies: photometry
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1 INTRODUCTION

Morphological classification proposed byHubble (1926,1936),and later revised bySandage (1961,

1975)andde Vaucouleurs (1959,1974)has been the basis of extragalactic studies because the

revised Hubble type shows reasonably good correlations with various physical parameters of

galaxies (e.g.Abraham 1998;van den Bergh 1998). The revised Hubble classification was originally

based on the inspection of the image of galaxies on blue-sensitive photographic plates by eye, and

therefore more or less subjective.

With the advent of large data sets of digital images of both nearby and high-zgalaxies, various

machine-oriented, therefore subjective, methods of morphological classification have been

proposed. They include the two-dimensional bulgedisc decomposition (de Jong 1996;Ratnatunga,

Griffiths & Ostrander 1999;Peng et al. 2002;Im et al. 2002;de Souza, Gadotti & dos Anjos 2004;

Mllenhoff 2004,see, alsoOkamura et al. 1999), use of neural network (Burda & Feitzinger 1992;

Storrie-Lombardi et al. 1992;Serra-Ricart et al. 1993;Naim et al. 1995;Odewahn et al. 1996;Ball et

al. 2004,see, alsoSpiekermann 1992;Owens, Griffiths & Ratnatunga 1996;Naim, Ratnatunga &

Griffiths 1997;Bazell & Aha 2001;Odewahn et al. 2002;de la Calleja & Fuentes 2004,for similar

methods), use of various surface photometric parameters (Doi, Fukugita & Okamura 1993;Abraham

et al. 1994;Conselice, Bershady & Jangren 2000a;Abraham, van den Bergh & Nair 2003;Conselice

2003;Conselice et al. 2003;Lotz, Primack & Madau 2004), and use of shapelets (Refregier 2003;

Kelly & McKay 2004;Massey & Refregier2004). Most of the new classification methods aim to

reproduce or improve the Hubble sequence based on some objective and quantitative measures.

Using simple surface photometric parameters, the central concentration index (Cin) and the mean

surface brightness (SB) within the isophote of a fixed level,Doi et al. (1993)classified nearby

galaxies into two broad classes, early and late. Their classification was consistent with the

conventional visual classification at about 85 per cent level. However, if we want to classify distantgalaxies, we have to take into account the K-correction, image degradation, morphological K-

correction, etc. (Fukugita et al. 1995;Giavalisco et al. 1996). Especially, because SB strongly depends

on the redshift due to cosmological dimming, it is not easy to classify field galaxies at cosmological

distances using the CinSB diagram.

In the place of SB,Abraham et al.(1996, hereafter A96) used the rotational asymmetry A, which was

introduced for galaxy classification bySchade et al. (1995)as RA(see, alsoElmegreen, Elmegreen &

Montenegro 1992). The parameter Arepresents the irregularity in terms of the degree of asymmetry

with respect to the 180 rotation. Though Ahas a disadvantage that effects of image degradation

and resolution are not easily measurable, its dependence on the redshift is much weaker than SB.

Conselice et al.(2000a, hereafter C00) described a procedure to make the asymmetry parameterrobust. The log Clog Adiagram has been often taken as a tool to classify distant galaxies, with

emphasis on isolating irregular galaxies (e.g. A96;Smail et al. 1997;Brinchmann et al. 1998,

hereafter B98).

Recently, in addition to the asymmetry parameter, the importance of the use of some surface

photometric parameters representing the image structure was recognized in terms of the formation

history, that is, merging history, of galaxies.Conselice (2003)introduced a CASclassification based
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on the concentration (C), asymmetry (A), and clumpiness (S). For other type of such parameters

representing the image structure, see, for example,Lotz et al. (2004)andYamauchi et al. (2005),

and references therein.

The fiducial sample to calibrate the classification based on Aand Cwas taken fromFrei,

Guhathakurta & Gunn (1996),which presents the CCD images of 113 galaxies taken in two bands

(A96;Conselice 1997,hereafter C97), whileConselice (2003)used 240 galaxies by adding to the Frei

sample of 127 galaxies consisting of dE, starburst, dIrr and IRAS infrared galaxies, to calibrate their

CAS classification. The Frei et al. sample is intended to cover all morphological types, but only five

irregular galaxies (SdmIm) are included.

In this paper, we investigate the behaviour of the Aparameter as a tool of morphological

classification based on 349 nearby galaxies with d< 25 Mpc and MV18.5 and a larger magnitude-

limited sample of 707 galaxies. We describe the procedure to compute the Aparameter inSection 2.

Sample selection is described inSection 3.The behaviour of the Aparameter as a function of various

quantities is investigated inSection 4.Morphological classification based on Aand Cinis discussed in

Section 5.Summary is given inSection 6.


2 ASYMMETRY PARAMETER

We compute the asymmetry parameter Afor 791 nearby galaxies, using the digitized photographic

V-band images given in the Photometric Atlas of Northern Bright Galaxies (PANBG;Kodaira et al.

1990). The properties of the galaxies included in the PANBG are described inKodaira et al. (1990).

The 791 galaxies were exposed on 280 Schmidt photographic plates. The digitized images were

corrected for the non-linearity of the photographic plates by means of the calibration wedges

exposed on the four margins of each plate. The zero-point of photometry, that is, the sky

brightness, was obtained for each of the 280 plates by fitting the growth curve of at least one

calibration galaxy1with photoelectric magnitudes. The typical error of the growth curve fitting of a

calibration galaxy was 0.063 mag and the typical error of the zero-point of a plate was 0.101 mag,

including the former error. We use the sky-subtracted smoothed image with stars masked out. We

adopt a threshold surface brightness, th= 24.5 mag arcsec2. All the pixels with fluxes below this

threshold are discarded in the analysis, except for the computation of the noise. We follow the

method proposed by A96 and B98, with some modifications described below.

On the basis of the rotational symmetry, A96 defined the asymmetry parameter as

1

where Iijis the flux of the pixel at ( i,j), IRijis the flux of the pixel at the same location after the imageis rotated by 180 around the centre of the galaxy, and Bgalis the total flux of the galaxy computed as

2

The summation is taken over the area above the threshold.
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To determine the centre of the galaxy (ic,jc), we use the following procedure. First, we roughly define

the central region of a galaxy around the pixel of the highest intensity (ip,jp). Then, we bin the data

by kkto increase the signal-to-noise ratio. The icis computed by one-dimensional Gaussian,

3fitting to three binned points around the peak; KK(ipk), KpK(ip) and K+K(ip+k). We adopted k= 3

and calculated the following values:

Eliminating K0and 2, we obtain icas

4

Thejcis computed with the same procedure. In order to simplify the calculation of A0, we round off

the (ic,jc) to integer or half-integer. The rounding off makes the 180 rotation equivalent to taking a

mirror image. This rounding off does not affect our conclusion at all. When we artificially change the

centre by 0.5 pixel, Aincreases by about 8 per cent on average. C00 argued that Aminimization is

the best solution to determine the centre by 0.1 pixel. In our sample, however, as the noise statistics

among adjacent pixels are unclear, subpixel shift may introduce uncertain bias. This is the reason

why we adopt a kind of mirror image subtraction. We should also note that our sample is less

affected by the centre-determination uncertainty than C00, since our sample excludes

mergers/interactions, which should have different peak position from the axisymmetry centre. We

also tested minimum-search method with the PANBG images by 0.5-pixel precision to find that the

difference is log(A) 0.04. The difference does not affect the result in this paper.

We estimate the contribution of noise to the asymmetry parameter as follows. We calculate the

following parameter n1at one of the four corners of the image:

5

where is the pixel value before setting the isophotal threshold. Note that this xymirror

subtraction is the same as the subtraction of the 180-rotated image around (i,j) = (10, 10).Similarly, n2to n4are calculated at the remaining three corners. We define the noise factor N0as

6

where Sgis the area of the galaxy, measured by the number of pixels above the threshold, and Sskyis

the area of the four corners (1600 pixels) where we estimated nk. The noise-corrected asymmetry

parameter Ais defined as


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7


3 SAMPLE SELECTION

The PANBG gives surface photometric parameters of 791 nearby galaxies derived from the digitized

data of the Schmidt plates. The 791 PANBG galaxies are drawn from the Revised ShapleyAmes

Catalog (RSA;Sandage & Tammann 1987), which is magnitude limited at B 12.5 mag. The V-band

photographic plates were taken with the 105-cm Schmidt telescope at the Kiso Observatory,

University of Tokyo. Initial targets were 911 RSA galaxies accessible from the Kiso Observatory, that

is, with > 25. However, the plates had not been secured for some galaxies by the time when the

data analysis for the catalogue was completed. On the other hand, some RSA galaxies with < 25

were also included for which good plates were taken. Accordingly, the PANBG is not a complete

sample in any sense. However, it is not biased in terms of any intrinsic properties of galaxies. The

PANBG covers 63 per cent of the 1246 RSA galaxies.

The pixel size of the digitized data is different for galaxies of different apparent sizes, ranging from

1 to 4 arcsec except for several very large galaxies such as M31 and M33 for which larger pixel sizes

are used. The pixel size is always a multiple of 1 arcsec and was chosen so that the galaxy should fit

to a frame with a side of either 256 or 512 pixel.

The Cinand average SB within V= 24.5 mag arcsec2of the galaxies in the PANBG are computed by

Doi et al. (1993).They examined model profiles to examine the point spread function (PSF) effect. In

this study, 99 per cent of total sample, and 99 per cent of volume-limited sample satisfy the criteria

/re< 0.4 for E/S0 and /re< 0.6 for spirals. For actual data,Doi et al. (1995)showed that Cindoes

not get affected by seeing at the Kiso Observatory in B< 15 mag. As most of our sample satisfy B 0.8). C00 found a similar behaviour. On the other hand,

a correlation is seen inFig. 5(b).Late-Irr galaxies are distributed in the upper right-hand part (faint

and large A).

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Download as PowerPoint SlideFigure 5Asymmetry parameter Aplotted as a function of absolute magnitude MVfor the volume-limited

sample (a) and for the faint sample (b). Symbols are the same asFig. 2.

We investigated the possible dependence of Aon galaxy diameter, surface brightness, and apparent

magnitude, and no significant dependence was found.


5 CLASSIFICATION BASED ON ASYMMETRY ANDLUMINOSITY CONCENTRATION

5.1 Distribution of galaxies in the log Cinversus log Aplane

The luminosity Cinwhich we use below is taken fromDoi et al. (1993).Cinwas defined as

8

where 2rI(r) dris the differential flux between rand r+ dr, I(r) is the equivalent profile(areal profile,

de Vaucouleurs 1975), and Lis taken to be the detection threshold. This definition of Cinis almost

the same as that of the central concentration Cproposed by A96. The only minor difference is that

Cinis measured with the isophotal areas, while Cis based on the elliptical apertures of the fixed axis

ratio.Doi et al. (1993)circumvented the problem with galaxies having different axis ratios between

the inner and outer regions by using the isophotal areas. In fact, the two parameters are almost

identical in many cases, if we use the same data. Though many variants of the concentration indices

were proposed and investigated in detail (e.g.Graham, Trujillo & Caon 2001;Yamauchi et al. 2005),

we used classical Cinin this study so that we can compare our result withDoi et al. (1993).As the

parameters are not suitable for examining higher-redshift galaxies, because the threshold V= 24.5mag arcsec2is dependent on redshift, the robust indicator of physical surface brightness or the

relevant radius is needed, which will be investigated elsewhere.

Fig. 6(a)shows the log Cinversus log Aplot for the volume-limited sample. Symbols are assigned

according to our four-type classification as inFig. 2.There is a broad but rather well-behaved

correlation that regular galaxies exhibit. The distribution of regular galaxies is elongated and runs

from upper left to lower right, inFig. 6(a).Regular galaxies with smaller Cintend to have larger A. I0

galaxies have intermediate Cinand tend to show larger A.
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Figure 6The distribution of galaxies on the plane of the (Cin) versus asymmetry parameter (A) for the volume-

limited sample (a and b) and for the total sample (c). The symbols of (a) and (c) are the same as in

Fig. 2,while those of (b) are the same as inFig. 3(a)(see the text). The dotted line in (b) represents

the best-fitting boundary line of the earlylate classification (equation 9).

Fig. 6(b)shows the same plot asFig. 6(a),but the symbols are changed according to the

morphological-type index as inFig. 3(a).A very clear trend is seen that morphological types shift

from early (lower right-hand panel) to late (upper left-hand panel), along the elongated distribution

of regular galaxies. The early-type galaxies have large Cin(high central concentration) and small A

(less asymmetric), while late-type galaxies have small Cinand large A.

Fig. 6(c)shows the same plot asFig. 6(a)but for the total sample. There are three galaxies in the

lower left-hand part below the sequence of regular galaxies at 0.5 < log Cin< 0.3. The most

deviant two are dwarf elliptical galaxies (NGC 185 and NGC 205) with low central concentration and

little asymmetry. They are the only dwarf ellipticals in our sample. The result is similar to the result

byConselice, Gallagher & Wyse (2002)andConselice (2003),who showed that low-mass cluster

galaxies (LMCGs) in the Perseus cluster have a low concentration and a low asymmetry. Though NGC

185 and NGC 205 are field dwarf ellipticals, they might be the same population as LMCGs. Future

deep and wide surveys of galaxies will tell us in detail where these field dEs populate in this plot.

5.2 Regular versus irregular classificationA96 and B98 proposed a method for isolating distant irregular galaxies observed with the Hubble

Space Telescope(HST), using Cand A. Their fiducial samples are taken fromFrei et al. (1996).They

artificially redshifted galaxies taken fromFrei et al. (1996)and examined their distribution on the log

Cversus log Aplane to define the boundary lines for distant galaxies. They successfully separated

three morphological bins: early-type systems, intermediate-to-late-type spirals, and very late-type

spirals/irregulars/mergers.Bershady, Janglen & Concelise (2000)extended the analysis to C, A, SBe,

and BVspace. With the four parameters, they succeeded to classify galaxies into three types: early,

intermediate and late. It should be noted, however, that their sample contains only five irregular

(SdmIm) galaxies.

As shown inFigs 6(a) and (c),most of the Late-Irr galaxies are distributed in the upper left-handpart (low concentration and large asymmetry) of the log Cinlog Adiagram. However, some of them

are distributed in the right-hand part as well. The late-irregular galaxies (SdIm) have the whole

range of Cinthat regular galaxies have. C00 reached the same conclusion. As a result, regular and

late-irregular galaxies are not separated well on the log Cinlog Aplane, as inferred by A96. Hence,

the combination of asymmetry and central concentration is not very useful for the regularirregular

classification. However, we cannot constrain the usefulness of separating mergers/interacting
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galaxies from normal galaxies, as argued inConselice et al. (2000b),since such galaxies are not

included in our samples.

On the other hand, on the MVlog Aplane (Fig. 5b), the distribution of late-irregulars are clearly

different from that of regular galaxies. However, if we want to examine the usefulness of the MVlog

Adiagram in terms of the regularirregular classification, we need a sample of galaxies with known

redshift which contains large number of intrinsically faint galaxies.

B98 measured the central concentration index Cand the rotational asymmetry factor Aof the

CanadaFrance Redshift Survey (CFRS)/Autofib/Low-Dispersion Survey Spectrograph Redshift Survey

(LDSS) galaxies (z= 01.2), using the HSTI-band (F814W) images. When we compare their log Clog

Aplot (upper panel of their fig. 8) with ours (Figs 6a and c), we note a slight difference in the

distribution. Galaxies with medium and low concentration, which are mostly late types, have larger A

in our sample than theirs. The slope of the earlylate boundary line is also different. Their boundary

line is almost parallel to the log Aaxis. The characteristics they found are consistent with those

found by A96 (their fig. 2).

The galaxy sample of B98 consists of galaxies with z= 01.2. They used the Iband, while we use the

Vband. As is well known, many effects such as K-correction, morphological K-correction, (1 +z)4

dimming, colour dependence, and image resolution should be taken into account when we analyse a

sample of distant galaxies. Since we have the V-band images of nearby galaxies only, it is premature

to draw any conclusion from the comparison of the high-zsamples and ours.

5.3 Early versus late classification

We next investigate how useful the Cinand Adiagram is to classify galaxies into two broad types,

early (E) and late (L), in the framework of the revised Hubble classification. Such a classification with

the CinAdiagram was first proposed by A96 and later used by B98.Bershady et al. (2000)

investigated the usefulness of the combinations of parameters in type classification, and concluded

that Hubble type is not well discriminated in the CAplane.

We classify galaxies with T0 as early and those with T 1 as late. We set the boundary line in the

log Cinlog Aplane as

9

We consider the right-hand side of the line as the E region and the left-hand side as the L region.

We examined several different values of and adopted = 2.00 which worked best. We apply this

classification to our volume-limited sample and compute the completeness and contamination of E

and L sample as a function of offset. Results are shown inFig. 7.With the offset of -0.357, we

obtain the completeness of about 86 per cent for both the regions and contamination of about 10

per cent (L region) and 20 per cent (E region). The line with = 2.00 and offset =0.357 is shown inFig. 6(b).This classification is rather insensitive to the slope . Even if we change from 1 to 5, the

completeness changes only a few per cent.
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We compare this classification with that based on Cinand the mean SB, proposed byDoi et al. (1993).

The plot for our volume-limited sample is shown inFig. 8.The boundary line on this diagram is

given byDoi et al. (1993)as

10

The completeness and contamination as a function of offset for this classification is shown inFig. 9.With the offset of 3.33 (dotted curve inFig. 8), we obtain the completeness of about 85 per cent for

both the regions and contamination of about 10 per cent (L region) and 25 per cent (E region).


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Figure 8The distribution of galaxies in the volume-limited sample on the plane of mean SB versus Cin.

Symbols are the same as inFig. 3(a).The dotted curve represents the best-fitting boundary line of

the earlylate classification (equation 10).
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Figure 9Completeness and contamination of the E (solid) and L (broken) samples as a function of offset on

the SBCinplane (equation 9).

The earlylate classification based on Cinand Aworks equally well as that based on Cinand SB. The

CinAsystem gives slightly less contamination in the E region than the CinSB system.

5.4 Other correlationsFig. 10shows the asymmetry parameter Aas a function of (BV) colour.Figs 10(a) and (b)are the

same plot but with different symbols. Symbols inFig. 10(a)are assigned according to our four-type

classification as inFig. 2,while those inFig. 10(b)are assigned according to conventional types as in

Fig. 3(a).The correlation shown inFig. 10is remarkably similar to that between Aand Cin(Fig. 6).

This suggests a strong correlation between Cinand (BV) colour. The colourAcorrelation was

studied by C97, C00,Bershady et al. (2000)andConselice (2003). Conselice (2003)presented a fit
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between Aand (BV). The fit is consistent with ours if we convert their A(C00, R) to our Awith the

equation inAppendix A(Fig. 10c).
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Figure 10The distribution of galaxies in the volume-limited sample on the plane of asymmetry Aand

corrected BVcolour (BV)0T. The (BV)0Tis taken from RC2, and 248 data points are plotted. The

symbols in (a) and (b) are the same as those ofFigs 6(a) and (b).Figure (c) is the same as (b) but

limited in the galaxies in Frei et al. The dotted line in (c) is the fit byConselice (2003),converted

from the fit inAppendix A.

About type classification,Bershady et al. (2000)showed that the early-, intermediate-, and late-type

galaxies of Frei et al. can be discriminated well in the (BV) versus Aplane, which is not consistent

with our result inFig. 10(b).Part of the difference comes from type-mix of the samples, since the

Frei et al. sample is intended to cover all morphological types and not reflected the actual type-mix.

When we restrict our volume-limited sample in those in Frei et al., the result (Fig. 10c)resembles the

result byBershady et al. (2000).This point is already warned byBershady et al. (2000)as we

designated this as preliminary until larger, more comprehensive samples of galaxies are analysed

than in this study. Though the sample of this study is larger than previous studies, we should warn

that our sample is not completely selected. Larger and more well-controlled samples are required.

We note in passing an interesting feature of A, Cinand SB parameters. There are, rather, well-defined

correlations both between Aand Cin(Fig. 6a)and between SB and Cin. However, little correlation is

seen between Aand SB as shown inFig. 11.It implies that the manifold of galaxies in the ACinSB

space have the largest principal component close to the Cinaxis.


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Download as PowerPoint SlideFigure 11The distribution of galaxies in the volume-limited sample on the plane of asymmetry Aand mean SB.


6 SUMMARY

We compute the asymmetry parameter Afor a sample of 707 nearby galaxies, using almost the same

method as A96, B98 and C00. We examined the behaviour of Aas a function of the morphological

type and various photometric parameters. Examinations are mostly based on the volume-limited

sample of 349 galaxies (d 25 Mpc, MV18.5 mag) extracted from the total sample. The total

sample and the faint sample (d 10 Mpc, MV17.0 mag) are also used as complements.

We confirm the correlation of Awith morphological type. Late-type galaxies have larger Athan

early-type galaxies. Late-type irregular galaxies tend to have larger Athan spiral galaxies.

Effects are discussed which reduce the values of Afor distant galaxies. Highly inclined galaxies tend

to have large A. A part of this effect is ascribed to dust absorption. Intrinsically faint late-type

irregular galaxies have large A.

We investigate the usefulness of the Aversus Cindiagram as a tool for the regular versus late-

irregular classification and early versus late classification. The diagram is found to be not very useful

to the regular versus late-irregular classification, as inferred previously, but useful to the earlylate

classification.

The numerical data used in this study are available upon request.


Acknowledgments

We thank Michael Strauss for providing us with a code of computing distances to galaxies on the

infall model. We also thank the referee Dr Conselice for valuable suggestions and comments that

improved this work. This work was supported in part by Grants-in-Aid (07CE2002, 11640228,

10440062) from the Ministry of Education, Science, Sports and Culture of Japan.


Appendix


APPENDIX A: COMPARISON OF ASYMMETRY WITH OTHER STUDIES

We compare our Avalues with those given in A96, C97 and C00. There are 72 galaxies common tothe PANBG andFrei et al. (1996).Five of the 72 galaxies are not used in our study; three have low

A0/N0, and two show strong dust absorption. As a result, there are 67 galaxies whose Avalues are

measured by A96, C00, and this study, while only 37 galaxies are common to C97 and ours.Table

A1shows the summary of Ameasurements in the previous studies andTable A2gives the data

summary.

View this table:

Table A1
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Summary of Ameasurements for nearby galaxies in the previous studies. In the Formula

column, Irepresents pixel values after background subtraction, and IRrepresents those of the

180-rotated image. In the Noise correction column, A0represents the asymmetry of the target,

and N0represents the asymmetry of a blank region normalized by the flux of the target.

Reference Data Formula Noise correction

A96 Frei et al. Correcteda

C97 Frei et al. Not corrected

C00 Frei et al. min(A0)min(N0)

This paper PANBGaNo detailed description.

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Table A1Summary of Ameasurements for nearby galaxies in the previous studies. In the Formula column, I

represents pixel values after background subtraction, and IRrepresents those of the 180-rotated

image. In the Noise correction column, A0represents the asymmetry of the target, and N0

represents the asymmetry of a blank region normalized by the flux of the target.

View this table:

Table A2

The data used in the Ameasurements.

Data Band Pixel scale Mean seeingFrei et al. (Lowell)R, BJ1.35 arcsec pixel

1 3.3 arcsec

PANBG (Kiso) V Various (14 arcsec pixel1) 3.9 arcsec

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Table A2The data used in the Ameasurements.

The comparison of Ais shown inFig. A1.Note that the definition of asymmetry by C00 differs from

that of A96, C97, and ours by a factor of 2. We therefore take the abscessa ofFig. A1as A(C00)/2,and plot the Avalues of A96 (crosses), C97 (filled squares), and this study (open circles). Since it is

unclear whether A96 measured Ausing the BJ-band image or the R-band image byFrei et al. (1996),

we show the same data for both bands in (a) and (b).
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Figure A1Comparison of Avalues based on the PANBG image (this study) and those based on the BJ-band

image (a) and the R-band image (b) ofFrei et al. (1996).Abscissa is the half of A(C00) values. The

ordinates are the Avalues of other studies; A96 (crosses), C97 (filled squares), and this study (open

circles). A96 data are plotted both in (a) and (b).

As shown inFig. A1,Avalues of A96, C97, and ours all show more or less similar correlations with

A(C00), with similar slopes but different offsets. The offsets are summarized inTable A3.The fits are

(A1)

View this table:

Table A3Mean offsets of the Avalues.

Offset BJbandRband

A(A96)A(C00)/2 0.02 0.01

A(C97)A(C00)/2 0.06 0.03

A(ours)A(C00)/2 0.06 0.07
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Table A3Mean offsets of the Avalues.

As discussed in C00, the offsets due to the difference of colour band are small. We also found that

the offsets due to the difference of pixel scales and seeing sizes between the PANBG andFrei et al.

(1996)do not affect largely the Avalues of these well-resolved galaxies. The offsets between this

study and C00 are 0.06(BJ) and 0.07(R), on average. These values are comparable to those seen

among previous studies, and they do not affect our conclusions.

The offset between A(ours) and A(C00) may be explained by the combination of the following

factors.

i. In both C00 and this study, the effect of photon noise of the galaxy flux was notcorrected for in computing A. A96 estimated the effect for bright galaxies as A

0.05. Some part of the offset may be explained by the difference of photon noise

statistics between the PANBG andFrei et al. (1996).However, the PANBG is based on

the digitized photographic data, and it is quite difficult to evaluate the photon noise of

the galaxies in each pixel.

ii. The PANBG images have larger region than Frei et al. samples. We measured Aat V

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