Small Galaxy Groups Clustering

and the Evolution of Galaxy Clustering

Leopoldo InfantePontificia Universidad Católica de Chile

Bonn, June 2005

Talk Outline

Introduction

The Two-point Correlation Function

Clustering of Small Groups of Galaxies – SDSS results

Evolution of Clustering – MUSYC results

Conclusions

Rich Clusters

Groups

Galaxies

How do we characterizeclustering?

Correlation Functionsand/or

Power Spectrum

Random Distribution

1-Point

2-Point

N-Point

Clustered Distribution

2-Point

r

dV1

dV2

Continuous Distribution

Fourier Transform

Since P depends only on k

2-Dimensions - Angles

Estimators

In Practice

AA BB

r0 vs dc

On the one hand, The Two point Correlation Function is an statistical tool that tells us how strongly clustered structures are. Amplitud (A), or Correlation length (r0)

On the other, we need to characterize the structure in a statistical way Number density (nc) Inter-system distance (dc)

The co-moving Correlation Length

Proper Correlation length

Proper Correlation distance

Clustering evolutionindex

Assumed Power Law 3-D Correlation Function

Assumed Power Law Angular Correlation Function

To go from r

Must do a 2D 3D de-projection Limber in 1953 developed the inversion

tool Two pieces of information are required:

A Cosmological ModelThe Redshift Distribution of the Sample dN

dz

Proper Correlation Length and Limber’s inversion

12

1 3

00 2

0

( ) (1 )dN

H z x z dzdz

r A CdN

dzdz

3

0 0( ) (1 ) (1 )H z z

1

( )

dx

dz H z

With z information

• Redshift space correlation functions– Given sky position (x,y) and redshift z,

one measures s

• Sky projection, p, and line of sight, , correlation functions– Given an angle, , and a redshift,

z, one measures rp,

Problem; choose upper integration limit

Inter-system distance, dc

systemsc

Nn

V

1/31

cd n

Mean separation of objects

Space density of galaxy systems

As richer systems are rarer, dc scales with richness or mass

of the system

Proper Volume

CLUSTERING Measurements from Galaxy

Catalogsand

Predictions from Simulations

Galaxy Clustering: Two examples

APM angular clusteringSDSS spatial clustering

APM

Sloan Digital Sky SurveySloan Digital Sky Survey

•2.5m Telescope•Two Surveys

•Photometric•Spectroscopic

•Expect•1 million galaxies with spectra•108 galaxies with 5 colorsCurrent resultsCurrent results

DR2 2500 deg.2

200,000 galaxies, r<17.7Median z 0.1

SDSS DR2

Zehavi et al., 2004

Clustering of Galaxy Clusters

Richer clusters are more strongly clustered.

Bahcall & Cen, 92, Bahcall & West, 92

However this has been disputed: • Incompleteness in cluster samples (Abell,

etc.)• APM cluster sample show weaker trend

3

0.40.4o c

c

r dn

Galaxy Groups Clustering

Simulations2dFGG clusteringLCDCS clustering

SDSS DR2 clustering

N body simulations

• Bahcall & Cen, ‘92, ro dc

• Croft & Efstathiou, ‘94, ro dc but weaker

• Colberg et al., ‘00, (The Virgo Consortium)– 109 particles– Cubes of 3h-1Gpc (CDM)

CDM =0.3 =0.7 h=0.5 =0.17 8=0.9

CDMdc = 40, 70, 100, 130 h-1Mpc

Dark matter

2dF data, 2PIGG galaxy groups sampleEcke et al., 2004

19,000 galaxies 28,877 groups of at least 2 members<z> = 0.11

Padilla et al., 2004

Galaxies2dFGRS

Groups2PIGG

1/31

cc

dn

2 2ps r

Las Campanas Distant Cluster Survey

• Drift scan with 1m LCO.• 1073 clusters @ z>0.3• 69 deg.2

• 78o x 1.6o strip of the southern sky (860 x 24:5 h-1 Mpc at z0.5 for m=0.3 CDM).

• Estimated redshifts based upon BCG magnitud redshift relation, with a 15% uncertainty @ z=0.5.

Gonzalez, Zaritsky & Wechler, 2002

Gonzalez, Zaritsky & Wechler, 2002

1/31

cc

dn

Clustering of

Small Groups of GalaxiesfromSDSS

• Objective: Understand formation and evolution of structures in the universe, from individual galaxies, to galaxies in groups to clusters of galaxies.

• Main data: SDSS DR1• Secondary data: Spectroscopy to get

redshifts.• Expected results: dN/dz as a function of z,

occupation numbers (HOD) and mass. Derive ro and d=n-1/3 Clustering Properties

Bias

• The galaxy distribution is a bias tracer of the matter distribution.– Galaxy formation only in the highest peaks of density

fluctuations.– However, matter clusters continuously.

• In order to test structure formation models we must understand this bias.

Halo Occupation Distribution, HOD

Bias, the relation between matter and galaxy distribution, for a specific type of galaxy, is defined by: The probability, P(N/M), that a halo of virial mass M

contains N galaxies.

The relation between the halo and galaxy spatial distribution.

The relation between the dark matter and galaxy velocity distribution.

This provides a knowledge of the relation between galaxies and the overall distribution of matter, the Halo Occupation Distribution.

In practice, how do we measure HOD?

Detect pairs, triplets, quadruplets etc. n2 in

SDSS catalog.

Measure redshifts of a selected sample.

With z and N we obtain dN/dz

Develop mock catalogues to understand the

relation bewteen the HOD and Halo mass

Collaborators:

M. StrausN. PadillaG. GalazN. Bahcall& Sloan consortium

OUR PROJECT: We are carrying out a project to find galaxies in small groups using SDSS data.

The DataSeeing 1.2” to 2”Area = 1969 deg2

Mags. 18 < r < 20

Selection of Galaxy Systems

Find all galaxies within angular separation between 2”<<15” (~37h-1kpc) and 18 < r < 20

Merge all groups which have members in common.Define a radius group: RG

Define distance from the group o the next galaxy;

RN

Isolation criterion: RG/RN 3

Sample

3980 groups with 3 members pairs 68,129

Mean redshift = 0.22 0.1

Galaxy pairs, examples

Image inspection showsthat less than 3% are spurious

detections

Galaxy groups, examples

Results

A = 13.54 0.07 = 1.76

A = 4.94 0.02 = 1.77

arcsec arcsec

Results

galaxies

tripletspairs

•Triplets are more clustered than pairs•Hint of an excess at small angular scales

Space Clustering Properties

-Limber’s Inversion-– Calculate correlation amplitudes from ()– Measure redshift distributions, dN/dz– De-project () to obtain ro, correlation lengths– Compare ro systems with different HODs

The ro - d relation

3/11

n

d

Correlation scaleAmplitude of the

correlation function

Mean separationAs richer systems are rarer,

d scales with richness or mass of the system

12

1 3

00 2

0

( ) (1 )dN

H z x z dzdz

r A CdN

dzdz

Rich Abell Clusters:•Bahcall & Soneira 1983•Peacock & West 1992•Postman et al. 1992•Lee &Park 2000

APM Clusters:•Croft et al. 1997•Lee & Park 2000

EDCC Clusters:Nichol et al. 1992

X-ray Clusters:•Bohringer et al. 2001•Abadi et al. 1998•Lee & Park 2000

Groups of Galaxies:•Merchan et al. 2000•Girardi et al. 2000

LCDM (m=0.3, L=0.7, h=0.7)SCDM (m = 1, L=0, h=0.5)Governato et al. 2000Colberg et al. 2000Bahcall et al. 2001

Galaxy Triplets

Results so far...We select galaxies within 1980 deg2, withmagnitudes 18 < r* < 20, from SDSS DR1

data.We select isolated small groups.

We determine the angular correlation function.We find the following:

•Pairs and triplets are ~ 3 times more strongly clustered than galaxies.•Logarithmic slopes are = 1.77 ± 0.04 (galaxies and pairs)() is measured up to 1 deg. scales, ~ 9 h-1Mpc at <z>=0.22. No breaks.•We find ro= 4.2 ± 0.4 h-1Mpc for galaxies and 7.8 ± 0.7 h-1Mpc for pairs•We find d = 3.7 and 10.2 h-1Mpc for galaxies and pairs respectively.•LCDM provides a considerable better match to the data

Follow-up studiesdN/dz and photometric redshifts.

Select groups over > 3000 deg2 area from SDSS

Clustering evolution with redshift.

Results from MUSYC

CollaboratorsN. Padilla, S. Flores, R. Asseff, E.

Gawiser, & d. Christlein

Evolution of the bias factor (Seljak & Warren

2004)

Evolution of the clustering of the dark-matter in a Lambda-CDM

Cosmology

MUSYC:• Multiwavelength survey by Yale-Chile• 1 deg2, 4 fields (eHDFS, CDF-S, SDSS

1030+05, 1256+01)• AB depths of U,B,V,R=26.5 and K(AB)=22.5 Current analysis - eHDFS• 18<R<24.3• Aditional information on B,V,I, and z• c < 0.8 (SExtractor)• Using BPZ• ~20,000 galaxies with 0.4<z<2• Errors ~ 0.1 in redshift

Real and Mock HDF-S:

• MUSYC

• Hubble Volume

Dark Matter, z=0

Galaxies, z=0

Redshift distributions in real and Semianalytic mock (at z=0)

A set of homogeneous subsamples of galaxies in the

HDF-S

The method: getting r0(z)• First step: calculate for

different errors in redshift:

z=0.0 z=0.1

>1

<1

=1

Correlation function in redshift-space is not useful in this analysis:

The projected correlation function can be made stable:

1300

0

2 ,h Mpc

d

MA

SS

, z=

0G

AL

AX

IES

, z=

0M

AS

S, E

VO

LU

TIO

N

MOCKS

RESULTS:

• Correlation length• Halo masses• Bias factors

Comparison with VVDS (Le Fevre

et al. 2004) and CNOC2:

This work

6

4

2

0

Conclusions• 15,000 HDF-S, MUSYC galaxies• Photo-zs with an error of z=0.1• Method for estimating evolution of

correlation length, mass of galaxy host haloes and bias factors.

• Mock catalogues -> Calibration• Results compatible with the evolution

of clustering of the mass in a CDM cosmology

• Consistent with results from VVDS and CNOC

FIN

SDSS DR1 18 < r < 20

CNOC2 SurveyCNOC2 Survey

Measures clustering evolution up to z 0.6 for Lateand Early type galaxies.

1.55 deg.2

~ 3000 galaxies 0.1 < z < 0.6

Redshifts for objects with Rc< 21.5Rc band, MR < -20 rp<10h-1Mpc

SEDs are determined from UBVRcIc photometry

Projected

Correlation Length

dlogN/dm=0.46Turnover at r* 20.8

De-reddened Galaxy Counts

Thin lines are counts on each of the 12 scanlines