Small Galaxy Groups Clustering and the Evolution of Galaxy Clustering Leopoldo Infante Pontificia 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 characterize clustering? Correlation Functions and/or Power Spectrum

Random Distribution 1-Point 2-Point N-Point Clustered Distribution 2-Point r dV 1 dV 2

Continuous Distribution Fourier Transform Since P depends only on k

2-Dimensions - Angles  Estimators In Practice A B

r 0 vs d c 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 (r 0 ) On the other, we need to characterize the structure in a statistical way  Number density (n c )  Inter-system distance (d c )

The co-moving Correlation Length

Proper Correlation length Proper Correlation distance Clustering evolution index 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 Model The Redshift Distribution of the Sample

Proper Correlation Length and Limber’s inversion

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  r p,   Problem; choose upper integration limit

Inter-system distance, d c

Mean separation of objects Space density of galaxy systems As richer systems are rarer, d c scales with richness or mass of the system Proper Volume

CLUSTERING Measurements from Galaxy Catalogs and Predictions from Simulations

Galaxy Clustering: Two examples APM angular clustering SDSS spatial clustering

APM

Sloan Digital Sky Survey 2.5m Telescope Two Surveys Photometric Spectroscopic Expect 1 million galaxies with spectra 10 8 galaxies with 5 colors Current results DR deg ,000 galaxies, r<17.7 Median 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 d isputed: Incompleteness in cluster samples (Abell, etc.) APM cluster sample show weaker trend

Galaxy Groups Clustering Simulations 2dFGG clustering LCDCS clustering SDSS DR2 clustering

N body simulations Bahcall & Cen, ‘92, r o  d c Croft & Efstathiou, ‘94, r o  d c but weaker Colberg et al., ‘00, (The Virgo Consortium) –10 9 particles –Cubes of 3h -1 Gpc (  CDM)  CDM  =0.3  =0.7 h=0.5  =0.17  8 =0.9

 CDM d c = 40, 70, 100, 130 h -1 Mpc Dark matter

2dF data, 2PIGG galaxy groups sample Ecke et al., ,000 galaxies  28,877 groups of at least 2 members = 0.11

Padilla et al., 2004 Galaxies 2dFGRS Groups 2PIGG

Las Campanas Distant Cluster Survey Drift scan with 1m LCO z> deg o x 1.6 o strip of the southern sky (860 x 24:5 h -1 Mpc at z  0.5 for  m =0.3  CDM). Estimated redshifts based upon BCG magnitud redshift relation, with a 15% z=0.5. Gonzalez, Zaritsky & Wechler, 2002

Clustering of Small Groups of Galaxies from SDSS

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 r o 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. n  2 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. Straus N. Padilla G. Galaz N. Bahcall & Sloan consortium OUR PROJECT: We are carrying out a project to find galaxies in small groups using SDSS data.

The Data  Seeing  1.2” to 2”  Area = 1969 deg 2  Mags. 18 < r < 20

Selection of Galaxy Systems  Find all galaxies within angular separation between 2”<  <15” (~37h -1 kpc) and 18 < r < 20  Merge all groups which have members in common.  Define a radius group: R G  Define distance from the group o the next galaxy; R N  Isolation criterion: R G /R N  3 Sample 3980 groups with 3 members pairs 68,129 Mean redshift = 0.22  0.1

Galaxy pairs, examples Image inspection shows that less than 3% are spurious detections

Galaxy groups, examples

Results A  =  0.07  = 1.76 A  = 4.94  0.02  = 1.77 arcsec

Results galaxies triplets pairs 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 r o, correlation lengths –Compare r o systems with different HODs

The r o - d relation Correlation scale Amplitude of the correlation function Mean separation As richer systems are rarer, d scales with richness or mass of the system

Rich Abell Clusters: Bahcall & Soneira 1983 Peacock & West 1992 Postman et al Lee &Park 2000 APM Clusters: Croft et al Lee & Park 2000 EDCC Clusters: Nichol et al X-ray Clusters: Bohringer et al Abadi et al Lee & Park 2000 Groups of Galaxies: Merchan et al Girardi et al LCDM (  m =0.3,  L =0.7, h=0.7) SCDM (  m = 1,  L =0, h=0.5) Governato et al Colberg et al Bahcall et al Galaxy Triplets

Results so far... We select galaxies within 1980 deg 2, with magnitudes 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 -1 Mpc at =0.22. No breaks. We find r o = 4.2 ± 0.4 h -1 Mpc for galaxies and 7.8 ± 0.7 h -1 Mpc for pairs We find d = 3.7 and 10.2 h -1 Mpc for galaxies and pairs respectively. LCDM provides a considerable better match to the data Follow-up studies dN/dz and photometric redshifts. Select groups over > 3000 deg 2 area from SDSS

Clustering evolution with redshift. Results from MUSYC Collaborators N. 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 deg 2, 4 fields (eHDFS, CDF-S, SDSS , ) 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 r 0 (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:

MASS, z=0 GALAXIES, z=0 MASS, EVOLUTION MOCKSMOCKS

RESULTS: Correlation length Halo masses Bias factors

Comparison with VVDS ( Le Fevre et al. 2004) and CNOC2: This work

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 Survey Measures clustering evolution up to z  0.6 for Late and Early type galaxies deg. 2 ~ 3000 galaxies 0.1 < z < 0.6 Redshifts for objects with R c < 21.5 R c band, M R < -20  r p <10h -1 Mpc SEDs are determined from UBVR c I c photometry

Projected Correlation Length

dlogN/dm=0.46 Turnover at r *  20.8 De-reddened Galaxy Counts Thin lines are counts on each of the 12 scanlines