How to find groups of galaxies.III A volume-limited sample in the SDSS DR6 : pro et contra
Erik Tago
J.Einasto, E.Saar, E.Tempel, M.Einasto, P.Heinamäki, P.Nurmi Tartu Observatory, Tuorla Observatory Tartu-Tuorla meeting Motel Waide, Oct 2-3, 2008
In the beginning God created the heaven and the earth In the beginning God created the heavens and the earth
In the beginning of the 21.century the Sloan Survey team created the Digital Sky
To Read : Skies Sky of main galaxies Sky of Luminous red galaxies Sky of quasars DAS sky , CAS sky etc etc etc My sky in this report : sky of groups of galaxies x
Contents
1) Introduction: related references, and recent examples why groups are important for cosmology 2) Briefly about the data used 3) Our groupfinder : modified FoF 4) Problems of volume-limited samples of groups 5) Our volume-limited samples in SDSS Data Release 6, a few applications
1.Introduction: 1.1 Historical references
E.Tago et al. How to find a group of galaxies. I. A new 2dF GRS group catalogue (2005) (Astron.Nach. 327, No.4, 365, 2006) II. Groups of galaxies in the SDSS DR5 (2007) (A&A 479, 927, 2008) These both papers were dedicated to flux limited samples : they were limited by apparent magnitude, therefore, at various distances different absolute magnitude limit has been applied.
1.2 Groups and clusters are important for cosmology
Dark Matter Halo (DMH) as a widely accepted paradigm. An example that dynamical and evolutionary state of clusters is in contradiction with DMH embedding cluster. 1) Coziol etal 2008 : The dynamical state of brightest cluster galaxies and the formation of clusters. A sample of more than 1400 clusters shows that large relative peculiar velocity of Brightest Cluster Galaxies is in contradiction with DMH which dominates formation and evolution of clusters, and, rather supports the scenario of merging groups .
Multi-nucleus cluster of galaxies : an evidence for group merging
CL0958-4702 Spitzer (NASA)
FoF result for 2dF GRS at A933 cluster
1.2b Groups and clusters are important for cosmology
2) Plionis et al 2008 (dynamical evolution of ACO clusters; dependence on richness) 3) The “Bullet” cluster
“Bullet cluster” of galaxies – encounting clusters
SDSS DR6 : Data
Total area 9583 sq. deg 287 million unique objects Imaging Average wavelengths and magnitude limits ugriz 3551Å 4686Å 6165Å 7481Å 8931Å 22.0 22.2 22.2 21.3 20.5
SDSS DR6 imaging sky coverage
SDSS DR6 sky coverage by spectroscopy
SDSS DR6 spectroscopy
Total area 7425 sq. deg Galaxies 790,860 Quasars (z <2.3) 90,108 Quasars (z ≥2.3) 13,539 Limit in Petrosian r mag <17.77 Redshift accuracy 30 km/s (main gal)
How to define groups of galaxies
• There is a problem because if to start from a group defined in flux-limited ces then after FoF procedure redshift (distance) change and in fact galaxy may be excluded from the sample
Problem with goups
GROUPFINDER METHOD
Cluster analysis , Friends-of-Friends method (FoF)
Hierarchy in the world of galaxies: Groupfinder as Equalizer
• • • • • Isolated galaxies Pairs of galaxies Local group N=3 Sp+ 40 dw Clusters of galaxies Shapely supercluster : includes 33 Abell clusters
Interacting pair of galaxies The Mice in the Coma cluster 10 kpc
The Coma cluster 3 Mpc
Selection efects and corrections
correction to apparent magnitude K correction E correction
to redshift CMB motion COMOVING distance
From SDSS DR6 FITS data to VOLUME LIMITED GROUP CATALOGUE Applied Procedures :
1) Read selected columns from FITS data file into ASCII table 2) Select sample galaxies: a) discard raw error (n=585990) b) reject duplicate redshifts (n=575544 nde1=1350 nde2=9096) c) apply flux-limited sample limits (n=481090) 0.009 < z_ori < 0.2 12.5 < r_mag < 17.7 -75 < lambda < +75 -40 < eta < +45
Applied Procedures
3) Apply K+ E correction to magnitudes 4) apply CMB correction to redshifts and find comoving cosmological distances 5) apply FoF method to obtain flux-limited sample of groups (separate tables for clusters and galaxies)(nclu1=263360, nclu2=64989) 6) Find volume-limited sample limits 7) Select volume-limited samples of galaxies 8) Apply FoF method to each sample to obtain volume-limited samples of groups
Distribution of DR6 galaxies in RA and DEC coordinates
Our full DR6 galaxy sample in lambda and eta coordinate
Our full flux-limited sample of DR6 galaxies: absolute magn in r vs redshift
Difference between K+E corrected and uncorrected M_r mag
FoF linking length scaling law as a function of redshift
Lum-Dist relation of four volume-limited samples in the SDSS DR6
Velocity dispersion vs distance for four volume-limited samples
Maximum projected size in sky vs distance in DR6 vol.-lim. Groups
Richness vs distance in DR6 vol.lim. groups
Number density of galaxies in 4 vol.-lim. samples DR6
Group number density vs distance
What kind of problems ?
• Distorsions in redshift space Selection effects depending on distance due to flux limited samples : a) number density decrease b) richness decrease c) volume effect – distant clusters are larger • Luminosity-density relation in groups and clusters
Problems2
• Restrict samples by low (SDSS incomplete) and high redshift • Luminosity corrected by weigth • Perform FoF in two direction – radial and transversal • Linking Length scaling
Groupfinder and catalogue: our case
• We use Friends of Friends (FoF) groupfinder (cluster analysis) • Selection effects in flux limited samples • How to overcome them ?
applying linking length LL scaling
calibrating observed groups by shifting to higher distances. For volume limited samples LL scaling by dilution of closer subsample.
The steps of LL scaling
• Selection of initial nearby groups • Shift the groups step by step to larger distances and calculatate their properties • Drop the group members which do not satisfy visibility conditions for the catalogue luminosity window using Minimal spanning tree method determine new LL which is needed to keep group in one at new distance Find LL law and perform final FoF
Lum-Dist relation of four volume-limited samples in the SDSS DR6
Improvement of useful fraction of galaxies for volume-limited groups
• One of the worst properties of volumelimited samples is a low fraction of galaxies involved in groups if to compare initial data • solution-could be a larger number of samples spaced for example at every 0.5 mag and etc etc
8 volume-limited samples
Results
• 64989 flux-limited groups in the SDSS DR6 • 4 volume-limited samples of groups in the SDSS DR6 : ( -18.00 … -19.00) Nclu= 3300 ( -18.00 … -20.00) Nclu= 5000 ( -18.00 … -21.00) Nclu= 10000 ( -18.00 … -22.00) Nclu= 7000
Benefit for astronomy, applications
• Comparison of volume-limited samples with numerical simulations ( P.Nurmi, P.Heinämäki) • Application for creation of supercluster samples (M.Einasto et al) • Application for luminosity density field (J.Einasto et al) • Comparison with QSO distribution (H.Lietzen et al)