How to find groups of galaxies.IIIA volume-limited sample

in the SDSS DR6 : pro et contraErik 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 galaxiesSky of Luminous red galaxiesSky of quasarsDAS sky , CAS skyetc etc etc

My sky in this report : sky of groups of galaxiesx

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

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)

1.Introduction: 1.1 Historical references

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 areimportant 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 table2) 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 samplein lambda and eta coordinate

Our full flux-limited sample ofDR6 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 distancefor 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 volume-limited 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)