How to find groups of galaxies . III A volume-limited sample in the SDSS DR6 : pro et contra

1. How to find groups of galaxies.IIIA 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

2. In the beginning God created the heaven and the earth In the beginning God created the heavens and the earth

3. 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

4. Contents • 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

5. 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 Groups of galaxies in the SDSS DR5(2007) (A&A 479, 927, 2008) Introduction: 1.1 Historical references These both papers were dedicated toflux limited samples : they were limited by apparent magnitude, therefore,at various distances differentabsolute magnitude limit has been applied.

6. 1.2 Groups and clusters are important for cosmology Dark Matter Halo (DMH) as a widely accepted paradigm. An example thatdynamical 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 thatlarge relative peculiarvelocity of Brightest Cluster Galaxies is in contradiction with DMH which dominates formation and evolution of clusters, and, rather supports the scenario ofmerging groups.

7. Multi-nucleus cluster of galaxies :an evidence for group merging CL0958-4702 Spitzer (NASA)

8. FoF result for 2dF GRS at A933 cluster

9. 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

10. “Bullet cluster” of galaxies –encounting clusters

11. SDSS DR6 : Data Total area 9583 sq. deg 287 million unique objects Imaging Average wavelengths and magnitude limits ugriz3551Å4686Å6165Å7481Å8931Å 22.022.222.221.320.5

12. SDSS DR6 imaging sky coverage

13. SDSS DR6 sky coverage by spectroscopy

14. SDSS DR6 spectroscopy Total area 7425 sq. deg Galaxies790,860 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)

15. 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

16. Problem with goups

17. GROUPFINDER METHOD Cluster analysis , Friends-of-Friends method (FoF)

18. 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

19. The Coma cluster 3 Mpc Interacting pair of galaxies The Mice in the Coma cluster 10 kpc

20. Selection efects and corrections correction to apparent magnitude K correction E correction to redshift CMB motion COMOVING distance

21. From SDSS DR6 FITS data to VOLUME LIMITED GROUP CATALOGUEApplied Procedures : • Read selected columns from FITS data file into ASCII table • 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

22. 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

23. Distribution of DR6 galaxies in RA and DEC coordinates

24. Our full DR6 galaxy samplein lambda and eta coordinate

25. Our full flux-limited sample ofDR6 galaxies: absolute magn in r vs redshift

26. Difference between K+E corrected and uncorrected M_r mag

27. FoF linking length scaling law as a function of redshift

28. Lum-Dist relation of four volume-limited samples in the SDSS DR6

29. Velocity dispersion vs distancefor four volume-limited samples

30. Maximum projected size in sky vs distance in DR6 vol.-lim. Groups

31. Richness vs distance in DR6 vol.-lim. groups

32. Number density of galaxies in 4 vol.-lim. samples DR6

33. Group number density vs distance

34. 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

35. 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

36. Groupfinder and catalogue: our case • We use Friends of Friends (FoF) groupfinder (cluster analysis) • Selection effects in fluxlimited 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.

37. 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 newLL which is needed to keep group in one at new distance Find LL law and perform final FoF

38. Lum-Dist relation of four volume-limited samples in the SDSS DR6

39. 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

40. 8 volume-limited samples

41. 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

42. 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)