How to find groups of galaxies'III A volumelimited sample in the SDSS DR6 : pro et contra

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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

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In the beginning God created the heaven and the
earth

• In the beginning God created the heavens
  
• and the earth

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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

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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

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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)

• Introduction
• 1.1 Historical references

II. Groups of galaxies in the SDSS DR5 (2007)
(AA 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.
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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 .

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Multi-nucleus cluster of galaxies an evidence
for group merging
CL0958-4702 Spitzer (NASA)
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FoF result for 2dF GRS at A933 cluster
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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

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Bullet cluster of galaxies encounting clusters
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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

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SDSS DR6 imaging sky coverage
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SDSS DR6 sky coverage by spectroscopy
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SDSS DR6 spectroscopy

• Total area 7425 sq. deg
• Galaxies 790,860
• Quasars (z lt2.3) 90,108
• Quasars (z 2.3) 13,539
• Limit in Petrosian r mag lt17.77
• Redshift accuracy 30 km/s (main gal)

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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

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Problem with goups
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GROUPFINDER METHOD

• Cluster analysis , Friends-of-Friends method
  (FoF)

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Hierarchy in the world of galaxies Groupfinder
as Equalizer

• Isolated galaxies
• Pairs of galaxies
• Local group N3 Sp 40 dw
• Clusters of galaxies
• Shapely supercluster includes 33 Abell clusters

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Interacting pair of galaxies The Mice in the
Coma cluster 10 kpc

The Coma cluster 3 Mpc
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Selection efects and corrections

• correction
• to apparent magnitude
• K correction
• E correction
• to redshift
• CMB motion
• COMOVING distance

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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 (n585990)
• b) reject duplicate redshifts (n575544
  nde11350
• 
  nde29096)
• c) apply flux-limited sample limits
  (n481090)
• 0.009 lt z_ori lt 0.2
• 12.5 lt r_mag lt 17.7
• -75 lt lambda lt 75 -40 lt eta lt
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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)(nclu1263360, nclu264989)
• 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

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Distribution of DR6 galaxies in RA and DEC
coordinates
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Our full DR6 galaxy samplein lambda and eta
coordinate
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Our full flux-limited sample ofDR6 galaxies
absolute magn in r vs redshift
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Difference between KE corrected and uncorrected
M_r mag
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FoF linking length scaling law as a function of
redshift
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Lum-Dist relation of four volume-limited samples
in the SDSS DR6
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Velocity dispersion vs distancefor four
volume-limited samples
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Maximum projected size in sky vs distance in DR6
vol.-lim. Groups
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Richness vs distance in DR6 vol.-lim. groups
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Number density of galaxies in 4 vol.-lim. samples
DR6
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Group number density vs distance
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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
• 
  

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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
  
  

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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.

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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

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

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8 volume-limited samples
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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

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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)