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Small Galaxy Groups Clustering
and the Evolution of Galaxy Clustering
Leopoldo InfantePontificia Universidad Católica de Chile
Bonn, June 2005
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Talk Outline
Introduction
The Two-point Correlation Function
Clustering of Small Groups of Galaxies – SDSS results
Evolution of Clustering – MUSYC results
Conclusions
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Rich Clusters
Groups
Galaxies
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How do we characterizeclustering?
Correlation Functionsand/or
Power Spectrum
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Random Distribution
1-Point
2-Point
N-Point
Clustered Distribution
2-Point
r
dV1
dV2
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Continuous Distribution
Fourier Transform
Since P depends only on k
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2-Dimensions - Angles
Estimators
In Practice
AA BB
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r0 vs dc
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 (r0)
On the other, we need to characterize the structure in a statistical way Number density (nc) Inter-system distance (dc)
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The co-moving Correlation Length
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Proper Correlation length
Proper Correlation distance
Clustering evolutionindex
Assumed Power Law 3-D Correlation Function
Assumed Power Law Angular Correlation Function
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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 ModelThe Redshift Distribution of the Sample dN
dz
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Proper Correlation Length and Limber’s inversion
12
1 3
00 2
0
( ) (1 )dN
H z x z dzdz
r A CdN
dzdz
3
0 0( ) (1 ) (1 )H z z
1
( )
dx
dz H z
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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 rp,
Problem; choose upper integration limit
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Inter-system distance, dc
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systemsc
Nn
V
1/31
cd n
Mean separation of objects
Space density of galaxy systems
As richer systems are rarer, dc scales with richness or mass
of the system
Proper Volume
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CLUSTERING Measurements from Galaxy
Catalogsand
Predictions from Simulations
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Galaxy Clustering: Two examples
APM angular clusteringSDSS spatial clustering
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APM
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Sloan Digital Sky SurveySloan Digital Sky Survey
•2.5m Telescope•Two Surveys
•Photometric•Spectroscopic
•Expect•1 million galaxies with spectra•108 galaxies with 5 colorsCurrent resultsCurrent results
DR2 2500 deg.2
200,000 galaxies, r<17.7Median z 0.1
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SDSS DR2
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Zehavi et al., 2004
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Clustering of Galaxy Clusters
Richer clusters are more strongly clustered.
Bahcall & Cen, 92, Bahcall & West, 92
However this has been disputed: • Incompleteness in cluster samples (Abell,
etc.)• APM cluster sample show weaker trend
3
0.40.4o c
c
r dn
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Galaxy Groups Clustering
Simulations2dFGG clusteringLCDCS clustering
SDSS DR2 clustering
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N body simulations
• Bahcall & Cen, ‘92, ro dc
• Croft & Efstathiou, ‘94, ro dc but weaker
• Colberg et al., ‘00, (The Virgo Consortium)– 109 particles– Cubes of 3h-1Gpc (CDM)
CDM =0.3 =0.7 h=0.5 =0.17 8=0.9
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CDMdc = 40, 70, 100, 130 h-1Mpc
Dark matter
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2dF data, 2PIGG galaxy groups sampleEcke et al., 2004
19,000 galaxies 28,877 groups of at least 2 members<z> = 0.11
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Padilla et al., 2004
Galaxies2dFGRS
Groups2PIGG
1/31
cc
dn
2 2ps r
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Las Campanas Distant Cluster Survey
• Drift scan with 1m LCO.• 1073 clusters @ z>0.3• 69 deg.2
• 78o x 1.6o strip of the southern sky (860 x 24:5 h-1 Mpc at z0.5 for m=0.3 CDM).
• Estimated redshifts based upon BCG magnitud redshift relation, with a 15% uncertainty @ z=0.5.
Gonzalez, Zaritsky & Wechler, 2002
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Gonzalez, Zaritsky & Wechler, 2002
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1/31
cc
dn
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Clustering of
Small Groups of GalaxiesfromSDSS
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• 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 ro and d=n-1/3 Clustering Properties
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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.
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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.
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In practice, how do we measure HOD?
Detect pairs, triplets, quadruplets etc. n2 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
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Collaborators:
M. StrausN. PadillaG. GalazN. Bahcall& Sloan consortium
OUR PROJECT: We are carrying out a project to find galaxies in small groups using SDSS data.
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The DataSeeing 1.2” to 2”Area = 1969 deg2
Mags. 18 < r < 20
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Selection of Galaxy Systems
Find all galaxies within angular separation between 2”<<15” (~37h-1kpc) and 18 < r < 20
Merge all groups which have members in common.Define a radius group: RG
Define distance from the group o the next galaxy;
RN
Isolation criterion: RG/RN 3
Sample
3980 groups with 3 members pairs 68,129
Mean redshift = 0.22 0.1
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Galaxy pairs, examples
Image inspection showsthat less than 3% are spurious
detections
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Galaxy groups, examples
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Results
A = 13.54 0.07 = 1.76
A = 4.94 0.02 = 1.77
arcsec arcsec
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Results
galaxies
tripletspairs
•Triplets are more clustered than pairs•Hint of an excess at small angular scales
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Space Clustering Properties
-Limber’s Inversion-– Calculate correlation amplitudes from ()– Measure redshift distributions, dN/dz– De-project () to obtain ro, correlation lengths– Compare ro systems with different HODs
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The ro - d relation
3/11
n
d
Correlation scaleAmplitude of the
correlation function
Mean separationAs richer systems are rarer,
d scales with richness or mass of the system
12
1 3
00 2
0
( ) (1 )dN
H z x z dzdz
r A CdN
dzdz
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Rich Abell Clusters:•Bahcall & Soneira 1983•Peacock & West 1992•Postman et al. 1992•Lee &Park 2000
APM Clusters:•Croft et al. 1997•Lee & Park 2000
EDCC Clusters:Nichol et al. 1992
X-ray Clusters:•Bohringer et al. 2001•Abadi et al. 1998•Lee & Park 2000
Groups of Galaxies:•Merchan et al. 2000•Girardi et al. 2000
LCDM (m=0.3, L=0.7, h=0.7)SCDM (m = 1, L=0, h=0.5)Governato et al. 2000Colberg et al. 2000Bahcall et al. 2001
Galaxy Triplets
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Results so far...We select galaxies within 1980 deg2, withmagnitudes 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-1Mpc at <z>=0.22. No breaks.•We find ro= 4.2 ± 0.4 h-1Mpc for galaxies and 7.8 ± 0.7 h-1Mpc for pairs•We find d = 3.7 and 10.2 h-1Mpc for galaxies and pairs respectively.•LCDM provides a considerable better match to the data
Follow-up studiesdN/dz and photometric redshifts.
Select groups over > 3000 deg2 area from SDSS
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Clustering evolution with redshift.
Results from MUSYC
CollaboratorsN. Padilla, S. Flores, R. Asseff, E.
Gawiser, & d. Christlein
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Evolution of the bias factor (Seljak & Warren
2004)
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Evolution of the clustering of the dark-matter in a Lambda-CDM
Cosmology
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MUSYC:• Multiwavelength survey by Yale-Chile• 1 deg2, 4 fields (eHDFS, CDF-S, SDSS
1030+05, 1256+01)• 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
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Real and Mock HDF-S:
• MUSYC
• Hubble Volume
Dark Matter, z=0
Galaxies, z=0
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Redshift distributions in real and Semianalytic mock (at z=0)
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A set of homogeneous subsamples of galaxies in the
HDF-S
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The method: getting r0(z)• First step: calculate for
different errors in redshift:
z=0.0 z=0.1
>1
<1
=1
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Correlation function in redshift-space is not useful in this analysis:
The projected correlation function can be made stable:
1300
0
2 ,h Mpc
d
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MA
SS
, z=
0G
AL
AX
IES
, z=
0M
AS
S, E
VO
LU
TIO
N
MOCKS
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RESULTS:
• Correlation length• Halo masses• Bias factors
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Comparison with VVDS (Le Fevre
et al. 2004) and CNOC2:
This work
6
4
2
0
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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
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FIN
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SDSS DR1 18 < r < 20
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CNOC2 SurveyCNOC2 Survey
Measures clustering evolution up to z 0.6 for Lateand Early type galaxies.
1.55 deg.2
~ 3000 galaxies 0.1 < z < 0.6
Redshifts for objects with Rc< 21.5Rc band, MR < -20 rp<10h-1Mpc
SEDs are determined from UBVRcIc photometry
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Projected
Correlation Length
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dlogN/dm=0.46Turnover at r* 20.8
De-reddened Galaxy Counts
Thin lines are counts on each of the 12 scanlines
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