Weak Lensing and Galaxy Dynamics in SDSS Groups and Clusters

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Weak Lensing and Galaxy Dynamics in SDSS Groups
and Clusters

• Tim Mckay, Ben Koester, Gus Evrard University of
  Michigan
• Jim Annis Fermilab
• Risa Wechsler, Erin Sheldon, Sarah Hansen, Erwin
  Lau University of Chicago
• Dave Johnston Princeton University
• Ryan Scranton University of Pittsburgh

OSU Meeting on Lensing, Dark Matter and Dark
Energy
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What to do with weak lensing measurements?

• Lensing uses distant sources to probe the
  intervening universe
• Reveals the mass as expressed in geometry
• Much of the signal comes from zlt1
• Lensing signals alone can be studied
• Cosmic shear etc., intrinsically noisy

• Other information about the intervening universe
  is available
• Galaxies, groups, clusters, and LSS also reveal
  the mass distribution
• These labels can be observed at high S/N and are
  observationally rich

Focus here on galaxy clusters individually
identifiable halos
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Galaxy cluster detection

• Clusters appear in many guises
• Concentrations of galaxies
• Pools of hot gas
• SZ decrements
• Peaks in shear maps
• To theorists
• Dark matter halos

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Finding clusters in SDSS data

• Early type galaxies w/old stellar populations and
  uniform colors label groups and clusters
• Color maps to redshift
• Widefield multicolor CCD data has revitalized
  optical cluster finding
• Clustering in position-color space eliminates
  projection
• Cluster finder measures position of BCG,
  redshift, and richness (Ngals)
• Detection thresholds very low (just a few
  galaxies)

Z0.165
SDSS image of Abell 1553
SDSS data is great for this photo spectro
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Example color cluster images from the SDSS
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(No Transcript)
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SDSS DR3 maxBCG catalogs
dN/dNgals
Ngals richness function

• 5000 sq. degrees of DR3 sky
• 800,000 groups, clusters of 1-100 Ngals
• 0.05 lt z lt 0.3
• 22,000 with Ngals gt 10
• 1,600 Ngals gt 20
• Very close to volume-limited

Ngals
?z 0.015
BCG photometric z
Catalogs originally built by Jim Annis at
Fermilab. DR3 catalogs by Ben Koester at Michigan
Photo-z
BCG spectroscopic z
24,000 BCG redshifts
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Completeness tests
recovered
Cluster redshift
Annis FNAL
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What to do with 22,000 clusters?

• Measure mean properties vs. richness
• Cluster-galaxy correlation function galaxy
  content, and mass through dynamics
• Cluster-mass correlation function mass through
  lensing

• These measurements provide direct information
  relating the cluster properties to dark matter
  mass distribution
• This exercise is a precursor for future high-z
  (DE oriented) cluster cosmology projects

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Cluster-mass correlation functions mass through
weak lensing

• Measurements of shear and lens geometry yield
  surface mass density contrast

Lens geometry
100 Kpc
Shear
10 Mpc
Erin Sheldon in prep
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Cluster-mass correlation functions mass through
weak lensing
Erin Sheldon in prep
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Cluster-mass correlation functions mass through
weak lensing
NFW fits

• This ?? measurement can be inverted to obtain
  M(r) in a non-parametric way
• This yields virial mass and radius estimates for
  each richness bin
• High S/N measurements extend beyond Rvir

4.5x1013 M?
Ng10
0.10
1.0
10.0
r (Mpc/h)
5x1014 M?
Ng45
0.10
1.0
10.0
r (Mpc/h)
Erin Sheldon in prep Dave Johnston inversion
methods in prep
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Cluster-mass correlation functions mass through
weak lensing

• This is the full cluster mass correlation
  function
• Part is due to the cluster, and part is the due
  to environment?
• In halo models one halo and two halo terms

NFW fits
PS?mb
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Cluster mass functions through weak lensing
In principle we can measure a kind of mass
function very precisely number selected vs.
observable mass indicator The problem we need
very precise predictions of exactly what we
measure
There are vertical error bars here.
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Cluster-galaxy correlations galaxy density
profiles and cluster R200

• Assume all galaxies along line of sight are at
  cluster redshift
• Compute r? in Mpc and Mabs for all
• Subtract distribution measured around random
  points
• Do this in richness bins

Follow profiles until density is 200x mean galaxy
density. Use this to define a size-richness
(R200N vs. Ngals) relation
Hansen et al., astro-ph/0410467
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Cluster-galaxy correlations Size richness
relation
R200 ? Ngals0.57
Hansen et al., astro-ph/0410467
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Cluster-galaxy correlations dynamical structure
and mass

• Many BCGs have spectroscopic redshifts
• For each, search for any other nearby redshifts
• Measure ?v vs. R?to examine velocity structure

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Ng1 ?v144
Ng2 ?v253
Ng6 ?v352
Ng9 ?v374
Measure ?diff within a projected R200 for each
richness
Ng36 ?v815
Ng25 ?v670
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Cluster-galaxy correlations dynamical structure
and mass
?diff 150Ngal0.48
?diff
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Where are we?

• Very large cluster sample
• Well measured lensing signals, galaxy profiles
  (and LFs), a galaxy dynamics
• Lensing signals permit non-parametric mass
  estimation

• These precise measurements need precise
  prediction for interpretation
• Theory predicts things we cant observe (dN/dM200
  for halos, not detected clusters)
• We need simulated universes to observe

Monte Carlo is required to allow comparison of
theory to data at the observable level!
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Simulating complex physics
Galaxy cluster observations
Collider observations

• N-body dark matter simulations well developed
• Galaxy formation is complex
• Directly simulate dark matter and insert
  realistic galaxies with constraints from data

• B-quark production diagrams are well understood
• Jet formation is complex
• Directly simulate collisions and insert realistic
  jets with constraints from data

In both cases this is done because of complexity
not unknown physics
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Simulations for cluster finding

• Start with N-body realization of the dark matter
  universe
• Insert the galaxies we know exist (, LF, colors
  from SDSS)
• Do the insertion to match luminosity dependent
  galaxy clustering

Simulated SDSS galaxy distribution
Wechsler will discuss details later
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The Annis maxBCG sample
SDSS galaxy distribution (Those with spectra)
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SDSS cluster distribution (BCGs with spectra)
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Simulated galaxy distribution (with spectra)
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Simulated spectroscopic cluster sample (BCGs with
spectra)
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Could these simulations be right?
Simulated (halo velocity)
Real
?diff
N-body mass threshold
Test against observables we didnt tune for
cluster-galaxy correlations in velocity space
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What do simulations tell us?

• They allow identification of identified clusters
  with DM halos
• Includes all details
• Predicts observables dN/dNgals, ?diff vs. Ngals,
  ?? vs. Ngals, clustering vs. Ngals
• Ultimately provides M200 vs. Ngals

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Conclusions

• SDSS maxBCG cluster catalogs are
• Very large
• Testably complete and pure
• In hand
• We have established simulations capable of
  predicting cluster observables

• Testing simulations against data in many ways
• Producing many measurements of cluster properties
  and observable scaling relations
• Cluster profiles, scaling laws, mass functions
  soon

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Cluster-galaxy correlations luminosity functions
Unsubtracted around clusters
Provides cluster LF vs. richness, measured within
R200. Can be done vs. radius, in different
colors, etc
Unsubtracted around random points
All galaxies
Background subtracted around clusters
30 lt Ngals lt 66
BCGs excluded
Hansen et al., astro-ph/0410467
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Cluster-galaxy correlations dynamical structure
and mass
M200?2R200?diff2/G
4.5x1013 M?
Lensing and dynamical masses are in reasonable
agreement
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Cluster-mass correlation functions mass through
weak lensing
Virial mass vs. Ngals scaling directly from
lensing measurements
3.8x1013 M?
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Finding red sequence clusters

• Clustering in position-color space essentially
  eliminates contamination by projection
• Gladders Yee (2000), Goto et al. (2001), Annis
  et al. (2004)
• E/SO ridgeline provides extremely accurate
  (?zlt0.02) photometric redshift
• Red sequence in place throughout SDSS volume and
  beyond, to zgt1.

E/SO ridgeline
g-r color
i magnitude
Red sequence galaxies at z1.27 (van Dokkum et
al, 2000)