Talk Overview

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Talk Overview

• Over view of methods of cross-correlation weak
  lensing

• New results from the SDSS MaxBCG Cluster catalog
• Stacked weak lensing mass profiles
• Stacked dynamical measurements

• Measurement of
• mass richness relation
• the scatter in the mass richness relation
• halo profiles fits and scaling relations

• Cosmological constraints using these methods for
  this
• Data-set as well as future data sets

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Cosmology from Clusters
Cluster number counts are a strong function of
sigma_8 and Omega_M
Variation with Sigma_8
Variation with Omega_M

• This requires that you can
• Find Clusters with an understandable selection
  function
• Calibrate the masses of the clusters -gt weak
  lensing

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Cross-correlation lensing
Multiple galaxy clusters
Multiple background (source) galaxies
Average the tangential shear over all
lens-source Pairs for some annulus R
R
A stacking method
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What is measured with weak lensing around
clusters?
Centered on galaxy clusters
3D density
Average mass density of Universe
Lensing is only sensitive to the projection of
mass
2D density
a non-local equation
And the observable tangential shear
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Inversion methods
(Johnston et al. 2007)
differentiate this
and this local equation is useful only because
Von Zeipels formula (1908, from globular cluster
work)
An Abel type deprojection
This assumes spherical symmetry which should
be the case for a stacked sampled of clusters
There exists a similar formula for the mass
profile M ( r )
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SDSS galaxy clusters - The MaxBCG catalog
A new red sequence optically selected clusters
catalog from the SDSS data (Koester et al 2007).
Colors give a good photoz (redshift estimate)
Largest galaxy clusters catalog to date by about
a factor of 10 500,000 group/clusters detected
to lowest richness 20,000 over 1013 solar
masses
Redshift range z 0.05 to 0.3 so probes the low
z universe
All clusters has a Photometric redshift, z, and
two Measures of richness

• N200 - Number of galaxies
• L200 - Total luminosity

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Lensing and Inversions Results for one richness
bin
The measured shear
The inverted quantities
Can obtain virial masses
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NFW Halos and virial masses
Universal halo profiles are a generic
prediction of CDM simulations (Navarro, Frenk
White 1997)

or
A two parameter model, usually re-parametrized by
is radius at which
And concentration parameter
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One halo term
Halo model decomposition
Two-halo term
Three parameter fit
The data seems to Be well fit by the Halo model
Is predicted from Simulations to be a Universal
2-parameter Function - The NFW profile
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A more complicated model for the profile
1) A point-mass term to model stars
2) The NFW profile for correctly centered
clusters
3) The NFW convolved with a Gaussian to model
the clusters with Non-central or miscentered
clusters
4) The two-halo term for the contribution of
neighboring clusters (halos)
This is a 6 parameter model!
There are also various other corrections
needed Profiles are fit with an MCMC fitting
routine
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6-parameter fit for one richness bin
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6-parameter fit for one richness bin
Point mass term
NFW correctly centered
NFW convolved with a Gaussian Miscentered Clusters
Sum of all
Two-halo term
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Halo fits for the 12 N200 richness bins
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Mass-richness relations
N200 binning
L200 binning
These mass-richness relations allow a mass
calibration of the entire sample
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The Mass Function
Not sufficiently calibrated This assumes a
Volume-limited sample (I.e. no selection
function)
Our official result will be Project led by
Eduardo Rozo (Chicago)
Dominant errors will be selection function
correction and sample variance
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NFW parameter scaling relations
Halo Concentration
The drop off with mass is a generic prediction of
CDM structure formation
Bias or Amplitude of two-halo term
Increase with mass also A generic prediction
of CDM structure formation
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Some attempts to model our c(M) relation
Doug Rudd (Chicago) student of Kravtsov
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Dynamical measures of mass
Our main alternative way of measuring mass
Stack the velocity differences of satellite
galaxies around The BCG
Project lead by Tim McKay and student Matt
Becker (Michigan)
Simplest Method fit a Gaussian plus a constant
However there is likely to be a spread of mass
and so a spread in sigma
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Velocity histograms can be fit with a
mixture-model of Gaussians
S - lognormal scatter in velocity dispersion
Becker et al. (astroph Thursday) Has about 5
algorithms For determining

• The mean sigma
• The scatter in sigma

Most info is in the second And fourth moments
I.e. Variance and kurtosis
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Velocity histograms for different cluster
richness bins
Richer clusters have wider velocity histograms
indicating higher mass
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Main Results
Scatter decreases With richness
Mean velocity dispersion (Mass) increases with
richness
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Lensing versus dynamical mass measurements
Velocity dispersion converted to mass with Evrard
et al. 2007 formula
Universal relation from DM sims
Weak lensing masses and dynamical masses in
agreement to within 20-30
Any differences can be attributed to any of

• velocity bias
• velocity-to-mass error
• photoz error
• shear calibration error
• mass modeling error
• ????

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Ways of constraining cosmology with clusters

• The cluster mass function
• the most common method

Small scale lensing signal
Large scale lensing signal

• Using the lensing data to remove the bias
• And directly probe the growth of the linear
  correlation function

Measuring both the cluster-mass
correlation Function and the cluster-cluster
correlation function Allows for a direct
measurements of
The linear growth factor

• Measuring baryon wiggles in the cluster shear
  signal

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Measuring the mass function
Harder than you think
Requires understanding

• Mass richness calibration
• Scatter in mass richness relation
• Purity and completeness of sample
• The relationship between halos and clusters

Eduardo Rozo et al. 2007 astroph-0703571 analysis
of SDSS clusters Uses HOD formalism and mock
catalogs to marginalize Over many nuisance
parameters regarding the selection function
With flatCMBSN priors
Main result is
The first result does not include
mass-richness Constraints from Lensing. Lensing
addition is forthcoming
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Large scale cosmological constraints
Weak lensing of clusters gives you a measure of
Cluster auto-correlations gives you a measure of
Can rearrange these two equations to separate
scale dependence from Mass dependence
Should be mass independent and measures the
linear growth factor D(z)
Should be scale independent
Main weakness is that it Will have large sample
variance
Both of these constrain cosmology
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Detecting Baryonic features with Weak Lensing
The baryon bump
The shear profile by itself has a plateau from
BAO but not as prominent and More difficult to
measure
SDSS has good Measurements to 30 Mpc/h
Large area surveys like LSST DUNE, SNAP will be
able to Measure this scale length
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Conclusions

• New weak lensing techniques solving an old
  problem of how to
• calibrate the masses of clusters

• Exciting SDSS cluster science results are
  forthcoming which
• will provide a strong consistency test on
  current LCDM
• cosmological models

• Near term and future missions will have the
  ability to exploit these
• methods much further and should provide a new
  way to probe
• dark energy

• SNAP
• DUNE
• LSST

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The End
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Beyond the SDSS - Whats next?
Future lensing and clusters surveys will be able
to greatly extend the sensitivity of the SDSS
through larger volumes and deeper Measurements
and more lensing source galaxies.

• Near term projects from the ground, Dark Energy
  Survey, Pan-starrs

Jason Rhodes, Mike Seiffert, Lexi Moustakis and I
are investigating ways of Getting JPL/Caltech
involved in these, RTD proposal

• Near term projects from space COSMOS and other
  HST projects

Jason and Caltech group active in COSMOS. We are
beginning to make SDSS-type clusters
measurements in collaboration w. Alexi Leauthaud
and JPL SURF student Greg Haislip (Princeton)
We are making lensing measurements around high
redshift Clusters with data from HST. This is a
piggy-back project of the HSTclusterSN project
headed by Permutters SN group (Berkeley) Involves
JPLers Mark Brodwin, Peter Eisenhardt, Jason
Rhodes SURF student Leyan Lo 20 high redshift
z1 clusters with multiple epoch data

• Long term Plans - JDEM, SNAP, LSST, GRALE

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Constraining Dark Energy with Clusters
These more ambitious experiments allow for better
constraints on parameters And ability to probe
Dark Energy models
Deeper surveys allow for constraints on the
evolution of the Cluster mass function since they
probe earlier cosmic times. They Compliment
other dark energy probes since they are mostly
affected by The growth of structure rather than
expansion rate probes such as SN and BAO
Bahcall Bode (2003)
SDSS - z 0.15 COSMOS - z
0.5 HSTclusterSN z 1.0 SNAP, LSST z 1.5 ?
These WL mass calibration techniques will be
adapted to other cluster finding Methods such as
Sunyaev Zeldovich effect which can find clusters
efficiently To high redshift. Example Dark Energy
Survey will overlap with the South Pole
Telescope SZ survey
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