On ‘cosmology-cluster physics’ degeneracies and cluster

surveys(Applications of self-calibration)

Subha MajumdarCanadian Institute for Theoretical Astrophysics

Distant Clusters of GalaxiesRingberg Castle Workshop, Oct 24-28, 2005

Graham Cox, Joe Mohr, Howard Yee, Mike Gladders, Henk Hoekstra, Jose Diego

Distant Clusters of Galaxies

Ringberg Workshop 2005

Cluster Redshift Distribution: cosmological sensitivity

Cluster redshift distribution probes:

dN(z)dzd

dVdzd

n z cH z dA

2 1 z 2 dM f M dn M , z dM0

1) volume-redshift relation : (H(z))

2) abundance evolution --- growth function : (H(z))

density fluctuation: 8, ns

3) cluster structure and evolution.

f(M) contains the connections between observables and mass (which connects to theory/simulations).

Distant Clusters of Galaxies

Ringberg Workshop 2005

Mass-observable relations...

)1()()( 3/2 zzEMAfS SZ

Option 1: Existing cluster catalogs give us an idea of these scalings.However, much difference between observational and simulation results.

A biased (incorrect) scaling between mass-observable may give us tight constraints but wrong cosmological parameter estimates. (Pratt’s talk: plot of sigma8 as fn of M-T normalization)

Two simple scaling relations:

Example 1: SZ flux scaling reln (Benson etal 2004, Motl etal 2005)

Example 2 : Galaxy Bgc scaling relation (Yee & Ellingson 2003, Hicks etal 2005)

)1( zBAM gcBgc

Distant Clusters of Galaxies

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Mass-Observable relation continued...

Option 2: Self-Calibration (Majumdar & Mohr 2003,2004; Hu 2003)

Take cluster parameters (Amp, ) as completely unknown.If there are enough clusters in a sample then it is possible to determinecosmology and cluster scaling parameters from the same data. Itappears that all large yield surveys have this capability!!

Crucial Assumption: scaling relations exist (tractable & preferably simple)Smaller assumption: simulations give tight mass fn (dn/dM)

some universality of cluster DM structure (NFW)

It is also possible to determine unknown evolution () from the same databut at the price of having weaker constraints.

Distant Clusters of Galaxies

Ringberg Workshop 2005

More on self-calibration (unashamedly copied from one of Joe Mohr’s astro-ph submissions )

The implications for self-calibration are quite broad. It is more than calibratingthe mass-observable relation from observations!

Uncertainties in absolute calibration (perhaps due to uncertainties in effective areaof the telescope) will self-calibrate out.

A redshift or mass dependence in AGN contamination will self-calibrate out mainlyin (for Xray surveys).

Angular filtering in SZ surveys will introduce redshift dependent errors, but that would be taken care by .

Systematic photometric redshift uncertainties will self-calibrate out (again in )

Systematic redshift dependence of completeness in Bgc (as proxy for mass) will self-calibrate out as a non-standard evolution .

Even, redshift dependence of theoretical halo-mass dependence will self-calibrateout as one can solve for a scaling between simulation defined halo mass and cluster observable.

The functional form of the sacling can be checked with observed and predictedmass functions.

Distant Clusters of Galaxies

Ringberg Workshop 2005

‘Self-Calibration’ Techniques:0. Just let dn/dz information self-calibrate the survey with simple scaling reln.

However, extra informations help!

1.Limited mass follow-up (using XRay temp/weak lensing) (Majumdar & Mohr 2003,2004, Majumdar 2005)2.Using shape of mass-function in redshift slices (Hu 2003)3.Using the cluster power spectrum and P(k) oscillations (Majumdar & Mohr 2004, Hu & Haiman 2004, Huetsi 2005)4.Adding information from counts-in-cell (Lima & Hu 2004, 2005)5.Time or flux slicing of survey: using shape of dndz

(Majumdar 2005)6. For SZ surveys, adding SZ rms distortions to number counts

(Diego & Majumdar, 2004)

Scatter: As long as scatter is ~25%, self-cal is possible but weaker constraints(Levine etal 2002, Lima & Hu 2005, Cox&Majumdar, in prep)

Bias : of more concern, must be ~10% (Lima & Hu 2005)

Distant Clusters of Galaxies

Ringberg Workshop 2005

Doing cosmology AND cluster physics with actual data: RCS1

RCS: the resultsM = 0.34 +/- 0.064 (0.29 +/- 0.07)

8 = 1.05 +/- 0.14 (0.9 +/- 0.1)

log(ABgc) = 10.95 +/- 0.78(z=0.3) (10.05 +/- 0.89)

= 1.64 +/- 0.28 (1.58 +/- 0.27)

= 0.28 +/- 0.35 (-0.5 +/- 0.5)

RCS1: the survey 76 deg2, Bgc > 300, -detection > 3.3 Bgc < 0.5, z= 0.2 – 1, ~1100 clusters Completeness fraction corrected from simulated catalogs + Yeong Loh’s estimate of evolution of blue fraction with redshift.

Changing redshift dependent completeness does not change cosmology much which is a big endorsement of the self-calibration technique!

Distant Clusters of Galaxies

Ringberg Workshop 2005

Degeneracies in RCS1 ...

Distant Clusters of Galaxies

Ringberg Workshop 2005

The prospect of doing ‘precision’ cosmology AND cluster physics (SPT as an example of a SZ survey)

10 parameter MCMC analysis (going beyond simple Fisher Matrix)

SPT: the survey 4000 deg2, 10 mJy@150 GHz z=0 – 1.3, 22000 clusters

SPT: the forecasts

M = 0.261 +/- 0.0258 = 0.935 +/- 0.071w0 = -1.059 +/- 0.352wa = 0.284 +/- 0.768log(ASZ) = -16.72 +/- 0.423 = 1.68 +/- 0.030 = -0.216 +/- 0.713

Cox & Majumdar, in prep

Distant Clusters of Galaxies

Ringberg Workshop 2005

Degeneracies and Constraints (SPT) :

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More on degeneracies (SPT contd.)

Distant Clusters of Galaxies

Ringberg Workshop 2005

Effect of Mass Followup: (SPT as an example, RCS-1 results not too far)

Distant Clusters of Galaxies

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Post Mass-Followup: How do we fare now?10 parameter combined MCMC analysis

SPT survey: dn/dz of 22000 clusters + Independent mass determination of 100 clusters with 30% mass uncertainty.

SPT: the forecastsM = 0.0188 = 0.039w0 = 0.018wa = 0.585log(ASZ) = 0.281 = 0.020 = 0.168

0.0250.0710.3520.7680.4230.0300.713

Cox & Majumdar, in prep

Distant Clusters of Galaxies

Ringberg Workshop 2005

Where do cluster upcoming surveys stand?

Only dN/dz, no extrainformation. Majumdar 2005

Competetive!Complimentary!

Distant Clusters of Galaxies

Ringberg Workshop 2005

ConclusionsSelf-calibrating cluster surveys are possible with large

yield, thus reducing mass-observable uncertainties. Way to do cosmology and cluster physics at the same time.

It is important to understand cosmology-gas physics degeneracies to get accurate constraints. Additional information (like limited independent mass followup) can break these degeneracies. We need

observed lensing masses. We need simulations connecting lensing masses with other observables.

First results from RCS shows that it is now possible to do cosmology and cluster physics with cluster dndz. Moreover, agreement with RCS results with other probes comes as an important endorsement for self-calibration. These results also endorse the promise of doing precision cosmology with upcoming surveys (whether in Optical, SZ or Xray)