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On ‘cosmology-cluster physics’ degeneracies and cluster surveys (Applications of self-calibration)

On ‘cosmology-cluster physics’ degeneracies and cluster surveys (Applications of self-calibration). Subha Majumdar C anadian I nstitute for T heoretical A strophysics. Graham Cox, Joe Mohr, Howard Yee, Mike Gladders, Henk Hoekstra, Jose Diego. Distant Clusters of Galaxies

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On ‘cosmology-cluster physics’ degeneracies and cluster surveys (Applications of self-calibration)

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  1. On ‘cosmology-cluster physics’ degeneracies and cluster surveys(Applications of self-calibration) Subha Majumdar Canadian Institute for Theoretical Astrophysics Graham Cox, Joe Mohr, Howard Yee, Mike Gladders, Henk Hoekstra, Jose Diego Distant Clusters of Galaxies Ringberg Castle Workshop, Oct 24-28, 2005

  2. Cluster Redshift Distribution: cosmological sensitivity Cluster redshift distribution probes: 1) volume-redshift relation : f(H(z)) 2) abundance evolution --- growth function : f(H(z)) density fluctuation: s8, ns 3) cluster structure and evolution. f(M)contains the connections between observables and mass (which connects to theory/simulations).

  3. Mass-observable relations... 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) 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)

  4. Mass-Observable relation continued... Option 2: Self-Calibration (Majumdar & Mohr 2003,2004; Hu 2003) Take cluster parameters (Amp, a) as completely unknown. If there are enough clusters in a sample then it is possible to determine cosmology and cluster scaling parameters from the same data. It appears 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 (g) from the same data but at the price of having weaker constraints.

  5. 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 calibrating the mass-observable relation from observations! Uncertainties in absolute calibration (perhaps due to uncertainties in effective area of the telescope) will self-calibrate out. A redshift or mass dependence in AGN contamination will self-calibrate out mainly in g (for Xray surveys). Angular filtering in SZ surveys will introduce redshift dependent errors, but that would be taken care by g . Systematic photometric redshift uncertainties will self-calibrate out (again in g) Systematic redshift dependence of completeness in Bgc (as proxy for mass) will self-calibrate out as a non-standard evolution g. Even, redshift dependence of theoretical halo-mass dependence will self-calibrate out 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 predicted mass functions.

  6. ‘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)

  7. Doing cosmology AND cluster physics with actual data: RCS1 RCS: the results WM = 0.34 +/- 0.064 (0.29 +/- 0.07) s8 = 1.05 +/- 0.14 (0.9 +/- 0.1) log(ABgc) = 10.95 +/- 0.78 (z=0.3) (10.05 +/- 0.89) a = 1.64 +/- 0.28 (1.58 +/- 0.27) g = 0.28 +/- 0.35 (-0.5 +/- 0.5) RCS1: the survey 76 deg2, Bgc > 300, s-detection > 3.3 DBgc < 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!

  8. Degeneracies in RCS1 ...

  9. The prospect of doing ‘precision’ cosmology AND cluster physics (SPT as an example of a SZ survey) SPT: the survey 4000 deg2, 10 mJy@150 GHz z=0 – 1.3, 22000 clusters SPT: the forecasts WM = 0.261 +/- 0.025 s8 = 0.935 +/- 0.071 w0 = -1.059 +/- 0.352 wa = 0.284 +/- 0.768 log(ASZ) = -16.72 +/- 0.423 a = 1.68 +/- 0.030 g = -0.216 +/- 0.713 10 parameter MCMC analysis (going beyond simple Fisher Matrix) Cox & Majumdar, in prep

  10. Degeneracies and Constraints (SPT) :

  11. More on degeneracies (SPT contd.)

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

  13. 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 forecasts DWM = 0.018 Ds8 = 0.039 Dw0 = 0.018 Dwa = 0.585 Dlog(ASZ) = 0.281 Da = 0.020 Dg = 0.168 0.025 0.071 0.352 0.768 0.423 0.030 0.713 Cox & Majumdar, in prep

  14. Where do cluster upcoming surveys stand? Only dN/dz, no extra information. Majumdar 2005 Competetive! Complimentary!

  15. Conclusions Self-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 degeneraciesto 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 animportant endorsement for self-calibration.These results also endorse the promise of doing precision cosmology with upcoming surveys (whether in Optical, SZ or Xray)

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