Cosmology with the XMM Cluster Survey (XCS)

1. Cosmology with the XMM Cluster Survey (XCS) Martin Sahlén University of Sussex with Pedro Viana (Porto), Andrew Liddle, Kathy Romer (PI) and others (XCS Consortium) arXiv:soon

2. Outline • Why Galaxy Clusters? • From Theory to Predictions: Simulation and Observation • The XMM Cluster Survey • Forecasting by MCMC • Results • Status and Conclusions M. Sahlén - Cosmology with the XCS

3. Why Galaxy Clusters? • Galaxy clusters: largest grav. bound objects, hot intracluster gas – bremsstrahlung (X-ray) • Cluster abundance exponentially sensitive to σ8 and ΩM → good constraining power • Probe structure formation; constraints complementary to CMB, SNIa, etc. Knop et al. 2003 Allen et al. 2004 M. Sahlén - Cosmology with the XCS

4. Theoretical Components • n(M, z) – comoving number density of clusters • M(O, z) – relation between halo mass and direct observable • dV/dz – cosmic volume evolution • fsel(O,z) – probability of detecting a given cluster • Uncertainties in observables and distribution M. Sahlén - Cosmology with the XCS

5. Dynamics of Cluster Science THEORY SIMULATIONS FITTING FORMULAE IC’s Particle physics Gravita-tional theory Cosmo-dynamics Cluster dynamics Halo conc. Neto et al. 2007 Bias Sheth & Tormen 1999 Mass function Jenkins et al. 2001 e.g. Virgo Hubble Volume e.g. XCS Mass-observable relations Muanwong et al. 2006 OBSERVATIONS

6. Mass Function Pδ(k) - PS of density contrast; depends on primordial PS, transfer function and perturbation growth suppression factor Primordial spectrum specified, transfer function and growth factor determined by cosmology Use parameterisation for σ(R); Viana & Liddle 1996 Jenkins mass function; Jenkins et al. 2001 M. Sahlén - Cosmology with the XCS

7. Mass-Observable Relations • Luminosity-Temperature • Mass-Temperature • Evolution (γ, δ, η, ν) • Self-similar γ = 1/2, η = 1/3 • Scatter (σlogL, σlogT) • Self-calibration and follow-up e.g. Levine et al. 2002, Lima & Hu 2004, 2005, Majumdar & Mohr 2004 M. Sahlén - Cosmology with the XCS

8. XMM Cluster Survey (XCS) • Mining XMM-Newton images • X-ray temperature, luminosity, redshift • 2 keV < T < 8 keV, zmax = 1.45 • 500 □˚ • http://xcs-home.org M. Sahlén - Cosmology with the XCS

9. Selection Function Calculated using the cluster detection pipeline with mock clusters - numerically very intensive to compute (months) Dependencies include: • Halo model • X-ray spectrum • Detector characteristics • Cosmology M. Sahlén - Cosmology with the XCS

10. Detecting Mock Clusters Mock source detection Original XMM-Newton image Mock cluster added to image Original source detection M. Sahlén - Cosmology with the XCS

11. Detecting Mock Clusters Mock source detection Original XMM-Newton image Mock cluster added to image M. Sahlén - Cosmology with the XCS

12. Selection Function Thanks to Mark Hosmer M. Sahlén - Cosmology with the XCS

13. From Theory to Predictions • N-body/hydrodynamic simulations - full non-linear treatment, necessary! • Mass function, mass-observable relations, bias etc. calibrated to simulations/observations • Selection function determined through simulations using the detection pipeline • Used along with cosmology to make predictions M. Sahlén - Cosmology with the XCS

14. Forecasting • generate catalogues of clusters, as observed by XCS, for fiducial cosmology • perform MCMC parameter estimation using the catalogues to forecast performance of real observations (cf. Fisher matrix – idealised case) M. Sahlén - Cosmology with the XCS

15. Generating the Data • Construct a grid in (T, z) • Calculate the expected mean number of clusters in each bin • Draw clusters from a Poisson distribution with calculated mean, within each bin M. Sahlén - Cosmology with the XCS

16. Expected Number Counts M. Sahlén - Cosmology with the XCS

17. MCMC: Likelihood Function • Poissonian probability of observing clusters in bin {i,j}, [assume no clustering, given XCS’ serendipitous nature] Sahlén et al., in prep. Holder 2006 Hu & Cohn 2006 M. Sahlén - Cosmology with the XCS

18. Implementation Custom-written MCMC code • “Arbitrary” cosmology, measurement errors, scaling-relation evolution and scatter, etc. • Multidim. integrals • CUBPACK; Cools and Haegemans, ACM Trans. Math. Software 2003 M. Sahlén - Cosmology with the XCS

19. Expected Constraints, full XCS Fiducial: ΩM = 0.3 ΩΛ = 0.7 σ8 = 0.8 500 □˚ 2 keV < T < 8 keV 0.1 < z < 1 M. Sahlén - Cosmology with the XCS

20. Status • XCS DR1 • 168 □˚ • Exp. ~70 clusters with >500 photons and T > 2 keV • 166 candidates, 119 confirmed with redshift, BUT clusters with T < 2 keV not excluded yet • Results expected late 2008 • Full XCS • 500 □˚ • Exp. ~210 clusters with >500 photons and T > 2 keV • Results expected 2010 M. Sahlén - Cosmology with the XCS

21. Conclusions • Cosmology with clusters can be modeled with the help of N-body/hydrodynamic simulation results tuned to observations • A comprehensive forecasting and data analysis code based on MCMC has been developed M. Sahlén - Cosmology with the XCS

22. Conclusions • XCS DR1 to measure σ8 to ~15% and ΩM to ~25% in 2008 (comparable to WMAP3) • Full XCS to measure σ8 and ΩM to ~5% in 2010 • Information on M-T scatter and L-T evolution necessary for recovering σ8 (self-calibration/follow-up) • Cluster physics uncertainties do NOT affect ΩM M. Sahlén - Cosmology with the XCS