Cosmology and astrophysics with galaxy clusters

Talk @ Multiwavelength Cosmology, Mykonos Island, June 18 th 2003 Cosmology and astrophysics with galaxy clusters Stefano Borgani Dept. of Astronomy, Univ. of Trieste http://www.daut.univ.trieste.it/borgani (a) Cosmology with galaxy clusters after WMAP: What did WMAP tell us about cosmological parameters? Can we learn something more/different from LSS/clusters? (b) Toward precision cosmology with clusters (mostly X-ray) Current status of parameter constraints (σ 8 Ω m ) What's needed to do any better? (c) Cluster cosmology or astrophysics: the role of hydro simulations.

The COBE and WMAP Snapshots

Cosmology with WMAP (I) Spergel et al. (2003) see talk by N. Wright WMAP with no priors: acceptable with Ω Λ =0: Ω M = 1.28, H 0 = 32.5 WMAP + H 0 >50 (weak pr.) 0.98 < Ω tot < 1.08 at 95% c.l. WMAP + PL ΛCDM h = 0.72 ± 0.05 (68% c.l.) n s = 0.99 ± 0.04 τ= 0.166 ± 0.074 σ 8 = 0.9 ± 0.1 Ω b = 0.047 ± 0.006 Ω m = 0.29 ± 0.07

Cosmology with WMAP (II) Spergel et al. (2003) WMAP + CBI + ACBAR + 2dFGRS + Ly-a: n s = 0.93 ± 0.03 dn s /dlnk = -0.031 ± 0.017 Ω b = 0.047 ± 0.006 Ω m = 0.27 ± 0.04 σ 8 = 0.84 ± 0.04 (0.78 ; Ω m =0.3) h = 0.71 ± 0.04 τ = 0.17 ± 0.06

Beyond the standard LCDM model WMAP and Dark Energy (Spergel et al. 03) = w p ; w 1 w < -0.78 (95% c.l.) Non-Gaussianity (Komatsu et al. 03) Φ(x): Bardeen curvature perturbation Φ L : Gaussian perturb. with Φ L =0 58 < f NL < 134 (95%c.l.) f NL ~10-1 for single scalar field inflation.

Why clusters are useful for cosmology?

Because they are the largest collapsed Why clusters are useful for cosmology? structures in the Universe!

Because they are the largest collapsed Why clusters are useful for cosmology? structures in the Universe! (a) Gas fraction f gas : IF clusters are fair containers of cosmic baryons (see talks by S. Allen and S. Ettori) Local clusters: Ω m once Ω b known from BBN and/or CMB (weak dependence on H 0 ). Distant clusters: f gas (z) = f gas [d A (H 0,Ω m,ω DE,w)] = f gas (z=0) geometry. (b) Mass function of clusters and its evolution: Direct probe of σ 8, i.e. P(k) amplitude at the cluster mass scale; Dynamical (not geometrical) probe of cosmology, through the linear growth rate of perturbations: D(z) = D(z; Ω m,ω DE,w) (c) Large-scale distribution and clustering of clusters: Geometrial probe through the P(k) shape (assuming the DM content); Cosmology with clustering evolution along the light-cone: ξ(r,z), P(k,z)

SB & Guzzo '01 Evolution of hot (T> 3 kev) clusters

What's needed for cosmology with clusters? (a) A reliable and flexible tool to compute the mass function for a given cosmological model (b) An efficient method to find clusters: sensitivity to detect clusters at high redshift negligible impact of false and spurious detections. (c) A precise knowledge of the selection function searching volume within which a cluster is found. : sky-coverage : luminosity distance : flux : max. z for the given f lim (d) A reliable method to measure cluster masses better if given by the observable on which cluster selection is based.

The Press-Schechter Approach and Beyond Assumptions: Spherical collapse + Gaussian density fluctuations d c : critical density constrast for spherical collapse (=1.69 for EdS) p(d c,m): Gaussian probability for a perturbation of mass M to exceed d c Mass variance at the scale M and redshift z for the filter function W M (k). D(z)=D(Ω m,ω DE,w): linear growth rate of density fluctuations. Too many low-m and too few high-m halos predicted; Need to account for the non-spherical nature of collapse (e.g. Sheth & Tormen 1999)

Toward a Universal Mass Function Testing against N-body over a large dynamical range (a) Corrections to the PS MF can be found, which has still a universal (i.e. model-independent) shape. Jenkins et al. 2001

Toward a Universal Mass Function Testing against N-body over a large dynamical range Evrard et al. '02 (a) Corrections to the PS MF can be found, which has still a universal (i.e. Model-independent) shape. (b) Agreement with the simulated MF always within <10% at the cluster mass-scale.

Toward a Universal Mass Function Testing against N-body over a large dynamical range White '02 (a) Corrections to the PS MF can be found, which has still a universal (i.e. Model-independent) shape (Jenkins et al. '01). (b) Agreement with the simulated MF always within <10% at the cluster mass-scale (Evrard et al. '02). (c) Effects of cosmic variance may be comparable to statistical uncertainties (Hu & Kravtsov '02, White '02).

The mass function as a cosmological test Changing the P(k) normalization Changing the density parameter RBN '02

Galaxy clusters and Dark Energy Henry '00 Henry 2000: local XTF from 20 HEAO-1 clusters and XTF evolution from 16 EMSS clusters with ASCA T X : Weak contraints on Ω Λ

Galaxy clusters and Dark Energy Henry '00 Henry 2000: local XTF from 20 HEAO-1 clusters and XTF evolution from 16 EMSS clusters with ASCA T X : Weak contraints on Ω Λ Schuecker et al 2002: REFLEX n(z) (assuming CDM) + Type-Ia SN: Purely geometrical; DE consistent with a Λ-term. Schuecker et al. '02

Galaxy clusters and Dark Energy Henry 2000: local XTF from 20 HEAO-1 clusters and XTF evolution from 16 EMSS clusters with ASCA T X : Weak contraints on Ω Λ Schuecker et al 2002: REFLEX n(z) (assuming CDM) + Type-Ia SN: Purely geometrical; DE consistent with a Λ-term. Constraints from future widearea deep X-ray and SZ surveys (DUET Team '01, Hu & Kravtsov '02, Majumdar & Mohr '03).

Galaxy clusters and non-gaussianity Cluster n(m) sensitive to the high-density tail of the PDF (Lucchin & Matarrese 88, Oukbir et al. 97, Koyama et al. 99, Matarrese et al. 00, Willick 00). P(δ M ): non-gaussian probability density fct. Robinson et al. 2000: How much non- Gaussianity is needed for Ω m =1 to agree with the XTF evolution? Robinson et al.00

Why X-ray X clusters? Search volume of X-ray surveys (1) Clusters are sharply defined in X-ray: dl X /dv ρ g 2 T 1/2 (2) Sky coverage and search volume are well defined. RBN '02 (3) L X and, even better, T X, are closely related to the cluster collapsed mass.

The L X -z coverage of X-ray surveys RDCS 115 Clusters Spectr. Conf. 37 at z> 0.5 22 at z> 0.6 10 at z> 0.8 4 at z> 1 Chandra/XMM Limit

X-ray surveys: where are we? RBN '02 WFXT DUET

RBN02 Distant (z>0.7) clusters in the Chandra archive Redshift Luminosity 0.75 Mpc

The Cluster X-ray X LF Remarkable agreement among all the local surveys (unlike for the galaxy LF) Robust reference for the evolution of the cluster population!

The Cluster X-ray X LF Remarkable agreement among all the local surveys (unlike for the galaxy LF) Bulk of cluster population already in place at z 1. Moderate negative evolution in the bright-end. Robust reference for the evolution of the cluster population!

How to estimate cluster masses? (a) Dynamics of the collisionless component (galaxies) Assuming virialization of a spherical system: s V : velocity dispersion of member galaxies. R V : virial radius. Applied to: ENACS, CNOC, 2dFGRS, SDSS (b) Dynamics of the collisional component (gas) Hydrostatic equilibrium + isothermal b-model: β = β spec = µm p σ r / k B T ( 1-1.2 from M-T of simulations) k B T from X-ray and SZ observations. (c) Weak and strong gravitational lensing (d) Phenomenological scaling relations (talks by S. Ettori) L X ~ T a (1+z) A ; L X ~ M g (1+z) G

The observed L -T X X relation The L X -T T evolution: Mushotzky & Scharf (1996) SB, Rosati et al. (2001) Holden et al. (2002) Novicki et al. (2002) Ettori et al. (2003) Steepening below T~1 kev. No evidence for evol. out to z ~1 (cf. Vikhlinin et al. 2002) See talk by S. Ettori

The mass-temperature relation Isothermal gas + β-model (Finoguenov, Reiprich & Boehringer '01) Resolved T X profiles with Beppo-SAX (Ettori, De Grandi & Molendi '02) ~40% lower normalization than expected from simulations: β spec 0.7 vs. β spec 1 Possibly steeper for groups. Nature of the scatter: (a) intrinsic vs. observational (b) how is it distributed? Need to be extended to distant clusters (see talk by S.Ettori)

The observed M-LM X relation Reiprich & Boehringer 02 ROSAT + ASCA Hydrostatic equil. + isothermal -model Resolved T X profiles with Beppo-SAX (Ettori, De Grandi & Molendi '02) Well-defined relation with ~20-40% scatter! To be extended at high z with Chandra/XMM data (Ettori et al., in prep)

Constraints from flux- limited surveys SB, Rosati et al. '01 Rosati, SB & Norman '03 RDCS 160 sq. deg RDCS: 104 clusters F lim = 3 10-14 cgs out to z = 0.83 (Rosati, SB, Norman 2002) 160 sq.deg.: 200 clusters F lim = 3.7 10-14 cgs out to z = 0.58 (Vikhlinin et al. '98, Mullis et al. '03) Remarkable agreement!!

Constraints from flux- limited surveys SB, Rosati et al. '01 Rosati, SB & Norman '03 Results dependent on ICM physics... Ω m <0.6 at >3σ! σ 8 somewhat small: σ 8 = 0.72 ± 0.05 (Ω m = 0.3) for the reference analysis. cf. poster by Vauclair et al. and talk by A. Blanchard

What's the correct σ 8? Pierpaoli et al. '01 As of 2001 (Pierpaoli et al. 01) local XTF and M-T relation from simulations: σ 8 Ω m 0.53 = 0.50 ± 0.06 σ 8 = 1.02 ± 0.07 for Ω m = 0.3 Seljak 02: observed M-T lower than simulated σ 8 = 0.77 ± 0.06 for Ω m = 0.3

What's the correct σ 8? As of 2001 (Pierpaoli et al. 01) local XTF and M-T relation from simulations: σ 8 Ω m 0.53 = 0.50 ± 0.06 σ 8 = 1.02 ± 0.07 for Ω m = 0.3 Seljak 02: observed M-T lower than simulated σ 8 = 0.77 ± 0.06 for Ω m = 0.3 Schuecker et al. 02: n(z) and ξ cl (r) from REFLEX (CDM + prior on h) σ 8 = 0.71 ± 0.03 for Ω m = 0.3 Schuecker et al '02

What's the correct σ 8? Ikebe et al. '02 Pierpaoli et al. '01 As of 2001 (Pierpaoli et al. 01) local XTF and M-T relation from simulations: σ 8 Ω m 0.53 = 0.50 ± 0.06 σ 8 = 1.02 ± 0.07 for Ω m = 0.3 Seljak 02: observed M-T lower than simulated σ 8 = 0.77 ± 0.06 for Ω m = 0.3 Schuecker et al. 02: n(z) and ξ cl (r) from REFLEX (CDM + prior on h) σ 8 = 0.71 ± 0.03 for Ω m = 0.3 Ikebe et al. 02: local XTF from HIFLUGCS + uncertainties in the M-T relation: Ω m = 0.06 0.38 σ 8 = 0.57 1.33 (see also Viana et al. '03)

What's the correct σ 8? Ikebe et al. '02 As of 2001 (Pierpaoli et al. 01) local XTF and M-T relation from simulations: σ 8 Ω m 0.53 = 0.50 ± 0.06 σ 8 = 1.02 ± 0.07 for Ω m = 0.3 Seljak 02: observed M-T lower than simulated σ 8 = 0.77 ± 0.06 for Ω m = 0.3 Schuecker et al. 02: n(z) and ξ cl (r) from REFLEX (CDM + prior on h) σ 8 = 0.71 ± 0.03 for Ω m = 0.3 Ikebe et al. 02: local XTF from HIFLUGCS + uncertainties in the M-T relation: Ω m = 0.06 0.38 σ 8 = 0.57 1.33

Intrinsic scatter in the M-LM X relation Pierpaoli, SB, Scott & White 03 Convolution with intrinsic (log-normal) scatter inflates the predicted XLF Lower σ 8 required to fit the observed XLF

Intrinsic scatter in the M-LM X relation Pierpaoli, SB, Scott & White 03 Convolution with intrinsic (log-normal) scatter inflates the predicted XLF Lower σ 8 required to fit the observed XLF No scatter 20% 40%

Marginilize over the statistical errors Pierpaoli, SB, Scott & White 03 Statistical errors in the M-L X relation widen the confidence contours. Important question: What's the prior for the error distribution?

Marginilize over the statistical errors Pierpaoli, SB, Scott & White 03 Error marginal. Statistical errors in the M-L X relation widen the confidence contours. Important question: What's the prior for the error distribution? No error

A Tree+SPH simulation of of the the cosmic web (see (see poster poster by by G. G. Murante) Murante) Collab. with A. Diaferio, K. Dolag, L. Moscardini, G. Murante, V. Springel, G. Tormen, L.Tornatore, P.Tozzi Code: Tree + SPH GADGET (Springel et al. 2001, 2002) www.mpa-garching.mpg.de/gadget Radiative cool.+uv backgr. Multiphase model for star-formation and galactic winds. ΛCDM cosmology: Ω m = 1-Ω L =0.3, Ω bar 0.02h -2, h=0.7, σ 8 =0.8 L = 192 h -1 Mpc ; N gas =N DM = 480 3 ε Pl = 7.5 h -1 kpc ; m gas = 6.9 10 8 h -1 M 40,000 CPU hours and 100 Gb RAM, using 64 processors of IBM-SP4 in CINECA (INAF grant); about 1.2 Tb of data produced.

~ 400 clusters with > 10 4 particles. X-ray cluster scaling properties and nature of their scatter. Contribution of diffuse gas to the soft X-ray X background. SZ effect from clumped and diffuse gas. Comparing cluster masses: X-ray, lensing, optical and SZ. Diffuse intracluster light on a statistical basis. Zoom-in simulations of clusters and other interesting regions. Populate the box with simulated and SAM galaxies.

The L X -T X Relation at z=0 The observed L X -T X is reproduced at the cluster scale, T X >2 kev. Up-scattered points due to the contribution of ''cooling cores''. No bending at the scale of groups, T X <1 kev. Need to increase the feedback efficiency? Account for the contribution from cooling cores.

The mass-temperature relation at z=0 Normalization ~30%higher than observed: No much effect of cooling in increasing T X in central regions. Only possible by further steepening T X profiles! Small but sizeable effect when using emissivity in a finite energy band.

Observational biases in the M-T X scaling? β-model for ρ gas (r). T X profiles from polytropic model: T(r) ~ [ρ[ gas (r)] γ-1 Mass computed from hydrostatic equilibrium: Actual M-T relation possibly higher than measured: β spec spec 1 Need to mimick more closely the observational setup.

The cluster XLF Local XLF: (a) Excess of low L X system Simulated groups are too bright. (b) Excellent agreement in the XLF bright end. Lack of evolution of the XLF faint end out to z=1. In line with observational results from deep surveys.

The cluster XTF Local XTF: Good agreement with the XTF by Ikebe et al.('03) The local XTF supports σ 8 0.8

The cluster XTF Local XTF: Good agreement with the XTF by Ikebe et al.('03) The local XTF supports σ 8 0.8 The XTF of distant clusters: Lack of significant evolution for T<3 kev out to z=1. Marginal evidence for a deficit of hotter systems.

Concluding remarks: (a) Galaxy clusters ARE cosmological probes! Evolution of the mass function: 0.2 < m < 0.5 at > 3 c.l. = 8 0.80 ± 0.05 (stat.) ± 0.05 (syst.) for m =0.3 Tension with WMAP results? Lower than σ 8 from high from high-l C l excess? (b) What's needed for precision (post-wmap) cosmology? ( m and 8 to < 10%, dark energy, non-gaussianity...) Mass estimates from as many as possible independent methods (X-ray, σ v, lensing, SZ) for ~100 clusters out to z~0.5. Brute force: massive surveys (~10 4 clusters) to kill systematics with statistics. Use hydro symulations to better understand what a cluster is.

Cosmology and Astrophysics with Galaxy Clusters borgani@ts.astro.it

Which is the correct value of σ 8? Pierpaoli, SB, Scott & White 03