Cosmological constraints from estimates of Mgas-

Mtot-c in X-ray luminous

clustersS. Ettori (INAF/OA Bologna)

with F. Gastaldello, M. Meneghetti,

I. Balestra, S. Borgani, S. Molendi, P. Tozzi et al.

Potsdam, September 23, 2009: cosmological constraints from X-ray luminous clusters

Outline

• How good are the estimates of Mgas , Mtot , c: results from hydrodynamical simulations

• Clusters as cosmological probes: uncertainties are in the outskirts

• Concentration – Mtot relation & fgas: a new approach to constrain σ8 & Ωm

X-ray vs lensing mass: simulations

Hydrodynamical simulations of 3 massive clusters(0.7-1.1e15 Msun).

Analyzed after convolution with X-ray (XMAS) andlensing (SkyLens)exposures.

Meneghetti et al. 09 subm

X-ray vs lensing mass: simulations

Meneghetti et al. 09 subm

XMAS SkyLens

X-ray total & gas mass

whatever the projection/method is Mgas is recovered within few (~5) %

MX vs Mtrue: -12 (rms: 5) %

ML vs Mtrue: 2 (rms: 16) %

Mtot

Mgas

X-ray vs lensing mass: simulations

Considering only the projection of g1 & g72:

• c from X-ray analysis: biased low by 10-20 (rms 13) %• c from W only: +88 (rms 50) %, S only +12 (38) %• c from W+S lensing: good agreement (rms 14) %

Concentration from fitting a NFW profile

Gas mass fraction

We combine a dynamical and a geometrical method

(see also Allen et al, Blanchard et al., Ettori et al, Mohr et al) :

• baryonic content of galaxy clusters is representative of the cosmic baryon fraction Ωb / Ωm (White et al. 93)

• fgas is assumed constant in cosmic time in very massive systems (Sasaki 96, Pen 97)

To constrain the cosmological model

Ωm +Ω +Ωk =1

X-ray total massTotal mass from X-ray is determined by assuming

1. spherical symmetry, 2. hydrostatic equilibrium

n~ -2/-2.4 T~ 0/-0.8

€

M tot (< r)∝ r × Tgas(r) × (−α n −α T )

€

M tot < r( ) = −kTgas(r) r

Gμmp

∂ ln ngas∂ ln r

+∂ ln Tgas∂ ln r

⎛

⎝ ⎜

⎞

⎠ ⎟

An example: RXJ1252, z=1.235

An example: RXJ1252, z=1.237

We fit a single absorbed MEKAL to measure Te(Rosati et al. 04).

The deprojected Sb provides ne that is then fitted with a functional form.

NOTE: 850 cts <35”, 1220 cts <59” (rc~10”, 250 cts)

Systematics on Ωm- Ω -w assuming T(r) as observed in local systems (e.g. Vikhlinin et

al. 06)

For details see Ettori et al. 09, arXiv:0904.2740

WMAP-5

Bkg: dominant in GCs Bkg: dominant in GCs outskirtsoutskirts

Simulation for 3keV cluster @ R200Simulation for 3keV cluster @ R200

Gal foreground

Ins. background

Residual CXB

Source

ICM at R200: Observed clusters

A1795 with Suzaku by M.Bautz et al. : T ~ r -0.9, M500 ~20-30% < expected

XMM (Leccardi & Molendi 08)

Study of Sb at r >0.7 R200 in a sample of high-z (z>0.3) objects with CXO (Ettori & Balestra 09)fit of the derivative of ln(Sb)/ln( r):

at 0.7 R200: -3.9 ± 0.7, at R200: -4.3 ± 0.9

On the Temperature profile

Chandra

XMM

EDGE 1Msec

arXiv:0707.4103

On the Temperature profile

Chandra

XMM

WFXT 50ksec

The c-Mtot relation

We (Ettori et al. 09 in prep) recover Mgas & Mtot from 44 X-ray luminous galaxy clusters observed with XMM-Newton in the z-range 0.1-0.3 (from

Leccardi & Molendi 2008) to constrain (σ8, Ωm).

We use 2 independent methods & check several systematics on Mtot

The c-Mtot relation: σ8-Ωm

Dotted lines: Eke et al. (01)for a given ΛCDM at z=0 (from top to bottom: σ8=0.9 and 0.7).

Shaded regions: Maccio’ et al. (08, see Bullock et al. 01) for WMAP-1, 5 and 3 years (from the top to the bottom, respectively).

Dashed lines (thin: z=0.1, thick: z=0.3) indicate the best-fit range at 1σ in a WMAP-5 yrs cosmology from Duffy et al. (08)

z<0.15 0.15<z<0.25 z>0.25

The c-Mtot relation: σ8-Ωm

• We constrain (σ8, Ωm) by comparing our estimates of (c200, M200) to the predictions tuned from CDM simulations (black contours)

• We consider both systematics (e.g. different T profiles; fitted ngas; no-limits on

rs; two methods: ~10%) in our measurements & scatter from numerical predictions (~20%, e.g. Neto et al. 07)

• We add constraints from fbar (red contours).

Eke et al. 01

σ8 = 0.94±0.25Ωm=0.25+0.2

-0.1

σ8 = 0.86±0.06Ωm=0.28±0.01

CONCLUSIONS on c–Mtot-fgas• X-ray techniques provide Mgas & Mtot with a good control of both statistical & systematic uncertainties

• A selection of relaxed, massive objects over a large z-range can constrain some cosmological parameters (σ8, Ωm, ΩΛ) through estimates in the c-Mtot-fgas plane

• CAVEAT: N-body community ’d realize an adequate sets of cosmological simulations over a large box to properly predict the expected concentration associated to the massive (>1014 Msun) DM halos as function of (σ8, Ωm; z)