The Sunyaev-Zel dovich Effect as a cosmic thermometer. Methods, results, future prospects

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1 The Sunyaev-Zel dovich Effect as a cosmic thermometer Methods, results, future prospects L. Lamagna Eperimental Cosmology Group Dept. of Physics - University of Rome La Sapienza XCV Congresso Nazionale SIF Bari, Oct. 1 st, 29

2 T CMB (z): why measure it? Observational test of the standard model: T CMB (z)=t (1+z) T = (2.725±.2)K solar system value measured by COBE/FIRAS (Mather et al.1999) Test of the nature of redshift (test of the Tolman s law (Tolman. R. C., 193, Proc. Nat. Acad, Sci., 16, 511) ) ; Sandage 1988; Lubin & Sandage 21) Constraints on alternative cosmological models (which rely on the physics of the matter and radiation content of the Universe): Λ-decaying models (Overduin and Cooperstock, Phys.Rev.D, 58 (1998)); (Puy,A&A,24); (Lima et al., MNRAS, 312 (2)) Decaying scalar field cosmologies Possible constraints on the variation of fundamental constants over cosmological time

3 T CMB (z): measurements Measurements of CMB temperature traditionally through the study of ecitation temperatures in high redshift molecular clouds. First attempt pionered by (Bahcall and Wolf, 1968) Many high redshift estimates of T CMB at redshift of absorbers (Songaila et al 1994; Lu et al. 1996; Ge et al 1997; Roth and Bauer, 1999; Srianand et al 2; losecco et al. 21; Levshakov et al. 22; Molaro et al. 22; Cui et al. 25) Systematics: CMB is not the only radiation field populating the energy levels, from which transitions occur. detailed knowledge of the physical conditions in the absorbing clouds is necessary (Combes and Wiklind, 1999; Combes,27) (LoSecco et. Al. Phys. Rev. D, 64, 123, 22)

4 The Sunyaev Zel dovich Effect (SZE) (I) Secondary CMB anisotropy Comptonization of the CMB by electrons in the hot gas of galay clusters. SZE = SZ TERM + SZ CIN + SZ COR REL k TCMB() e ΔI = σt n edl 1 + β h c ( e 1) [ θf ( ) β R(,θ, )] θ β = hν/kt = = kt e V/c /mc R function= relativistic corrections 2 (Rephaeli 1995-Itoh et al. ApJ 52, 7, 1998 Shimon & Rephaeli ApJ 575, 12, 22)

5 The Sunyaev Zel dovich Effect (SZE) (II) Properties: unique spectral shape Redshift independent electron pressure in cluster atmospheres (Carlstrom JE A&A, 4, 643, 22) Spectral distorsion of the CMB due to the SZE Xrays (Carlstrom JE A&A, 4, 643,22) Galay clusters Physics: τ optical depth T e electronic temperature v pec peculiar velocity Xrays Cosmology: Xrays H Ω B evolution of abundance of clusters T CMB (z)

6 (Fabbri R., F. Melchiorri & V. Natale. Ap&SS 59, 223, 1978; Rephaeli Y. Ap.J. 241, 858, 198) hν () z hν (1+ z) = = = ktcmb(z) kt (1+ z) T CMB (z) from SZE (I) ΔI SZ depends on frequency ν through the nondimensional ratio hν/kt: hν kt redshift-invariant only for standard scaling of T(z) In all the other non standard scenarios, the almost universal (remember rel. corrections!) dependence of thermal SZ on frequency becomes z-dependent, resulting in a small dilation/contraction of the SZ spectrum on the frequency ais. E: T CMB (z) = T CMB ()(1+z) 1-α (Lima et al. 2) ' hν (1+ z) (1 kt (1+ z) = = α ) hν kt CMB * where T * CMB = T CMB ()(1+z)-α

7 T CMB (z) from SZE (II) Steep frequency dependency of ΔI SZ T CMB (z) Ratio of ΔI SZ (ν 1 )/ΔI SZ (ν 2 ) weakly dependent on cluster properties (τ, T e, v pec ) Relative variation of SZ signal, evaluated for a typical 1-4 comptonization parameter at a T e =1keV, V pec =3km/s along l.o.s.

8 COMA observations SZ on A1656 by MITO ΔT ΔT ΔT τ (143GHz) (214GHz) (272GHz) = ( 184 ± 39) μk = ( 32 ± 79) μk = ( ± 36) μk = (5.5 ±.84) 1 3 (De Petris M. et al. Ap.JL 574, , 22 & Savini G. et al. New Astr. 8, 7, , 23) SZ on A1656 by OVRO+WMAP+MITO OVRO + MITO Complete SZ spectrum of COMA First SZ spectrum with 6 frequencies τ = (5.35 ±.67) 1 3 (Battistelli, et al. Ap.JL 23)

9 ( ) [ ] { } ( ) [ ] { } + + Ω Ω = Δ Δ ) ( ),, ( ) ( 1 ) ( ),, ( ) ( 1 ν ν ε β θ β θ τ ν ν ε β θ β θ τ d R f d e e d R f d e e A A G G S S j i j i j i j i Fit of measured SZ signals ratios with the epected values by changing T(z)/(1+z) as in the following: T CMB (z) from SZE: first application independent of absolute calibration uncertainties (T planet ); independent of τ, if KIN-SZ removed or β negligible; dependent on precise knowledge of AΩ i and ε i (ν) Ratios have non gaussian distributions and introduce correlations G i : Responsivity AΩ i :Throughput ε i (ν) :Transmission efficiency

10 T CMB (z) from SZE: first results COMA+A2163 OVRO+BIMA+SuZIE T T T CMB A1656 A2163 (z = ) = K (z =.231) = (z =.23) = K K COBE OVRO+MITO T(z) T(z) T(z) = = = T T T (1 (1 [ z) z) 1-α (1 + γ)z] Lo Secco et al. 21 Molaro et al α = (95%c.l.).32 d =.17 ±.36(95%c.l.) Molecular microwave transitions CONSISTENT (Battistelli et al., ApJL 58, 11, 22) Standard Model CONSISTENT

11 T CMB (z) from SZE: etended dataset SZ measurements of 14 clusters by different eperiments epressed in central thermodynamic temperature X-ray data (Bonamente et al., APJ,647,25,26) (De Gregori et al. Nuovo Cimento B, 122, 28)

12 T CMB (z) from SZE: improved statistical analysis Two main approaches: Ratios of SZ intensity change (RI) ΔI SZ (ν 1 )/ΔI SZ (ν 2 ) weakly dependent on IC gas properties if β negligible. Directly ΔI SZ measurements (DI) Priors: easier control of systematics more comple structure in the parameter space P(T ei ) = N(E(T ei ), σ(t ei )) P(v p ) = N( km/s,1 km/s) P(T CMB ) = flat P(τ) = flat (only for DI) P(C) = N(1,.1) Joint likelihood to etract the universal parameter α of the Lima model Joint likelihood to etract the universal parameter α of the Lima model single likelihoods for each cluster to provide individual determinations of T CMB (z) at z of each cluster independent from the particular scaling assumed for the temperature (i.e. the Lima model) only assumption ν(z)=ν (1+z) (Luzzi et al. ApJ, 29 accepted)

13 T CMB (z) from SZE: Ratios approach (RI) Likelihood of intensity ratios: weak dependence on cluster parameters (no marginalization on τ) not considered measurements at the crossover frequency (Cauchy tail) bias due to arbitrariness in selecting the intensity change used in denominator of ratios more precise SZ measurements or larger dataset bias removed Probability function for ratio r: Two measurements ρ 1 e ρ 2 with gaussian errors σ 1 e σ 2 : Etended to the case of n ratios

14 T CMB (z) from SZE: Direct approach DI multicluster likelihood: P(d α,τ,t e,v p,c) = i P(d i α,τ,t e,v p,c) P(α d) P(d α,τ,t e,v p,c) P(α)P(τ)P(T e )P(v p )P(C)dτ dt e dv p dc DI single likelihood for each cluster: MCMC algorithm (Metropolis-Hastings sampling; Gelman-Rubin test for convergence ) Posteriors for all parameters Study of correlations Main degeneracies: T(z) vs τ (2D numerical integration, Vp and C integration analytical) 2 [ χ ( τ,t, v,t,c)/2] P( d τ,t e, vp,tcmb,c) ep e p CMB T(z) vs v p always evident

15 T CMB (z) from SZE: Results Flat prior a [,1] (theoretical motivation) (Lima et al 2) All limits are at 68% probability level RI α.92 DI (JL) α.59 DI (SL-MCMC) α.12 (including lines α.79) From lines transition observations Consistency with std. Model Posterior for α

16 T CMB (z) from SZE: simulations Simulated observations of 5 well known clusters mock dataset analyzed to recover input parameters of the cluster Analysis: MCMC allows to eplore the full space of the cluster parameters and the T CMB (z) P(v p ) = N( km/s,1 km/s) P(v p ) = N( km/s,1 km/s) P(T e ) = N(6.5KeV,.14KeV )

17 SZE eperiments Ongoing and near future surveys with ACT, APEX-SZ, SPT, Planck and detailed mapping of a sample of nearby clusters with MAD and OLIMPO eperiments will provide much more precise and uniform datasets: bias in the ratio approach largely removed reduced skweness in τ and T cmb (z) distributions (DI)

18 Future SZE eperiments Accurate spectroscopic observations from space towards a limited number of clusters (like the proposed SAGACE satellite) would allow to control a large part of the degeneracies between T CMB (z) and cluster parameters.

19 SAGACE SAGACE (Spectroscopic Active Galaies and Clusters Eplorer) SAGACE is a space-borne differential spectrometer, coupled to a 3m telescope: able to cover the frequency ranges 1-45 and GHz; with angular resolution ranging from 4.2 to.7 arcmin; with photon-noise limited sensitivity (~ 1.5 Jy per second of integration for a 1 GHz resolution element, 5 mjy per second for 3 GHz resolution element) Designed to operate for 2 years Its main goal is to observe the SZ effect on galay clusters with 15 GHz resolution, providing, for the first time, precisely calibrated SZ spectral maps of clusters over its wide frequency range (no intercalibration of different eperiments). It will map and measure the physical parameters of the hot gas etended to the outskirts of a sample of ~2 clusters, and to eploit the full potential of the SZ effect as a probe for cosmology: Ho with a method completely independent of others Dark Matter and Dark Energy T CMB (z) with a method completely independent of others

20 The scientific impact of SAGACE The high accuracy of the spectral measurements allows to control a large part of the eisting degeneracies between the cluster parameters. SAGACE SAGACE Planck 3BP SAGACE SAGACE Planck 3BP 3BP

21 Conclusions Original tool to perform an observational test of the standard scaling of T CMB and its isotropy up to the redshift of galay clusters and to put constraints on alternative cosmological models. Information etracted *almost* for free from spectral SZ datasets. In the near future, SZE eperiments will allow precise measurements of the T CMB (z) scaling law to set constraints on the variation of fundamental constants over cosmological time.