The Sunyaev-Zel’dovich Effect as a cosmic thermometer

Methods, results, future prospects

L. Lamagna

Experimental Cosmology Group

Dept. of Physics - University of Rome “La Sapienza”

XCV Congresso Nazionale SIFBari, Oct. 1st, 2009

• Observational test of the standard model: TCMB(z)=T0(1+z)T0 = (2.725±0.002)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., 1930, Proc. Nat. Acad, Sci., 16, 511) ) ; Sandage 1988; Lubin & Sandage 2001)

• 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,2004); (Lima et al., MNRAS, 312 (2000))

– Decaying scalar field cosmologies

• Possible constraints on the variation of fundamental constants over cosmological time

TCMB(z): why measure it?

• Many high redshift estimates of TCMB at redshift of absorbers(Songaila et al 1994; Lu et al. 1996; Geet al 1997; Roth and Bauer, 1999; Srianand et al 2000; loSecco et al.2001; Levshakov et al. 2002; Molaro etal. 2002; Cui et al. 2005)

• Systematics: – CMB is not the only radiation field

populating the energy levels, fromwhich transitions occur.

– detailed knowledge of the physicalconditions in the absorbing cloudsis necessary (Combes and Wiklind, 1999; Combes ,2007)

TCMB(z): measurementsMeasurements of CMB temperature traditionally through the studyof excitation temperatures in high redshift molecular clouds. First attempt pionered by (Bahcall and Wolf, 1968)

(LoSecco et. Al. Phys. Rev. D, 64, 123, 2002)

Comptonization of the CMB byelectrons in the hot gas of galaxyclusters.

( ) ( ) ( )[ ]∫ +−−

= βθ,x,Rβxθfdlnσ1e

exch

)0(T2kΔI 1eT2x

x4

22

3CMB

3

V/cβ/mckTθ

/kThx2

e

==

= ν

(Rephaeli 1995-Itoh et al. ApJ 502, 7, 1998 – Shimon & Rephaeli ApJ 575, 12, 2002)

SZE = SZTERM + SZCIN + SZCOR REL

Secondary CMB anisotropy

The Sunyaev Zel’dovich Effect (SZE) (I)

R function= relativisticcorrections

• Properties:– unique spectral shape– Redshift independent– ∝ electron pressure in

cluster atmospheres

• Galaxy clusters Physics:– τ optical depth– Te electronic temperature– vpec peculiar velocity

• Cosmology:– H0– ΩB– evolution of abundance of clusters– TCMB(z)

XraysXrays Xrays

(Carlstrom JE A&A, 40, 643, 2002)

Spectral distorsion of the CMB due to the SZE (Carlstrom JE A&A , 40, 643,2002)

The Sunyaev Zel’dovich Effect (SZE) (II)

( )0

0

0

0

CMB kThν

z)(1kTz)(1hν

(z)kTzhνx =

++

==

(Fabbri R., F. Melchiorri & V. Natale. Ap&SS 59, 223, 1978; Rephaeli Y. Ap.J. 241, 858, 1980)

*kThν

z)(1kTz)(1hνx'

CMB

0)(1

0

0 =++

= −α

redshift-invariant only for standard scaling of T(z)

ΔISZ depends on frequency ν through the nondimensional ratio hν/kT:

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 axis.Ex:

T*CMB= TCMB(0)(1+z)-α

TCMB(z) = TCMB(0)(1+z)1-α

where

(Lima et al. 2000)

TCMB(z) from SZE (I)

•Steep frequency dependency of ΔISZ TCMB(z)

•Ratio of ΔISZ (ν1)/ΔISZ (ν2) weakly dependent on clusterproperties (τ, Te, vpec)

Relative variation of SZ signal, evaluated for a typical 10-4 comptonizationparameter at a Te=10keV, Vpec=300km/s along l.o.s.

TCMB(z) from SZE (II)

SZ on A1656 by MITO

30

0

0

0

100.84)(5.05τ

μK 36)172((272GHz)ΔTμK 79)32((214GHz)ΔTμK 39)184((143GHz)ΔT

−⋅±=⇒

±+=±−=±−=

OVRO + MITO

(De Petris M. et al. Ap.JL 574, 119-122, 2002 & Savini G. et al. New Astr. 8, 7, 727-736, 2003)

30 100.67)(5.35τ −⋅±=⇒

(Battistelli, et al. Ap.JL 2003)

First SZ spectrum with 6 frequencies

SZ on A1656 by OVRO+WMAP+MITOComplete SZ spectrum of COMA

COMA observations

( ) [ ]{ }

( ) [ ]{ }∫ ∫

∫ ∫∞

∞

⋅+−−

⋅+−−

ΩΩ

=ΔΔ

012

40

12

4

)(),,()(1

)(),,()(1

ννεβθβθτ

ννεβθβθτ

dxRxfde

ex

dxRxfde

ex

AA

GG

SS

jx

x

ix

x

j

i

j

i

j

i

Fit of measured SZ signals ratios with the expectedvalues by changing T(z)/(1+z) as in the following:

TCMB(z) from SZE: first application

•independent of absolute calibration uncertainties (Tplanet);•independent of τ, if KIN-SZ removed or β negligible;•dependent on precise knowledge of AΩi and εi(ν) •Ratios have non gaussian distributions and introduce correlations

Gi : ResponsivityAΩi :Throughputεi(ν) :Transmission efficiency

(Battistelli et al., ApJL 580, 101, 2002)

K3.3770.203)(zT

K2.7890.0231)(zT

K2.7250)(zT

0.1010.102A2163

0.0800.065A1656

0.020.02CMB

+−

+−

+−

==

==

==

)l.0.36(95%c.0.17d(95%c.l.)0.16 0.34

0.32

±−=−= +

−α

OVRO+MITO

OVRO+BIMA+SuZIE

COBE

Lo Secco et al. 2001

Molaro et al. 2002

Molecular microwave transitionsCONSISTENT

Standard ModelCONSISTENT

γ)z](1[1TT(z)z)(1TT(z)

z)(1TT(z)

0

-10

0

++=+=

+=α

COMA+A2163

TCMB(z) from SZE: first results

SZ measurements of 14 clusters by different experiments expressed in central thermodynamic temperature

(De Gregori et al. Nuovo Cimento B, 122, 2008)

TCMB(z) from SZE: extended dataset

X-ray data (Bonamente et al., APJ,647,25,2006)

Two main approaches:

P(Tei) = N(E(Tei),σ(Tei))

P(vp) = N(0 km/s,1000 km/s)

P(TCMB) = flat

P(τ) = flat (only for DI)

P(C) = N(1,0.1)

Priors:

(Luzzi et al. ApJ, 2009 accepted)

TCMB(z) from SZE: improved statistical analysis

Joint likelihood to extract the universal parameter α of the Lima model

•Ratios of SZ intensity change (RI) ΔISZ(ν1)/ΔISZ(ν2)

•weakly dependent on IC gas properties if β negligible.

•Directly ΔISZ measurements (DI)•easier control of systematics

•more complex structure in the parameter space

• Joint likelihood to extract the universal parameter α of the Lima model

• single likelihoods for eachcluster to provide individualdeterminations of TCMB(z) at z of each cluster

•independent from the particular scaling assumed forthe temperature (i.e. the Lima model)

• only assumption ν(z)=ν0(1+z)

Probability function for ratio r:Two measurements ρ1 e ρ2 with gaussianerrors σ1 e σ2:

•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

Likelihood of intensity ratios:

Extended to the case of n ratios

TCMB(z) from SZE: Ratios approach (RI)

TCMB(z) from SZE: Direct approach

•MCMC algorithm

(Metropolis-Hastings sampling;

Gelman-Rubin test for convergence )

•Posteriors for all parameters

•Study of correlations

•Main degeneracies:

•T(z) vs τ

•T(z) vs vp always evident

DI multicluster likelihood:

DI single likelihood for each cluster:

P(d|α,τ,Te,vp,C) = ∏i P(di|α,τ,Te,vp,C)

P(α|d) ∝ ∫ P(d|α,τ,Te,vp,C) P(α)P(τ)P(Te)P(vp)P(C)dτ dTe dvpdC

(2D numerical integration, Vp and C integration analytical)

( )[ ]/2C,T,v,Tτ,χexpC),T,v,Tτ,|dP( CMBpe2

CMBpe −∝

TCMB(z) from SZE: ResultsFlat prior a ∈ [0,1] (theoretical motivation) (Lima et al 2000)

All limits are at 68% probability level

RI α ≤ 0.092

DI (JL) α ≤ 0.059

DI (SL-MCMC) α ≤0.12 (including lines α ≤ 0.079)

Posteriorfor α

Consistency with std. Model

From lines transitionobservations

mock dataset analyzed to recover input parameters of the cluster

Analysis: MCMC allows to explore the full space of the cluster parameters and the TCMB(z)

Simulated observations of 50 well known clusters

P(vp) = N(0 km/s,1000 km/s)

P(vp) = N(0 km/s,100 km/s)

P(Te) = N(6.50KeV,0.14KeV )

TCMB(z) from SZE: simulations

•Ongoing and near future surveys with ACT, APEX-SZ, SPT, Planck and detailed mapping of a sample of nearby clusters with MAD and OLIMPO experiments will provide much more precise and uniform datasets:

•bias in the ratio approach largely removed •reduced skweness in τ and Tcmb(z) distributions (DI)

SZE experiments

Future SZE experiments

•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 degeneraciesbetween TCMB(z) and cluster parameters.

SAGACESAGACE (Spectroscopic Active Galaxies and Clusters Explorer)

SAGACE is a space-borne differentialspectrometer, coupled to a 3m telescope:

• able to cover the frequency ranges100-450 and 720-760 GHz;

• with angular resolution ranging from4.2 to 0.7 arcmin;

• with photon-noise limited sensitivity(~ 1.5 Jy per second of integration fora 1 GHz resolution element, 50 mJy per second for 30 GHz resolution element)

• Designed to operate for 2 years

Its main goal is to observe the SZ effect on galaxyclusters with 15 GHz resolution, providing, for the first time, precisely calibrated SZ spectral maps ofclusters over its wide frequency range (no intercalibration of different experiments).

It will map and measure the physical parameters of the hot gas extended to the outskirts of a sample of~200 clusters, and to exploit the full potential of the SZ effect as a probe for cosmology:

– Ho with a method completely independentof others

– Dark Matter and Dark Energy– TCMB(z) with a method completely

independent of others

The scientific impact of SAGACE

The high accuracy of the spectralmeasurements allows to control a largepart of the existing degeneraciesbetween the cluster parameters.

SAGACE

SAGACE SAGACE

SAGACE

3BPPlanck

Planck3BP

3BP

Conclusions

•Original tool to perform an observational test of the standard scaling of TCMB and its isotropy up to the redshift of galaxy clusters and to put constraints on alternative cosmological models.

•Information extracted *almost* for free from spectral SZ datasets.

•In the near future, SZE experiments will allow precise measurements of the TCMB(z) scaling law to set constraints on the variation of fundamentalconstants over cosmological time.