Measurement of the T CMB evolution from the Sunyaev-Zel'dovich effect
AAstronomy & Astrophysics manuscript no. TCMB_publi c (cid:13)
ESO 2018August 2, 2018
Measurement of the T CMB evolution fromthe Sunyaev-Zel’dovich effect
G. Hurier , N. Aghanim , M. Douspis , and E. Pointecouteau Institut d’Astrophysique Spatiale, CNRS (UMR8617) Université Paris-Sud 11, Bâtiment 121, Orsay, France CNRS; IRAP; 9 Av. colonel Roche, BP 44346, F-31028 Toulouse cedex 4, FranceUniversité de Toulouse; UPS-OMP; IRAP; Toulouse, Francee-mail: [email protected]
Received / Accepted
Abstract
In the standard hot cosmological model, the black-body temperature of the cosmic microwave background (CMB), T CMB , increaseslinearly with redshift. Across the line of sight CMB photons interact with the hot ( ∼ − K ) and di ff use gas of electrons fromgalaxy clusters. This interaction leads to the well-known thermal Sunyaev-Zel’dovich e ff ect (tSZ), which produces a distortion of theblack-body emission law, depending on T CMB . Using tSZ data from the
Planck satellite, it is possible to constrain T CMB below z = T CMB , we obtain T CMB ( z ) = (2 . ± . × (1 + z ) − β K with β = . ± . β = . ± . β =
0) Big-Bang model.
Key words.
Cosmology: observations – Cosmic background radiation – Galaxies: clusters: general
1. Introduction
The cosmic microwave background (CMB) radiation isa fundamental observational probe of the hot Big-Bangmodel. In standard Λ CDM cosmology, the CMB black-body temperature evolution as a function of redshift reads T CMB ( z ) = T CMB ( z =
0) (1 + z ) − β , with β = T CMB ( z = β = T CMB at z =
0, there arecurrently two direct observational methods to measure T CMB atredshifts z >
0. The first one uses the excitation of interstellar atomic or molecular species by CMB photons (e.g. Loseccoet al. 2001). This approach was used even before the CMBdiscovery (see Thaddeus 1972, for a review of early observa-tions). When in radiative equilibrium with the CMB radiation,the excitation temperature of molecular species equals that ofthe CMB. Thus, these species allow one to measure the CMBtemperature (Bahcall & Wolf 1968). The fact that the CMBis not the only heating source of the interstellar medium andthe lack of a detailed knowledge of the physical conditionsin the absorbing clouds are the main sources of systematicsand uncertainties (Combes & Wiklind 1999). They lead toupper limits or large error bars ( ∆ T ≥ . T CMB (Meyer et al. 1986; Songaila et al. 1994a,b; Lu et al.1996; Roth & Bauer 1999). Recently, Muller et al. (2013) haveperformed a comprehensive analysis that overcomes parts of thelimitations. In particular, they have made use of various atomicand molecular species simultaneously in order to completelymodel the observed cloud properties and hence to provide tightconstraints on T CMB .The second observational approach consists in measuring aweak spectral distortion of the CMB black-body in the direc-tion of galaxy clusters that is caused by the thermal Sunyaev-Zel’dovich (tSZ) e ff ect (Zel’dovich & Sunyaev 1969; Sunyaev& Zel’dovich 1972). This technique was originally proposed byFabbri et al. (1978) and Rephaeli (1980). Predictions for thesemeasurement with Planck have been discussed by Horellou et al.(2005) and de Martino et al. (2012). They predicted, in an opti-mistic case, an uncertainty on the T CMB evolution of ∆ β ∼ . ∆ T ≤ . Planck satellite now o ff ers anew and large sample of galaxy clusters (Planck Collaboration a r X i v : . [ a s t r o - ph . C O ] D ec . Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect results XXIX 2013) observed via the tSZ e ff ect that allows usto derive much tighter constraints on the evolution of the CMBtemperature.Galaxy cluster catalogs that reach deeper (e.g. SPT,Reichardt et al. (2013) and ACT, Hasselfield et al. (2013)) orlarger (e.g. MCXC, Pi ff aretti et al. (2011)) can also be used tocomplement the constraint from the Planck
SZ clusters.In this work, we focus on improving in the measurement of T CMB at redshifts z > Planck data using the tSZ e ff ectfrom galaxy clusters. In Sect. 2 we present the Planck intensitymaps and galaxy cluster catalog that were used. Sect. 3 brieflypresents the tSZ e ff ect. Then in Sect. 4, we present the stack-ing method used to extract the tSZ flux in the di ff erent Planck frequency channels to constrain T CMB . In Sect. 5, we estimatethe uncertainty levels on our measurement that are caused, onthe one hand, by foreground / background contributions to Planck intensity maps and, on the other hand, by instrumental system-atic e ff ects. Next in Sect. 6, we carefully model our measure-ment to determine T CMB from the tSZ spectral law. In Sect. 7,we present our results and compare them with previous mea-surements. Finally in Sect. 8, we discuss our results and theircosmological implications.
2. Data
Planck intensity maps
We used the six channel maps, 100 to 857 GHz, from the
Planck satellite (Planck Collaboration results I 2013). We refer to thePlanck Collaboration results VI (2013) and Planck Collaborationresults VIII (2013) for the generic scheme of time ordered infor-mation processing and map-making, as well as for the character-istics of the
Planck frequency maps. We used the
Planck chan-nel maps in
HEALPix (Górski et al. 2005) N side = Planck beams by e ff ectivecircular Gaussians (see Planck Collaboration results VII 2013,for more details). Planck
SZ catalog
We also used the
Planck catalog of tSZ detections (PlanckCollaboration results XXIX 2013, PSZ, ). It contains 1227sources, which is about six times larger than the
Planck
EarlySZ (ESZ) (Planck Collaboration early VIII 2011) sample and iscurrently the largest tSZ-selected catalog. The PSZ contains 861confirmed clusters to date.In the following, we only consider the sample of of 813
Planck cluster with redshifts up to ∼ Planck channel maps and thus allows us to con-strain T CMB up to z ∼
1, avoiding strong contamination by pointsources or galactic emission.
We complemented our analysis of the
Planck
SZ-cluster cata-log using X-ray selected clusters from the Meta Catalog of X-rayClusters (MCXC) (Pi ff aretti et al. 2011); and tSZ selected clus-ters from the Atacama Cosmological Telescope (ACT) (Hinckset al. 2010; Hasselfield et al. 2013) and the South Pole Telescope(SPT) tSZ catalogs (Chang et al. 2009; Song et al. 2012; The MCXC is a meta-catalog based on ROSAT All Sky Surveycatalogs (see Pi ff aretti et al. 2011, and reference therein). Table 1.
Main characteristics of the galaxy cluster catalogs. N cl is thenumber of objects in the catalog, N ∗ cl is the number of clusters in thepresent work, ¯ z is the mean redshift, z med is the median redshift, σ z isthe redshift dispersion of the catalog, and f sky is the sky coverage of thecatalog.catalog N cl N ∗ cl ¯ z z med σ z f sky Planck
SZ 1227 813 0.247 0.220 0.159 0.84MCXC 1743 823 0.222 0.166 0.172 — SPT 224 142 0.574 0.576 0.279 0.02ACT 91 61 0.586 0.570 0.267 0.01
Reichardt et al. 2013). Table 1 summarizes the main character-istics of these catalogs. In particular, for the present study, weconsidered subsamples from the MCXC, ACT, and SPT cata-logs that consist of clusters not included in the PSZ catalog; forthe MCXC clusters we also imposed that M ≥ M (cid:12) . Emission from radio point sources is a source of contaminationin the estimation of the tSZ flux (Planck Collaboration resultsXXIX 2013) that can lead to biases in tSZ Compton- y signal(see e.g. Hurier et al. 2013, for an example on the Virgo andPerseus galaxy clusters).The NRAO VLA Sky Survey (NVSS) (Condon et al. 1998) isa 1.4 GHz continuum survey covering the entire sky north ofDec > − ◦ . The associated catalog of discrete sources con-tains over 1.8 million radio sources. South of Dec < − ◦ andat galactic latitudes | b | > ◦ , the Sydney University MolongloSky Survey (SUMSS) (Mauch et al. 2003, 2008) is a 843 MHzcontinuum survey also providing a radio source catalog. SUMSSand NVSS have a similar sensitivity and angular resolutions, andcombined they cover the whole sky.We used these two surveys as tracers of the radio emission thatcontaminated our estimation of the tSZ flux to estimate the levelof bias in our measure.
3. The tSZ effect
The tSZ e ff ect is a distortion of the CMB black-body radiationthrough inverse Compton scattering. CMB photons receive anaverage energy boost by collision with hot (a few keV) ionizedelectrons of the intra-cluster medium. The tSZ Compton param-eter in a given direction, n , on the sky is given by y ( n ) = (cid:90) n e k B T e m e c , σ T ds (1)where d s is the distance along the line-of-sight, and n e and T e arethe electron number-density and temperature. In units of CMBtemperature, the tSZ e ff ect at a frequency ν is ∆ T CMB T CMB = g ( ν ) y . (2)Neglecting corrections due to the weakly relativistic high-end ofthe velocity distribution for the thermal electrons, we have g ( ν ) = (cid:20) x coth (cid:18) x (cid:19) − (cid:21) , (3)with the dimensionless frequency x = h ν/ ( k B T CMB ). h and k B represent the Planck and the Boltzmann constants. At z = T CMB ( z = = ± ff ect signal is
2. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect negative below 217 GHz and positive at higher frequencies. Thischaracteristic spectral signature is a unique tool for detecting ofgalaxy clusters. The spectral signature is directly related to T CMB through the x variable. They depend on the convolution of thetSZ intensity with the Planck frequency responses.
100 GHz 143 GHz 217 GHz 353 GHz 545 GHz
Figure 1.
From left to right: stack of
Planck intensity maps from 100 to545 GHz cleaned by the 857 GHz channel, centered on the location of
Planck tSZ detected clusters. From top to bottom: stacked signal fromtSZ detected clusters in di ff erent redshifts bins (from z = . z = . ◦ × ◦ .
4. Methodology
In this section, we describe the procedure that was used to ex-tract the tSZ signal from the full-sky
Planck intensity maps. Westart by considering clusters from the
Planck catalog, becausethey have a high signal-to-noise ratio and a low level of contam-ination. Then, we discuss the case of additional clusters from the
100 GHz 143 GHz 217 GHz 353 GHz 545 GHz
Figure 2.
Same as Fig. 1, but for redshift bins from z = = samples listed in Sect. 2.3.In a first step, we set all Planck frequency channels to a commonangular resolution of 10’, corresponding roughly to the angularresolution the lowest resolution channel at 100 GHz. Then, weextracted individual patches centered on the location of
Planck galaxy clusters and stacked them. Next, we cleaned the obtainedstacked patches from IR emission from galactic dust and extra-galactic IR galaxies using the 857 GHz channel. Finally, we es-timated the tSZ flux in each cleaned stacked patch.
To increase the significance of the tSZ signal per frequency, weperformed a stacking analysis in multiple redshift bins. Our sam-ple consists of 813 clusters with known redshifts, distributed in20 redshift bins from z = z =
1, with a binsize ∆ z = . z and the weighted meanover Y , z e ff only di ff ers at the third decimal. This shows thatthe SZ flux distribution over the bin is homogeneous and that thechoice of bins is a fair sampling of the redshift distribution forthe considered cluster sample. In the following, we use z e ff as themean value for our redshift bin.
3. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect We constructed a stacked patch per redshift bin. We thus ex-tracted individual patches of 2 ◦ × ◦ from the full-sky intensitymaps with pixels of 1.7’. The individual patches were centeredon the positions of the clusters in the considered redshift bin.The individual patches were re-projected using a nearest neigh-bor interpolation on a grid of 0.2’ pixels in gnomonic projection.This conserves the cluster flux. Note that re-projection e ff ectsare the same for all frequencies and consequently do not bias theestimation of T CMB since the latter only depends on the shape ofthe tSZ spectral law.For each redshift bin individual patches are cleaned from point-source contamination. To do this, we masked all sources fromthe
Planck
Catalog of Compact Sources (Planck Collaborationresults XXVIII 2013) detected above 10 σ in one of the six high-est frequency channels of Planck within an area of 30’ from thecluster center. Sources within a radius of 20’ from the consid-ered cluster were not masked. This process avoids biases in thedust-cleaning process (see Sect. 4.2).Finally in each redshift bin, the individual patches per frequencywere co-added with a constant weight. This choice is a two-fold one. It accounts for the fact that the main contribution tothe noise due to CMB is similar from one patch to the other.Furthermore, it avoids cases where a particular cluster will dom-inate the stacked signal. It is worth noting that this a choice isnot optimized for the signal-to-noise ratio of the flux.We verified that we derive similar results when applying ran-dom rotations to the extracted patches before stacking. This testdemonstrated that our stacking is not sensitive to specific ori-entations, produced, for example, by the thermal dust emissionfrom the Galactic plane.
To remove thermal dust contamination in stacked patches perfrequency, we used the 857 GHz channel. The thermal dustemission is known to have a varying spectral energy distribution(SED) across the sky (Planck Collaboration int. XIV 2013). Tocompute the e ff ective thermal dust SED for each stacked patchper frequency, we assumed that in a field of 2 ◦ × ◦ the thermaldust spectral properties can be well described by a single SED.This cleaning was performed for each redshift bin δ and foreach frequency i by computing the scale factor, ρ δ i , between thestacked patch at 857 GHz, M δ , and other stacked patches from100 to 545 GHz, M δ i . To avoid biases produced by correlationsbetween IR emission and the tSZ e ff ect, we computed ρ δ i by re-moving the central region of r < (cid:48) , with r the angular distanceto the clusters position. We checked that performing the clean-ing per cluster instead of per redshift bin provides comparableresults. ρ δ i = (cid:16)(cid:80) r > (cid:48) M δ M i (cid:17) / n − (cid:16)(cid:80) r > (cid:48) M δ (cid:17) (cid:16)(cid:80) r > (cid:48) M δ i (cid:17) / n (cid:16)(cid:80) r > (cid:48) ( M δ ) (cid:17) / n − (cid:16)(cid:80) r > (cid:48) M δ (cid:17) / n , (4)where n is the number of pixels satisfying the condition r > (cid:48) . Then, the stacked patches cleaned from thermal dust wereobtained by subtracting the 857 GHz from the other channels: M δ, cleaned i = M δ i − ρ δ i M δ . (5) We chose a constant patch size because the majority of clusters arepoint-like with respect to the adopted resolution of 10 (cid:48) . Di ff erences inthe physical extension of clusters have thus no significant impact on ourresults. This cleaning process has an impact solely on 353 and 545 GHzchannels with ρ δ i values varying only by 10% and 5% at 353and 545 GHz, from bin to bin. Dust-cleaned stacked patches foreach redshift bin are presented in Figs. 1 and 2. We clearly ob-serve (as reported in Planck Collaboration results XXIX 2013)the intensity decrement at low frequency ( <
217 GHz), the nulle ff ect at 217 GHz and the positive emission at high frequency( >
217 GHz). Note that we report a clear detection of the tSZe ff ect even in the 545 GHz Planck channel for redshifts up to0.6.
To measure the flux from the cleaned stacked patches at 100,143, 217, 353, and 545 GHz, we first derived the shape of thetSZ signal in the stacked patches. To do this, we computed aCompton- y parameter map for each cluster individually usingthe MILCA method (Hurier et al. 2013). Computing the y -mapon a stacked patch would lead to a poorer tSZ reconstruction.We then stacked the reconstructed y -maps for the clusters withina given redshift bin. We refer to them as tSZ filter or template.The tSZ signal in the stacked patches presents a circular sym-metry. We therefore computed the radial profile of the tSZ filterand re-projected it to construct a denoised tSZ filter, M δ tSZ . Weused M δ tSZ as a shape filter to measure the tSZ flux, F δ i , in eachcleaned stacked patch M δ, cleaned i .The tSZ flux was obtained by computing a linear fit of the de-noised tSZ filter on the cleaned stacked patches per frequency ina radius of 20’ around the cluster center, assuming homogeneousnoise and the following modeling M δ, cleaned i = F δ i M δ tSZ + b δ i + N δ i , (6)with b δ i a constant baseline accounting for large-scale ( > (cid:48) )residual contamination and N δ i the noise component includingastrophysical emissions and instrumental noise.From Eq. 6, we derived a tSZ emission law, (cid:98) F δ i , for each red-shift bin δ . The estimator (cid:98) F δ i of F δ i was obtained by adjustingboth F δ i and b δ i . Figure 3 presents the derived emission law forthe tSZ e ff ect for each redshift bin. The standard model is dis-played as a dashed red line. Measured fluxes, (cid:98) F δ i , were used toderive the value of T δ CMB for each redshift bin in Sect. 6.Note that using of a tSZ template induces no prior on thetSZ spectral law (considering that the spatial distribution of thetSZ signal is the same in all channels) and thus on (cid:98) F δ i . The smalldi ff erence between tSZ filters from bin to bin is due to the di ff er-ence in cluster extensions since the profiles used here were notrescaled with respect to their angular sizes contrary to Arnaudet al. (2010) and the Planck Collaboration int. V (2013).
5. Statistical and systematic uncertainties
We now discuss the sources of uncertainties and systematic er-rors on the measured fluxes (cid:98) F δ i . We first focus on the uncertain-ties produced by background and foreground signals, includinginstrumental noise. Then we address the astrophysical compo-nents correlated to the tSZ emission, and finally we discuss thesystematic errors caused by the instrument spectral responses. To estimate the uncertainty on (cid:98) F δ i caused by contamination byother sources signal, we extracted the flux at 1000 random po-
4. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Figure 3.
From left to right and top to bottom: Measured tSZ emission law in units of K CMB for each redshift bin form 0 to 1, with ∆ z = .
05. Notethat bins with 0 . ≤ z < .
85 and 0 . ≤ z < .
95 do not contain any cluster. Black stars denote the data and dashed red lines the theoretical tSZemission law. Error bars are strongly correlated between the di ff erent frequency channels, see Tab. 2. 5. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Table 2.
Correlation matrix of statistical uncertainties for the measure-ment of tSZ flux (cid:98) F δ i , estimated from 1000 random positions across thesky. Frequency (GHz) 100 143 217 353 545100 1 0.97 0.96 0.79 0.23143 0.97 1 0.99 0.83 0.26217 0.96 0.99 1 0.86 0.32353 0.79 0.83 0.86 1 0.61545 0.23 0.26 0.32 0.61 1 sitions across the sky for each denoised tSZ filter. We avoidedthe galactic plane area, which is not represented in our clusterdistribution.In the stacking process each cluster was considered to be un-correlated with others. Consequently, we derived the full covari-ance matrix for the flux estimate in frequency channels from 100to 545 GHz. An example of correlation matrix is presented inTable. 2. This correlation matrix only accounts for uncertaintiesproduced by uncorrelated components (with respect to the tSZe ff ect) in the flux estimation. This correlation matrix has a de-terminant of 10 − , which quantifies the volume occupied by theswarm of data samples in our five-dimension subspace (cleanedfrequencies from 100 to 545 GHz).At 100 to 217 GHz, the CMB anisotropies are the main sourceof uncertainties. This explains the high level of correlation inthe estimated fluxes. At higher frequencies, instrumental noiseand dust residuals become an important contribution to the totaluncertainties, which explains the lower level of correlation. Uncertainties produced by uncorrelated foregrounds, for in-stance, CMB, can be fairly estimated from measurements at ran-dom positions over the sky. However, these measurements do notaccount for noise or bias produced by correlated emissions, suchas, radio sources at low frequency, cosmic infrared background(CIB) at high frequency, and the kinetic SZ e ff ect. The CMB temperature measure is directly related to the fre-quency at which tSZ e ff ect is null, making it a key frequencyin our analysis. At 217 GHz, a contribution from the CIB (theintegrated IR emission from dust in distant galaxies (see e.g.,Hauser & Dwek 2001; Kashlinsky 2005; Lagache et al. 2005, forreviews)) is significant and is correlated to the tSZ signal (e.g.,Addison et al. 2012). In the following, we assumed a conserva-tive situation of full correlation between tSZ and CIB, ρ δ cor = z <
1. Consequently, the actual correlation factor ρ δ cor islower than one and depends on the completeness with respectto the redshift (see Planck Collaboration results XXIX 2013, formore details).Considering the CIB intensity at 217 GHz, (cid:96) C CIB (cid:96) = . µ K .sr, given by the Planck Collaboration early XVIII(2011), the CMB power spectrum at (cid:96) = (cid:96) C CMB (cid:96) (cid:39) µ K .sr, given in Planck Collaboration results XV (2013) andconsidering the contribution to tSZ power spectrum from oursample (cid:96) C tSZ (cid:96) (cid:39) . − y .sr (Planck Collaboration resultsXXI 2013), we can compute the bias due to the CIB contribu-tion. We furthermore assumed that 90% of the CIB is cleaned by the dust-cleaning process discussed in Sect. 4.2 and we defined f clean = . × CIB correlation for a given redshift bin δ : B δ CIB = ρ δ cor f CIB N bin (cid:115) C CIB (cid:96) g ( ν i ) C tSZ (cid:96) F δ i (cid:0) ∆ F δ (cid:1) CMB (1 − f clean ) , (7) f CIB ∼ .
05 is the fraction of CIB emission produced by objectsat redshift < N bin is the number of redshift bins, and (cid:16) ∆ F δ (cid:17) CMB is the contribution of the CMB to the uncertainties over F δ i .We derived a ratio between CMB and CIB fluctuations ofabout 0.2% on average per cluster. At most, we use about onehundred clusters in a single redshift bin. This reduced the CMBfluctuations by a factor 10. Consequently, in a conservative case,the CIB at 217 GHz contributes at the level of 2% of the intensityof CMB and can therefore be neglected. Radio sources within galaxy clusters can produce an overesti-mate of the flux at low frequencies, which in turn leads to anunderestimate of T CMB ( z ).Using the NVSS and the SUMSS catalogs of radio pointsources, we estimated the radio point-source contamination onthe measured tSZ flux. To do this, we projected the NVSSand the SUMSS catalogs on a full-sky map (considering onlySUMSS sources at Dec < − ◦ , and extrapolating their fluxesfrom 853 MHz to 1.4 GHz with a spectral index of -1). Then, wesmoothed the obtained map at 10’. We thus obtained a full-skymap of the combined radio sources at 1.4 GHz on which we es-timate the radio flux F δ rad for each stacked patch and redshift bin δ using the approach described in Sect. 4.3. Finally, we extrap-olated the radio emission from 1.4 GHz to Planck frequencies,assuming a spectral index of -1. We estimated the spectral indexby computing the cross power spectrum between the NVSS cata-log projected map and the
Planck
100 GHz channel. We derivedan averaged spectral index of − . ± . F δ rad , expressed in termsof percentage of the measured tSZ flux at 100 GHz are summa-rized in Table 3. Under the simple assumption of a single spectralindex -1, we show that the contamination by radio source emis-sion on the measured tSZ flux at 100 GHz is lower than 15%. Inthe analysis described in Sect. 6.2.2, we show how this contri-bution was modeled, fitted, and accounted for in the estimate ofthe uncertainties. The kinetic SZ e ff ect, kSZ, is the Doppler shift of CMB photonsthat scatter the intracluster electrons. This e ff ect is faint, one or-der of magnitude lower than the tSZ. It has the same spectraldependance as the CMB and is spatially correlated to the tSZsignal. The kSZ e ff ect can produce positive or negative CMBtemperature anisotropies. Consequently, this e ff ect will not biasthe tSZ measurement, but will enlarge the CMB dispersion atthe clusters position and therefore the error-bars. At Planck res-olution, the increase in CMB variance due to the kSZ is small(Planck Collaboration int. XIII 2013) and can be neglected inour analysis.In some nonstandard inhomogenous cosmological models (seee.g. Goodman 1995; Clarkson 2012), the kSZ monopole is dif-ferent from zero. This could induce a bias in the tSZ measure-
6. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Table 3.
Reshift binning used for our analysis, N cl is the number ofclusters per bin, ¯ z is the mean redshift, z e ff is the mean redshift weightedby the flux of each clusters Y (Planck Collaboration results XXIX2013) and F δ sync is the radio contamination in tSZ measured flux at 100GHz estimated from NVSS and SUMSS data. It is expressed in termsof percentage of the tSZ flux at 100 GHz.Redshift bin δ N cl ¯ z z e ff F δ sync (%)0.00-0.05 43 0.036 0.037 14.00.05-0.10 125 0.076 0.072 10.30.10-0.15 92 0.126 0.125 6.20.15-0.20 104 0.172 0.171 6.00.20-0.25 95 0.221 0.220 4.50.25-0.30 87 0.273 0.273 9.00.30-0.35 81 0.323 0.322 1.00.35-0.40 50 0.375 0.377 4.90.40-0.45 45 0.424 0.428 0.40.45-0.50 26 0.471 0.471 4.80.50-0.55 20 0.525 0.525 2.50.55-0.60 18 0.565 0.565 -0.50.60-0.65 12 0.619 0.618 2.50.65-0.70 6 0.676 0.676 -3.20.70-0.75 5 0.718 0.718 3.70.75-0.80 2 0.783 0.777 -2.80.80-0.85 0 — — —0.85-0.90 1 0.870 0.870 -0.30.90-0.95 0 — — —0.95-1.00 1 0.972 0.972 -0.3 ment. However, these models are now strongly constrained by Planck data (Planck Collaboration int. XIII 2013).
To measure the tSZ emission law in the
Planck channels weintegrated the tSZ emission law, g ( T δ CMB , T δ e , ν ) (see Eq. 3),over the Planck spectral responses (i.e., bandpasses), see PlanckCollaboration results IX (2013), H i , in the following manner: A i ( T δ CMB , T δ e ) = (cid:82) H i ( ν ) g ( T δ CMB , T δ e , ν )d ν (cid:82) H i ( ν ) C ( ν )d ν , (8)with, A i the tSZ transmission in the i -th Planck channel, C ( ν )the emission law of the calibrators, CMB, and planets (PlanckCollaboration results VIII 2013), and T δ e the e ff ective clustertemperature per redshift bin.The bandpasses present uncertainties that depend on the tSZspectral law. Given that T δ CMB and T δ e produce small variations ofthe tSZ, we can assume that the bandpass uncertainties are con-stant. We propagated the uncertainties on the bandpasses H i inour analysis by computing the uncertainties on the tSZ emissionlaw A i ( T CMB , T δ e ) after integrating over the bandpass. These turninto uncertainties on the recovered value of T δ CMB . We derived asystematic uncertainty of 0 .
010 K at z = T δ CMB ; it becomes0 . × (1 + z e ff ) K for each redshift bin.At low frequencies, the Planck data were calibrated with re-spect to CMB dipole ( T CMB ( z = T δ CMB ( z ). However, this source ofuncertainties is small, about 0.2% at 100 to 217 GHz channels(Planck Collaboration results VIII 2013). It was neglected in thefollowing.
6. Analysis
Our measurement at the i-th
Planck frequency can be modeledas F δ i = Y δ A i ( T δ CMB , T δ e ) + F δ rad A rad i + F δ ir A ir i , (9)with Y δ = (cid:82) δ (cid:82) y d Ω d z the integrated Compton parameter for aredshift bin δ , A rad i the radio source spectrum with spectral index-1 normalized to 1 at 100 GHz, and A ir i is the IR spectrum withdust temperature T d =
17K and spectral index β d = . A ir i SED theoretical model is consistent with thespectrum derived from our cleaning procedure.The adjustable parameters are Y δ , T δ CMB , T δ e , F δ rad the radiosource flux and F δ ir the IR contamination level including CIBemission. Figure 4.
Likelihood function of the measured tSZ emission law as afunction of T δ CMB and T δ e for redshift bins between z = .
05 and z = .
10. Confidence levels at 1, 2, and 3 σ are presented in light-blue, blue,and dark-blue areas. In the following, we perform a sensitivity analysis between T δ CMB and the other parameters of the model.
The relativistic corrections to the tSZ emission law has beencomputed numerically (see e.g. Rephaeli 1995; Pointecouteauet al. 1998; Itoh et al. 1998). If we assume that the relativisticcorrections can be described as a first-order approximation, ∆ T relatCMB ( T e ) = ∆ T unrelatCMB + T δ e ∆ T corCMB , (10)the averaged tSZ emission law can be described with an aver-aged temperature fitted as an e ff ective temperature, T δ e , for thestacked tSZ signal (see Nozawa et al. 2000, for a more detailedfitting formula).Figure 4 presents the likelihood function in the plane ( T δ CMB , T δ e ) for clusters in the redshift bin 0.05 to 0.10. The other red-shift bins present similar behaviors. The value we derived for T δ e is below 10 keV at 1 σ level and below 15 keV at 3 σ level, with abest-fitting value around 5 keV. This is consistent with the X-ray
7. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect derived temperatures for typical clusters in the Planck sample.Figure 4 shows no correlation between the recovered value of T δ CMB and T δ e . This Indicates that we can safely neglect relativis-tic corrections in our analysis. Figure 5.
Top panel: Likelihood function of the measured tSZ emissionlaw as a function of T δ CMB and the radio source flux, expressed in unitsof tSZ flux at 100 GHz, for redshifts between z = .
10 and z = . T δ CMB and the infrared contamination level, expressed inunits of tSZ flux at 353 GHz, for redshift between z = .
10 and z = . σ are represented in light-blue, blue, anddark-blue. Figure 6.2.2 presents the likelihood function in the plane ofthe radio contamination, F δ srad , and T δ CMB (top panel), and in theplane of the IR contamination, F δ IR , and T δ CMB (bottom panel) forclusters within a redshift bin 0.10 to 0.15. The other redshift binspresent similar behaviors. We found that the IR contamination,including CIB residuals, is compatible with 0 and does not biasour estimate of the tSZ flux. We also note that the derived valueof F δ IR is consistent with all f clean > . σ level, consistentwith the conservative case discussed in Sect. 5.2.1.Furthermore, we observed that the radio source contaminationproduces some bias on the T δ CMB measurement. This bias trans-lates into (cid:98) T δ CMB = T δ CMB − . × (1 + z e ff ) × F δ rad . Given the results of the sensitivity analysis discussed above, wecan simplify the model in Eq. 9 to F δ i = Y δ A i ( T δ CMB ) + F δ rad A rad i , (11)considering only the relevant parameters Y δ , T δ CMB and F δ rad .To fit T δ CMB in each redshift bin, we used a profile likelihoodapproach. First, we computed, through an unbiased linear fit, thetSZ flux, (cid:98) Y δ , of our measured spectral law for each value of T δ CMB and F δ rad . Given the similar amplitudes of the uncertainties onthe measurement (mainly CMB contamination) and the model(bandpasses), we used the following estimator for Y δ : (cid:98) Y δ = (cid:104) A T W A − Tr( C TA W ) (cid:105) − (cid:104) A T W (cid:98) F δ (cid:105) , (12)with A the tSZ transmission vector defined in Eq. 8, C A the A co-variance matrix , (cid:98) F δ the measured tSZ emission law (see Eq. 6),and W = C − F δ the inverse of the noise covariance matrix on (cid:98) F δ .Then, we computed the χ , for each paire of parameters( T δ CMB , F δ sync ) as χ = (cid:16)(cid:98) F δ − F δ (cid:17) T (cid:20) C F δ + (cid:16)(cid:98) Y δ (cid:17) C A (cid:21) − (cid:16)(cid:98) F δ − F δ (cid:17) . (13)Finally, we estimated the value of T δ CMB by marginalizingover F δ rad , considering a flat prior − < F δ rad <
15% (as ob-served in Sect. 5.2.2); and by computing the first-order momentof the likelihood function, L = e − χ / with respect to T δ CMB4 .We computed the uncertainties on T δ CMB using the second-order moment of L . Note that the uncertainties only di ff er atthe fourth decimal at 68% confidence level. We also computedthe covariance between each T δ CMB and separated the statisticaluncertainties that are fully uncorrelated between redshift bins,and the systematic errors that are fully correlated from one binto another.Table 4 summarizes our results for the derived T CMB ( z ) andthe associated statistical and systematic uncertainties. We ver-ified that removing clusters contaminated by very bright radiosources ( S ≥
250 mJy at 1.4 GHz) does not a ff ect our results.
7. Results
The measurement of the tSZ emission law allows us to constrainthe value of T CMB at z = Planck clusters, which constitutes our base dataset.We also discuss other cluster samples and finally we give thetightest constraints obtained by combining tSZ measures from
Planck clusters and measures from molecular and atomic ab-sorptions.
We computed the χ per degree of freedom (dof) between ourmeasurements of T δ CMB (red filled circles in Fig. 6) and the adi-abatic evolution of the CMB temperature (solid line in Fig. 6), The uncertainties on the response A rad i are lower than 1% and ne-glected. In contrast, the uncertainties on the response for the tSZ in the217 GHz channel is about 25% (Planck Collaboration results IX 2013). Note that the obtained T CMB value only di ff ers at the third decimalwhen the maximum likelihood is used as estimator.8. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Table 4.
Measured value of T δ CMB in Kelvin derived from the tSZ emis-sion law per redshift bin. Systematic errors are fully correlated from oneredshift bin to the next.Redshift bin δ N cl T δ CMB ∆ T CMB (stat) ∆ T CMB (syst)0.00-0.05 43 2.888 0.039 0.0110.05-0.10 125 2.931 0.017 0.0110.10-0.15 92 3.059 0.032 0.0120.15-0.20 104 3.197 0.030 0.0120.20-0.25 95 3.288 0.032 0.0130.25-0.30 87 3.416 0.038 0.0130.30-0.35 81 3.562 0.050 0.0140.35-0.40 50 3.717 0.063 0.0140.40-0.45 45 3.971 0.071 0.0150.45-0.50 26 3.943 0.112 0.0150.50-0.55 20 4.380 0.119 0.0160.55-0.60 18 4.075 0.156 0.0160.60-0.65 12 4.404 0.194 0.0160.65-0.70 6 4.779 0.278 0.0170.70-0.75 5 4.933 0.371 0.0170.75-0.80 2 4.515 0.621 0.0180.80-0.85 0 — — —0.85-0.90 1 5.356 0.617 0.0190.90-0.95 0 — — —0.95-1.00 1 5.813 1.025 0.020 with T CMB ( z = = . ± .
001 K. We obtained χ do f = . T CMB evolution.If we assume an adiabatic expansion, T CMB ( z ) is written as T CMB ( z ) = T CMB ( z = + z ) . (14)We derived T CMB ( z =
0) from the estimated T δ CMB for all theredshift bins δ probed by our sample of Planck clusters. Themeasurements are presented in Fig. 6 as red filled circles. Weobserve that all measurements are within a 2 σ from the adia-batic expansion evolution. The best fit, using all redshift bins,gives T CMB ( z = = . ± . ± .
011 K with statisticaland systematics uncertainties, respectively. Note that the errorsare dominated by the systematic uncertainty from the spectralresponses. It is fully correlated between redshift bins, and thuscannot be reduced. Our measurement of T CMB ( z =
0) from thetSZ emission law cannot compete, in terms of accuracy, with theCOBE-FIRAS T CMB ( z = = . ± .
001 K (Fixsen 2009).However, it is fully consistent.
Our analysis was based on a sample of 813
Planck clusters cov-ering a redshift range from 0 to 1. If we express T CMB ( z ) as inLima et al. (2000), T CMB ( z ) = T CMB ( z = + z ) − β , (15)it is possible to test the T CMB evolution in adiabatic expansion.We fit β using a maximum-likelihood analysis and a flat prior.Figure 7 presents the best-fitting value of β for each individualredshift bin δ , considering T CMB ( z = = . β = σ and that red-shift bins from z = .
05 to z = . β . Figure 7 also illustrates that our constraint on β are not domi-nated by a given bin, but that it uses the entire redshift range.We derived β = . ± .
017 from the tSZ emission lawin the 18 redshift bins used in the analysis, consistent with nodeviation from adiabatic evolution. Note that in contrast to the T CMB ( z =
0) measurement, β is not a ff ected by bandpass uncer-tainties because they are fully correlated for all redshift bins.We compared our result on β with the di ff erent constraintsobtained either from other tSZ measurements or molecular andatomic absorptions.Previous analyses have measured T CMB ( z ) either at low redshift(Luzzi et al. 2009) using the tSZ e ff ect on a small numberof clusters, or at higher redshifts (Cui et al. 2005; Ge et al.1997; Srianand et al. 2000; Molaro et al. 2002; Muller et al.2013) using atomic and molecular absorption. These T CMB mea-surements are presented in Fig. 8 with the standard adiabaticevolution shown as a solid black line.We derived for the above-mentioned measurements constraintson β using the same fitting procedure and a flat prior as in ouranalysis. Table 5 summarizes the results. We found that thetSZ emission law from Planck clusters provides the tightestconstraint on β . Errors are smaller by about a factor of twocompared with previous constraints, separately. Our result, β = . ± . ff ect in Planck clusters is at thesame level of precision and accuracy as the tightest constraint, β = . ± . Planck .By furthermore combining our new limit on β with the pre-vious data sets, we improved the derived constraint on the T CMB evolution. We found β = . ± .
8. Discussion
Our basic results presented in Sect. 7 were derived from the anal-ysis of tSZ emission law of 813 clusters from
Planck up to z ∼ β = . ± . T CMB .To explore the variation of this result with other clustersamples, we performed the same analysis, as in Sect. 6, onthe MCXC (Pi ff aretti et al. 2011) catalog. This allowed us toselect a large number of massive clusters (see Table 1). Toavoid significant radio contamination of the tSZ measurement,we considered only clusters with an intensity lower than500 µ K CMB in the 100 GHz channel. This process only removesthree clusters from our initial MCXC sample (see Sect. 2.3).We thus performed our analysis, and with the obtained T CMB measures ranging from z = β = . ± . β , because the tSZ signal inthe Planck intensity maps from the selected clusters is faint.Consequently, we did not include these measurements in theanalysis. Combining the constraints from the tSZ emission lawwith other direct measurement using molecular and atomicabsorption, we found the tightest limit on the T CMB evolution tobe β = . ± . T CMB evolution.Departures from an adiabatic evolution of T CMB can be testedthrough indirect measurements. In particular when CMB photonnumber is not conserved, β can be constrained by the distance
9. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Figure 6.
Measured T δ CMB from the
Planck data are shown as red filled circles. The theoretical T CMB ( z ) dependance in adiabatic expansion with T CMB ( z = = .
726 K is presented as black solid line. Note that the line is not a fit to the data points. Here, error bars only account for thestatistical dispersion. The uncertainties due to spectral responses are not displayed.
Table 5.
Measured values of T CMB and β re-derived, with our fitting procedure, from di ff erent subsamples of T CMB ( z ) measurements based on thetSZ e ff ect and atomic / molecular absorptions. We provide the χ dof with respect to the standard adiabatic evolution with T CMB = . ± .
001 Kand β =
0. Measurement method T CMB ∆ T CMB β ∆ β χ dof dof ReferencesC I and C II absorption 2.71 0.20 -0.002 0.067 0.09 4 (a)CO absorption 2.78 0.11 -0.018 0.033 0.14 5 (b)Various molecular species 2.69 0.05 0.022 0.031 0.52 1 (c)tSZ 2.66 0.05 0.034 0.078 1.01 13 (d)tSZ (this work) 2.72 0.01 0.009 0.017 0.89 18 (e)All atomic and molecular 2.71 0.05 0.003 0.021 0.16 10 (a,b,c)All tSZ 2.72 0.01 0.009 0.016 0.91 31 (d,e)All 2.72 0.01 0.006 0.013 0.74 41 (a,b,c,d,e)(a) using data samples from Cui et al. (2005); Ge et al. (1997); Srianand et al. (2000) and Molaro et al. (2002).(b) using data samples from Srianand et al. (2008) and Noterdaeme et al. (2011).(c) using data samples from Muller et al. (2013).(d) using data samples from Battistelli et al. (2002) and Luzzi et al. (2009).(e) The present analysis. duality relation violation (Avgoustidis et al. 2012, and referencestherein) or by combining the CMB and galaxy distribution (asin, e.g., Opher & Pelinson 2005). These indirect measurementsyield β = . ± .
020 and β ≤ . T CMB -redshift relation in decaying dark-energy (DE) models. Jetzer et al. (2011) predicted the following relation: T CMB ( z ) = T CMB ( z = × (1 + z ) (16) × (cid:32) ( m − Ω m ) + m (1 + z ) m − Ω Λ ( m − Ω m (cid:33) / , with Ω m and Ω Λ the matter and DE energy densities at z = m = w e ff +
1) is related to the e ff ective equation ofstate of the decaying DE, w e ff . Considering a flat Universe and Ω m = . ± .
020 (Planck Collaboration results XVI 2013),
10. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Figure 7.
Derived β values for each redshift bin δ considering T CMB ( z = = . σ levels. Errors bars are displayed centered on β = ff erent redshift bins δ . The dashed black line represents β = we derive w e ff = − . ± . T CMB with redshift can also be a ff ectedby time-varying fundamental constants (see Uzan 2011, fora recent review). Specifically for the tSZ-based constraints,variations of h and k B in Eq. 3 lead to deviations of β from zero hk B T CMB (0) (1 + z ) β = C ste . However, variations of the fundamentalconstants become small after the Universe enters its currentDE-dominated epoch (Barrow et al. 2002), and consequentlytSZ variations are less sensitive to these changes at z <
9. Conclusion
We have performed an analysis of the
Planck intensity datain the range of 100 to 857 GHz, aimed at deriving the CMBtemperature and its evolution via the tSZ emission law. Basedon the
Planck
SZ catalog, we measured T CMB ( z ) in the redshiftrange 0 < z <
1. This is the first measurement of T CMB ( z ) onsuch a large tSZ sample of clusters. It demonstrates the abilityof exploring the low-redshift range which cannot be covered bythe traditionally used optical / UV quasar absorption systems.We showed that clustered CIB and relativistic correctionsto the tSZ spectral law do not produce any significant bias onour result. We note that the main uncertainties are caused by the
Planck instrumental spectral responses, CMB contamination,and the radio source contamination. They were modeled and accounted for in the error bars in the determination of T CMB ( z ).Our measurement of T CMB ( z ) below z = z = .
65, about 1% for all binsbelow z = .
3, and better than 0.6% for the redshift between z = .
05 and z = .
10. This is the most precise measurementat z > T CMB ( z ) at low redshifts withresults from Muller et al. (2013) and references presentedin Fig. 8, we obtained the tightest constraints so far on the T CMB ( z ) = T CMB ( z = + z ) − β law, with β = . ± . z ( z > .
5) clusterswill bring a major improvement in T CMB ( z ) measurement fromthe tSZ emission law. In particular, SZ surveys such as Planckand SPT-3G and optical surveys such as the Dark EnergySurvey (The Dark Energy Survey Collaboration 2005) and Pan-STARRS (Kaiser et al. 2002; Tonry et al. 2012) will provide uswith much larger and deeper cluster samples. In the future, evenlarger and deeper samples of massive clusters will be constructedfrom from EUCLID (Amiaux et al. 2012; Amendola et al.2012), the Large Synoptic Survey Telescope (LSST ScienceCollaboration et al. 2009), and SRG-eROSITA (Merloni et al.2012; Pillepich et al. 2012). In combination with the fourth-generation CMB space mission, the tSZ emission law from clus-ters will strongly improve existing constraints on T CMB ( z ) up to z =
11. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Figure 8.
Top panel: T
CMB as a function of redshift. The red filled circles represent T CMB measured from the tSZ emission law in redshift bins of
Planck clusters. The green star shows COBE-FIRAS measurement at z = T CMB measurements usingindividual clusters (Battistelli et al. 2002; Luzzi et al. 2009). Dark-blue triangles represent measurements from C I and C II absorption (Cui et al.2005; Ge et al. 1997; Srianand et al. 2000; Molaro et al. 2002) at z = (1.8, 2.0, 2.3, 3.0). Blue diamonds show the measurements from CO absorptionlines (Srianand et al. 2008; Noterdaeme et al. 2011), and finally the light-blue asterisk is the constraint from various molecular species analysesby Muller et al. (2013). The solid black line presents the standard evolution for T CMB and the dashed black line represents our best-fitting modelcombining all the measurements. The 1 and 2 σ envelopes are displayed as shaded dark and light-gray regions. Bottom panel:
Deviation from thestandard evolution in units of standard deviation. The dashed and dotted black lines correspond to the 1 and 2 σ levels. Acknowledgements
We thank the anonymous referee for his or her comments. We aregrateful to J.F. Macías-Pérez, J.M. Diego, and R.Genova-Santosfor their comments and suggestions. Some of the results in thispaper have been derived using the
HEALPix package (Górskiet al. 2005).We acknowledge the support of the French
Agence Nationale dela Recherche under grant ANR-11-BD56-015.The development of Planck has been supported by: ESA;CNES and CNRS / INSU-IN2P3-INP (France); ASI, CNR, andINAF (Italy); NASA and DoE (USA); STFC and UKSA(UK); CSIC, MICINN and JA (Spain); Tekes, AoF and CSC(Finland); DLR and MPG (Germany); CSA (Canada); DTUSpace (Denmark); SER / SSO (Switzerland); RCN (Norway); SFI(Ireland); FCT / MCTES (Portugal); and The development ofPlanck has been supported by: ESA; CNES and CNRS / INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA andDoE (USA); STFC and UKSA (UK); CSIC, MICINN andJA (Spain); Tekes, AoF and CSC (Finland); DLR and MPG(Germany); CSA (Canada); DTU Space (Denmark); SER / SSO(Switzerland); RCN (Norway); SFI (Ireland); FCT / MCTES(Portugal); and PRACE (EU).
References
Addison, G. E., Dunkley, J., & Spergel, D. N. 2012, MNRAS, 427, 1741Amendola, L., Appleby, S., Bacon, D., et al. 2012, ArXiv e-printsAmiaux, J., Scaramella, R., Mellier, Y., et al. 2012, in Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series, Vol. 8442, Society ofPhoto-Optical Instrumentation Engineers (SPIE) Conference SeriesArnaud, M., Pratt, G. W., Pi ff aretti, R., et al. 2010, A&A, 517, A92Avgoustidis, A., Luzzi, G., Martins, C. J. A. P., & Monteiro, A. M. R. V. L. 2012,J. Cosmology Astropart. Phys., 2, 13Bahcall, J. N. & Wolf, R. A. 1968, ApJ, 152, 701Barrow, J. D., Sandvik, H. B., & Magueijo, J. 2002, Phys. Rev. D, 65, 063504Battistelli, E. S., De Petris, M., Lamagna, L., et al. 2002, ApJ, 580, L101Bennett, C. L., Halpern, M., Hinshaw, G., et al. 2003, ApJS, 148, 1Chang, C. L., Ade, P. A. R., Aird, K. A., et al. 2009, in American Instituteof Physics Conference Series, Vol. 1185, American Institute of PhysicsConference Series, ed. B. Young, B. Cabrera, & A. Miller, 475–477Clarkson, C. 2012, Comptes Rendus Physique, 13, 682Combes, F. & Wiklind, T. 1999, in Astronomical Society of the PacificConference Series, Vol. 156, Highly Redshifted Radio Lines, ed. C. L. Carilli,S. J. E. Radford, K. M. Menten, & G. I. Langston, 210Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998, AJ, 115, 1693Cui, J., Bechtold, J., Ge, J., & Meyer, D. M. 2005, ApJ, 633, 649de Martino, I., Atrio-Barandela, F., da Silva, A., et al. 2012, ApJ, 757, 144Fabbri, R., Melchiorri, F., & Natale, V. 1978, Ap&SS, 59, 223Fixsen, D. J. 2009, ApJ, 707, 916Fixsen, D. J., Cheng, E. S., Gales, J. M., et al. 1996, ApJ, 473, 576Freese, K., Adams, F. C., Frieman, J. A., & Mottola, E. 1987, Nuclear PhysicsB, 287, 797Ge, J., Bechtold, J., & Black, J. H. 1997, ApJ, 474, 67
12. Hurier et al.: Measurement of the T CMB evolution from the Sunyaev-Zel’dovich e ff ect Goodman, J. 1995, Phys. Rev. D, 52, 1821Górski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759Hasselfield, M., Hilton, M., Marriage, T. A., et al. 2013, e-printsArXiv:1301.0816Hauser, M. G. & Dwek, E. 2001, ARA&A, 39, 249Hincks, A. D., Acquaviva, V., Ade, P. A. R., et al. 2010, ApJS, 191, 423Horellou, C., Nord, M., Johansson, D., & Lévy, A. 2005, A&A, 441, 435Hurier, G., Hildebrandt, S. R., & Macias-Perez, J. F. 2013, e-printsArXiv:1007.1149Itoh, N., Kohyama, Y., & Nozawa, S. 1998, ApJ, 502, 7Jaeckel, J. & Ringwald, A. 2010, Annual Review of Nuclear and ParticleScience, 60, 405Jetzer, P., Puy, D., Signore, M., & Tortora, C. 2011, General Relativity andGravitation, 43, 1083Kaiser, N., Aussel, H., Burke, B. E., et al. 2002, in Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series, Vol. 4836, Society ofPhoto-Optical Instrumentation Engineers (SPIE) Conference Series, ed. J. A.Tyson & S. Wol ff , 154–164Kashlinsky, A. 2005, Phys. Rep., 409, 361Lagache, G., Puget, J.-L., & Dole, H. 2005, ARA&A, 43, 727Lima, J. A. S., Silva, A. I., & Viegas, S. M. 2000, MNRAS, 312, 747Lima, J. A. S. & Trodden, M. 1996, Phys. Rev. D, 53, 4280Losecco, J. M., Mathews, G. J., & Wang, Y. 2001, Phys. Rev. D, 64, 123002LSST Science Collaboration, Abell, P. A., Allison, J., et al. 2009, ArXiv e-printsLu, L., Sargent, W. L. W., Barlow, T. A., Churchill, C. W., & Vogt, S. S. 1996,ApJS, 107, 475Luzzi, G., Shimon, M., Lamagna, L., et al. 2009, ApJ, 705, 1122Mather, J. C., Fixsen, D. J., Shafer, R. A., Mosier, C., & Wilkinson, D. T. 1999,ApJ, 512, 511Matyjasek, J. 1995, Phys. Rev. D, 51, 4154Mauch, T., Murphy, T., Buttery, H. J., et al. 2003, MNRAS, 342, 1117Mauch, T., Murphy, T., Buttery, H. J., et al. 2008, VizieR Online Data Catalog,8081, 0Merloni, A., Predehl, P., Becker, W., et al. 2012, ArXiv e-printsMeyer, D. M., York, D. G., Black, J. H., Cha ff ee, Jr., F. H., & Foltz, C. B. 1986,ApJ, 308, L37Molaro, P., Levshakov, S. A., Dessauges-Zavadsky, M., & D’Odorico, S. 2002,A&A, 381, L64Muller, S., Beelen, A., Black, J. H., et al. 2013, A&A, 551, A109Murphy, M. T., Webb, J. K., & Flambaum, V. V. 2003, MNRAS, 345, 609Noterdaeme, P., Petitjean, P., Srianand, R., Ledoux, C., & López, S. 2011, A&A,526, L7Nozawa, S., Itoh, N., Kawana, Y., & Kohyama, Y. 2000, ApJ, 536, 31Opher, R. & Pelinson, A. 2005, Brazilian Journal of Physics, 35, 1206Overduin, J. M. & Cooperstock, F. I. 1998, Phys. Rev. D, 58, 043506Pi ff aretti, R., Arnaud, M., Pratt, G. W., Pointecouteau, E., & Melin, J.-B. 2011,A&A, 534, A109Pillepich, A., Porciani, C., & Reiprich, T. H. 2012, MNRAS, 422, 44Planck Collaboration early VIII. 2011, A&A, 536, A8Planck Collaboration early XIX. 2011, A&A, 536, A19Planck Collaboration early XVIII. 2011, A&A, 536, A18Planck Collaboration early XXVI. 2011, A&A, 536, A26Planck Collaboration int. V. 2013, A&A, 550, A131Planck Collaboration int. XIII. 2013, e-prints ArXiv:1303.5090Planck Collaboration int. XIV. 2013, e-prints ArXiv:1307.6815Planck Collaboration results I. 2013, e-prints ArXiv:1303.5062Planck Collaboration results IX. 2013, e-prints ArXiv:1303.5070Planck Collaboration results VI. 2013, e-prints ArXiv:1303.5067Planck Collaboration results VII. 2013, e-prints ArXiv:1303.5068Planck Collaboration results VIII. 2013, e-prints ArXiv:1303.5069Planck Collaboration results XV. 2013, e-prints ArXiv:1303.5075Planck Collaboration results XVI. 2013, e-prints ArXiv:1303.5076Planck Collaboration results XXI. 2013, e-prints ArXiv:1303.5081Planck Collaboration results XXIX. 2013, e-prints ArXiv:1303.5089Planck Collaboration results XXVIII. 2013, e-prints ArXiv:1303.5088Pointecouteau, E., Giard, M., & Barret, D. 1998, A&A, 336, 44Puy, D. 2004, A&A, 422, 1Reichardt, C. L., Stalder, B., Bleem, L. E., et al. 2013, ApJ, 763, 127Rephaeli, Y. 1980, ApJ, 241, 858Rephaeli, Y. 1995, ARA&A, 33, 541Roth, K. C. & Bauer, J. M. 1999, ApJ, 515, L57Roth, K. C., Meyer, D. M., & Hawkins, I. 1993, ApJ, 413, L67Song, J., Zenteno, A., Stalder, B., et al. 2012, ApJ, 761, 22Songaila, A., Cowie, L. L., Hogan, C. J., & Rugers, M. 1994a, Nature, 368, 599Songaila, A., Cowie, L. L., Vogt, S., et al. 1994b, Nature, 371, 43Srianand, R., Chand, H., Petitjean, P., & Aracil, B. 2004, Physical ReviewLetters, 92, 121302Srianand, R., Noterdaeme, P., Ledoux, C., & Petitjean, P. 2008, A&A, 482, L39 Srianand, R., Petitjean, P., & Ledoux, C. 2000, Nature, 408, 931Sunyaev, R. A. & Zel’dovich, Y. B. 1972, Comments on Astrophysics and SpacePhysics, 4, 173Thaddeus, P. 1972, ARA&A, 10, 305The Dark Energy Survey Collaboration. 2005, ArXiv Astrophysics e-printsTonry, J. L., Stubbs, C. W., Lykke, K. R., et al. 2012, ApJ, 750, 99Uzan, J.-P. 2011, Living Reviews in Relativity, 14, 2Uzan, J.-P., Aghanim, N., & Mellier, Y. 2004, Phys. Rev. D, 70, 083533Zel’dovich, Y. B. & Sunyaev, R. A. 1969, Ap&SS, 4, 301aretti, R., Arnaud, M., Pratt, G. W., Pointecouteau, E., & Melin, J.-B. 2011,A&A, 534, A109Pillepich, A., Porciani, C., & Reiprich, T. H. 2012, MNRAS, 422, 44Planck Collaboration early VIII. 2011, A&A, 536, A8Planck Collaboration early XIX. 2011, A&A, 536, A19Planck Collaboration early XVIII. 2011, A&A, 536, A18Planck Collaboration early XXVI. 2011, A&A, 536, A26Planck Collaboration int. V. 2013, A&A, 550, A131Planck Collaboration int. XIII. 2013, e-prints ArXiv:1303.5090Planck Collaboration int. XIV. 2013, e-prints ArXiv:1307.6815Planck Collaboration results I. 2013, e-prints ArXiv:1303.5062Planck Collaboration results IX. 2013, e-prints ArXiv:1303.5070Planck Collaboration results VI. 2013, e-prints ArXiv:1303.5067Planck Collaboration results VII. 2013, e-prints ArXiv:1303.5068Planck Collaboration results VIII. 2013, e-prints ArXiv:1303.5069Planck Collaboration results XV. 2013, e-prints ArXiv:1303.5075Planck Collaboration results XVI. 2013, e-prints ArXiv:1303.5076Planck Collaboration results XXI. 2013, e-prints ArXiv:1303.5081Planck Collaboration results XXIX. 2013, e-prints ArXiv:1303.5089Planck Collaboration results XXVIII. 2013, e-prints ArXiv:1303.5088Pointecouteau, E., Giard, M., & Barret, D. 1998, A&A, 336, 44Puy, D. 2004, A&A, 422, 1Reichardt, C. L., Stalder, B., Bleem, L. E., et al. 2013, ApJ, 763, 127Rephaeli, Y. 1980, ApJ, 241, 858Rephaeli, Y. 1995, ARA&A, 33, 541Roth, K. C. & Bauer, J. M. 1999, ApJ, 515, L57Roth, K. C., Meyer, D. M., & Hawkins, I. 1993, ApJ, 413, L67Song, J., Zenteno, A., Stalder, B., et al. 2012, ApJ, 761, 22Songaila, A., Cowie, L. L., Hogan, C. J., & Rugers, M. 1994a, Nature, 368, 599Songaila, A., Cowie, L. L., Vogt, S., et al. 1994b, Nature, 371, 43Srianand, R., Chand, H., Petitjean, P., & Aracil, B. 2004, Physical ReviewLetters, 92, 121302Srianand, R., Noterdaeme, P., Ledoux, C., & Petitjean, P. 2008, A&A, 482, L39 Srianand, R., Petitjean, P., & Ledoux, C. 2000, Nature, 408, 931Sunyaev, R. A. & Zel’dovich, Y. B. 1972, Comments on Astrophysics and SpacePhysics, 4, 173Thaddeus, P. 1972, ARA&A, 10, 305The Dark Energy Survey Collaboration. 2005, ArXiv Astrophysics e-printsTonry, J. L., Stubbs, C. W., Lykke, K. R., et al. 2012, ApJ, 750, 99Uzan, J.-P. 2011, Living Reviews in Relativity, 14, 2Uzan, J.-P., Aghanim, N., & Mellier, Y. 2004, Phys. Rev. D, 70, 083533Zel’dovich, Y. B. & Sunyaev, R. A. 1969, Ap&SS, 4, 301