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arXiv:0809.3734v1 [astro-ph] 22 Sep 2008

A measurement of large-scale peculiar velocities of clusters of

galaxies: results and cosmological implications.

A. Kashlinsky1, F. Atrio-Barandela2, D. Kocevski3, H. Ebeling4

ABSTRACT

Peculiar velocities of clusters of galaxies can be measured by studying the fluc-

tuations in the cosmic microwave background (CMB) generated by the scattering

of the microwave photons by the hot X-ray emitting gas inside clusters. While

for individual clusters such measurements result in large errors, a large statistical

sample of clusters allows one to study cumulative quantities dominated by the

overall bulk flow of the sample with the statistical errors integrating down. We

present results from such a measurement using the largest all-sky X-ray cluster

catalog combined to date and the 3-year WMAP CMB data. We find a strong and

coherent bulk flow on scales out to at least

This flow is difficult to explain by gravitational evolution within the framework

of the concordance ΛCDM model and may be indicative of the tilt exerted across

the entire current horizon by far-away pre-inflationary inhomogeneities.

>

∼300h−1Mpc, the limit of our catalog.

Subject headings: cosmology: observations - cosmic microwave background - early

Universe - large-scale structure of universe

In the gravitational-instability picture peculiar velocities probe directly the peculiar

gravitational potential [e.g. Kashlinsky & Jones 1991, Strauss & Willick 1995]. Inflation-

based theories, such as the concordance ΛCDM model, predict that, on scales outside

the horizon during the radiation-dominated era, the peculiar density field remained in the

Harrison-Zeldovich regime set during inflationary epoch and on these scales, the peculiar

bulk velocity due to gravitational instability should decrease as Vrms ∝ r−1and be quite

small. Peculiar velocities can be obtained from the kinematic SZ (KSZ) effect on the CMB

1SSAI and Observational Cosmology Laboratory, Code 665, Goddard Space Flight Center, Greenbelt MD

20771; e–mail: alexander.kashlinsky@nasa.gov

2Fisica Teorica, University of Salamanca, 37008 Salamanca, Spain

3Department of Physics, University of California at Davis, 1 Shields Avenue, Davis, CA 95616

4Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822

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photons by the hot gas in clusters of galaxies [e.g. Birkinshaw 1999]. For each cluster the

KSZ term is small, but measuring a quantity derived from CMB data for a sizeable ensemble

of many clusters moving at a coherent bulk flow can, however, overcome this limitation. As

proposed by Kashlinsky & Atrio-Barandela (2000, KA-B), such a measurement will be dom-

inated by the bulk-flow KSZ component with other contributions integrating down. This

quantity, the dipole of the cumulative CMB temperature field evaluated at cluster positions, is

used in this investigation of the 3-year WMAP data together with the largest X-ray selected

sample of clusters to date to obtain the best measurement yet of bulk flows out to scales of

∼300h−1Mpc. Technical details of the analysis are given in the companion paper (Kashlin-

sky et al 2008 - KA-BKE). Our findings imply that the Universe has a surprisingly coherent

bulk motion out to at least ≃ 300h−1Mpc and with a fairly high amplitude of

km/sec, necessary to produce the measured amplitude of the dipole signal of ≃2-3µK. Such

a motion is difficult to account for by gravitational instability within the framework of the

standard concordance ΛCDM cosmology but could be explained by the gravitational pull of

pre-inflationary remnants located well outside the present-day horizon.

>

>

∼600-1000

1. Method and data preparation

If a cluster at angular position ? y has the line-of-sight velocity v with respect to the CMB,

the CMB fluctuation caused by the SZ effect at frequency ν at this position will be δν(? y) =

δTSZ(? y)G(ν) + δKSZ(? y)H(ν), with δTSZ=τTX/Te,annand δKSZ=τv/c. Here G(ν) ≃ −1.85 to

−1.25 and H(ν) ≃ 1 over the WMAP frequencies, τ is the projected optical depth due to

Compton scattering, TXis the temperature of the intra-cluster gas, and kBTe,ann=511 keV.

Averaged over many isotropically distributed clusters moving at a significant bulk velocity

with respect to the CMB, the dipole from the kinematic term will dominate, allowing a

measurement of Vbulk. Thus KA-B suggested measuring the dipole component of δν(? y).

We use a normalized notation for the dipole power C1, such that a coherent motion

at velocity Vbulkleads to C1,kin= T2

?C1,kin≃ 1(?τ?/10−3)(Vbulk/100km/sec) µK. When computed from the total of Nclposi-

tions, the dipole will also have positive contributions from 1) instrument noise, 2) the thermal

SZ (TSZ) component, 3) the cosmological CMB fluctuation component arising from the last-

scattering surface, and 4) the various foreground components within the WMAP frequency

range. The last of these contributions can be significant at the lowest WMAP frequencies

(channels K & Ka) and, hence, we restrict this analysis to the WMAP Channels Q, V &

W which have negligible foreground contributions. The contributions to the dipole from the

above terms can be estimated as ?δν(? y)cosθ? at the Ncldifferent cluster locations with polar

CMB?τ?2V2

bulk/c2, where TCMB= 2.725K. For reference,

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angle θ. For Ncl≫ 1 the dipole of δνbecomes a1m≃ akin

is the residual dipole produced at the cluster locations by the primordial CMB anisotropies.

The dipole power is C1 =?m=1

correspond to the (x,y,z) components, with z running perpendicular to the Galactic plane

towards the NGP, and (x,y) being the Galactic plane with the x-axis passing through the

Galactic center. This dipole signal should not be confused with the ”global CMB dipole”

that arises from our local motion relative to the CMB. The kinematic signal investigated

here does not contribute significantly to the “global CMB dipole” arising from only a small

number of pixels. When the latter is subtracted from the original CMB maps, only a small

fraction, ∼ (Ncl/Ntotal)<

1m+ aTSZ

1m+ aCMB

1m

+σnoise

√Ncl. Here aCMB

1m

m=−1|a1m|2. The notation for a1m is such that m=0,1,−1

∼10−3, of the kinematic signal C1,kinis removed.

The TSZ dipole for a random cluster distribution is aTSZ

creasing with increasing Ncl. This decrease could be altered if clusters are not distributed

randomly and there may be some cross-talk between the monopole and dipole terms espe-

cially for small/sparse samples (Watkins & Feldman 1995), but the value of the TSZ dipole

will be estimated directly from the maps as discussed below and in greater detail in Kashlin-

sky et al (2008 - KA-BKE). The residual CMB dipole, C1,CMB, will exceed σ2

the intrinsic cosmological CMB anisotropies are correlated. On the smallest angular scales

in the WMAP data σCMB≃ 80µK, so these anisotropies could be seen as the largest dipole

noise source. However, because the power spectrum of the underlying CMB anisotropies is

accurately known, this component can be removed with a filter described next.

1m ∼ (?τTX?/Te,ann)N−1/2

cl

de-

CMB/Nclbecause

To remove the cosmological CMB anisotropies we filtered each channel maps separately

with the Wiener filter as follows. With the known power spectrum of the cosmological CMB

fluctuations, CΛCDM

ℓ

, a filter Fℓin ℓ-space which minimizes ?(δT − δinstrument noise)2? in the

presence of instrument noise is given by Fℓ= (Cℓ−CΛCDM

power spectrum of each map. Convolving the maps with Fℓ minimizes the contribution

of the cosmological CMB to the dipole. The maps for each of the eight WMAP channels

were thus processed as follows: 1) for CΛCDM

ℓ

for the WMAP data (Hinshaw et al 2007) available from http://lambda.gsfc.nasa.gov; 2)

each map was decomposed into multipoles, aℓm, using HEALPix (Gorski et al 2005); 3) the

power spectrum of each map, Cℓ, was then computed and Fℓconstructed; 4) the aℓmmaps

were multiplied by Fℓand Fourier-transformed back into the angular space (θ,φ). We then

removed the intrinsic dipole, quadrupole and octupole. The filtering affects the effective

value of τ for each cluster and we calculate this amount later.

ℓ

)/Cℓ, with Cℓbeing the measured

we adopted the best-fit cosmological model

Here we use an all-sky cluster sample created by combining the ROSAT-ESO Flux

Limited X-ray catalog (REFLEX) (Bohringer et al 2004) in the southern hemisphere, the

extended Brightest Cluster Sample (eBCS) (Ebeling et al 1998; Ebeling et al 2000) in the

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north, and the Clusters in the Zone of Avoidance (CIZA) (Ebeling et al 2002; Kocevski et al 2007)

sample along the Galactic plane. These are the most statistically complete X-ray selected

cluster catalogs ever compiled in their respective regions of the sky. All three surveys are

X-ray selected and X-ray flux limited using RASS data. The creation of the combined all-sky

catalogue of 782 clusters is described in detail by (Kocevski et al 2006) and KA-BKE.

We started with 3-year “foreground-cleaned” WMAP data (http://lambda.gsfc.nasa.gov)

in each differencing assembly (DA) of the Q, V, and W bands. Each DA is analyzed sepa-

rately giving us eight independent maps to process: Q1, Q2, V1, V2, W1,..., W4. The CMB

maps are pixelized with the HEALPix parameter Nside=512 corresponding to pixels ≃ 7′on

the side or pixel area 4 × 10−6sr. This resolution is much coarser than that of the X-ray

data, which makes our analysis below insensitive to the specifics of the spatial distribution

of the cluster gas, such as cooling flows, deviations from spherical symmetry, etc. In the

filtered maps for each DA we select all WMAP pixels within the total area defined by the

cluster X-ray emission, repeating this exercise for cluster subsamples populating cumulative

redshift bins up to a fixed z. In order to eliminate the influence of Galactic emission and

non-CMB radio sources, the CMB maps are subjected to standard WMAP masking. The

results for the different masks are similar and agree well within their statistical uncertainties.

The SZ effect (∝ ne, the electron density) has larger extent than probed by X-rays (X-

ray luminosity ∝ n2

(AKKE). As shown in AKKE, KA-BKE contributions to the TSZ signal are detected out to

e), which is confirmed by our TSZ study using the same cluster catalogue

>

∼30′. What is important in the present context, is that the X-ray emitting gas is distributed

as expected from the ΛCDM profile (Navarro et al 1996) scaling as ne∝ r−3in outer parts.

In order to be in hydrostatic equilibrium such gas must have temperature decreasing with

radius (Komatsu & Seljak 2001). Indeed, the typical polytropic index for such gas would

be γ ≃1.2, leading to the X-ray temperature decreasing as TX ∝ nγ−1

radii. This TX decrease agrees with simulations of cluster formation within the ΛCDM

model (Borgani et al 2004) and with the available data on the X-ray temperature profile

(Pratt et al 2007). For such gas, the TSZ monopole (∝ TXτ) decreases faster than the KSZ

component (∝ τ) when averaged over a progressively increasing cluster area. To account

for this, we compute the dipole component of the final maps for a range of effective cluster

sizes, namely [1,2,4,6]θX−rayand then the maximal cluster extent is set at 30′to avoid a few

large clusters (eg. Coma) bias the dipole determination. We note that at the final extent our

clusters effectively have the same angular radius of 0.5◦. Our choice of the maximal extent

is determined by the fact that the SZ signal is detectable in our sample out to that scale

(AKKE), which is ∼(3-4)Mpc at the mean redshift of the sample. Increasing the cluster

radius further to 1◦−3◦, causes the dipole to start decreasing with the increasing radius, as

expected if the pixels outside the clusters are included diluting the KSZ signal (KA-BKE).

e

∝ r−0.6at outer

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To estimate uncertainties in the signal only from the clusters, we use the rest of the map

for the distribution and variance of the noise in the measured signal. We use two methods

to preserve the geometry defined by the mask and the cluster distribution: 1) Nclcentral

random pixels are selected outside the mask away from the cluster pixels adding pixels within

each cluster’s angular extent around these central random pixels, iteratively verifying that

the selected areas do not fall within either the mask or any of the known clusters. 2) We

also use a slightly modified version of the above procedure in order to test the effects of the

anisotropy of the cluster catalog. There the cluster catalog is rotated randomly, ensuring

that the overall geometry of the cluster catalog is accurately preserved. Both methods yield

very similar uncertainties; for brevity, we present results obtained with the first method.

2. Results

Fig. 1 summarizes our results averaged over all eight DA’s. We find a statistically

significant dipole component produced by the cluster pixels for the spheres and shells ex-

tending beyond z ≃ 0.05. It persists as the monopole component vanishes and its statistical

significance gets particularly high for the y-component. The signal appears only at the clus-

ter positions and, hence, cannot originate from instrument noise, the CMB or the remaining

Galactic foreground components, the contributions from which are given by the uncertainties

evaluated from the rest of the CMB map pixels. The signal is restricted to the cluster pixels

and thus must arise from the two components of the SZ effect, thermal and/or kinematic.

The TSZ component, however, is given by the monopole term at the cluster positions

and cannot be responsible for the detected signal. For the largest apertures it vanishes within

the small, compared to the measured dipole, statistical uncertainty, and yet the dipole term

remains large and statistically significant. This is the opposite of what one should expect

if the dipole is produced by the TSZ component. Any random distribution, such as TSZ

emissions, would generate dipole ∝ ?τTXcosθ? which can never exceed (and must be much

less than) the monopole component of that distribution, ∝ ?τTX?. On the other hand, any

coherent bulk flow would produce dipole ∝ Vbulk?τ cos2θ?, which is bounded from below

by the amplitude of the motion. Furthermore, we find significant dipole from (at least)

zmean=0.035 (135 clusters) all the way to zmean=0.11 (674 clusters); its parameters do not

depend on the numbers of clusters, pixels used etc. Any dipole component arising from the

TSZ term would depend on these parameters as it reflects the (random) dipole of the cluster

sample and should thus decrease as more clusters are added in spheres out to progressively

larger z. To verify this, we compute the expected monopole and dipole terms produced by the

TSZ effect using the parameters of our cluster catalog as discussed in KA-BKE and recover