A new measurement of the bulk flow of X-ray luminous clusters of galaxies

Abstract

We present new measurements of the large-scale bulk flows of galaxy clusters
based on 5-year WMAP data and a significantly expanded X-ray cluster catalogue.
Our method probes the flow via measurements of the kinematic Sunyaev-Zeldovich
(SZ) effect produced by the hot gas in moving clusters. It computes the dipole
in the cosmic microwave background (CMB) data at cluster pixels, which
preserves the SZ component while integrating down other contributions. Our
improved catalog of over 1,000 clusters enables us to further investigate
possible systematic effects and, thanks to a higher median cluster redshift,
allows us to measure the bulk flow to larger scales. We present a corrected
error treatment and demonstrate that the more X-ray luminous clusters, while
fewer in number, have much larger optical depth, resulting in a higher dipole
and thus a more accurate flow measurement. This results in the observed
correlation of the dipole derived at the aperture of zero monopole with the
monopole measured over the cluster central regions. This correlation is
expected if the dipole is produced by the SZ effect and cannot be caused by
unidentified systematics (or primary cosmic microwave background anisotropies).
We measure that the flow is consistent with approximately constant velocity out
to at least 800 Mpc. The significance of the measured signal peaks around 500
Mpc, most likely because the contribution from more distant clusters becomes
progressively more diluted by the WMAP beam. We can, however, at present not
rule out that these more distant clusters simply contribute less to the overall
motion.

Full text

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arXiv:0910.4958v3 [astro-ph.CO] 11 Mar 2010
A new measurement of the bulk flow of X-ray luminous clusters of
galaxies
A. Kashlinsky1, F. Atrio-Barandela2, H. Ebeling3, A. Edge4, D. Kocevski5
ABSTRACT
We present new measurements of the large-scale bulk flows of galaxy clusters
based on 5-year WMAP data and a significantly expanded X-ray cluster cata-
logue. Our method probes the flow via measurements of the kinematic Sunyaev-
Zeldovich (SZ) effect produced by the hot gas in moving clusters. It computes
the dipole in the cosmic microwave background (CMB) data at cluster pixels,
which preserves the SZ component while integrating down other contributions.
Our improved catalog of over 1,000 clusters enables us to further investigate pos-
sible systematic effects and, thanks to a higher median cluster redshift, allows us
to measure the bulk flow to larger scales. We present a corrected error treatment
and demonstrate that the more X-ray luminous clusters, while fewer in number,
have much larger optical depth, resulting in a higher dipole and thus a more
accurate flow measurement. This results in the observed correlation of the dipole
derived at the aperture of zero monopole with the monopole measured over the
cluster central regions. This correlation is expected if the dipole is produced by
the SZ effect and cannot be caused by unidentified systematics (or primary cos-
mic microwave background anisotropies). We measure that the flow is consistent
with approximately constant velocity out to at least ≃800 Mpc. The significance
of the measured signal peaks around 500 h−1
tribution from more distant clusters becomes progressively more diluted by the
WMAP beam. We can, however, at present not rule out either that these more
distant clusters simply contribute less to the overall motion.
70Mpc, most likely because the con-
1SSAI and Observational Cosmology Laboratory, Code 665, Goddard Space Flight Center, Greenbelt MD
20771; alexander.kashlinsky@nasa.gov
2Fisica Teorica, University of Salamanca, 37008 Salamanca, Spain
3Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822
4Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK
5Department of Physics, University of California at Davis, 1 Shields Avenue, Davis, CA 95616

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Subject headings: Cosmology - cosmic microwave background - observations -
diffuse radiation - early Universe
The large-scale isotropy of the Universe and the small-scale inhomogeneities that evolved
into galaxies are thought to originate during inflationary expansion in the early Universe.
Inflation posits that the primeval space-time was inhomogeneous and this structure should
have been preserved on sufficiently large scales. At minimum large-scale peculiar velocities
should arise from gravitational instability caused by mass inhomogeneities seeded during
the inflationary expansion. On scales
robust predictions for these velocities. There the initial Harrison-Zeldovich slope of the mass
fluctuations is preserved, so peculiar velocities induced by gravitational instability must
decrease linearly with scale (e.g. Kashlinsky & Jones 1991); for the concordance ΛCDM
model Vrms∼ 250(100h−1Mpc
Our discovery of a coherent large-scale flow of galaxy clusters with significantly larger
amplitude than expected out to ≃ 300Mpc (Kashlinsky et al 2008, 2009 – KABKE1,2)
represents a challenge to the gravitational instability paradigm. Such a ”dark flow” could
indicate a tilt created by the pre-inflationary inhomogeneous structure of space-time (Turner
1991, Grishchuk 1992, Kashlinsky et al 1994, KABKE1) and might provide an indirect probe
of the Multiverse. Various explanations have been put forward, including that the flow
points to a higher-dimensional structure of gravity (Afshordi et al 2009, Khoury & Wyman
2009), or that it reflects the pre-inflationary landscape produced by certain variants of string
cosmology (Mersini-Houghton & Holman 2009, Carrol et al 2008).
>
∼100Mpc the standard inflationary scenario leads to
d
) km/sec at d>50–100h−1Mpc.
Making use of an expanded cluster catalog and deeper WMAP observations, we have
worked to verify, and expand the Dark Flow study through a program we have dubbed
SCOUT (Sunyaev-Zel’dovich Cluster Observations as probes of the Universe’s Tilt). First
results from this experiment are reported here.
1. Data and analysis
KABKE1,2 and this work utilize a method of Kashlinsky & Atrio-Barandela (2000, here-
after KA-B), which measures CMB dipole at the locations of X-ray clusters. When averaged
over many isotropically distributed clusters moving at a significant bulk flow with respect to
the CMB, the kinematic term dominates the SZ signal, thereby enabling a measurement of
Vbulkover that distance. In Atrio-Barandela et al (2008, hereafter AKKE) we demonstrated

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that 1) the thermal SZ (TSZ) signal from clusters extends well beyond the measured X-ray
extent ΘX, and 2) the intra-cluster gas distribution is well approximated by the NFW profile
(Navarro et al 1996) expected for dark matter in a ΛCDM model. The temperature TXof
hot gas distributed according to these profiles decreases significantly from the cluster cores to
the cluster outskirts (Komatsu & Seljak 2001), consistent with current measurements (Pratt
et al 2007) and numerical simulations (e.g. Borgani et al 2004). Consequently, the monopole
produced by the TSZ component (∝ τTX) decreases, as we increase the cluster aperture,
whereas the dipole due to the kinematic SZ (KSZ) component (∝ τ, the optical depth due
to Thomson scattering) remains measurable out to the aperture where we still detect the
TSZ decrement in unfiltered maps (KABKE2). As in KABKE1,2 our dipole coefficients
are normalized such that the dipole power C1due to a coherent motion at velocity Vbulkis
C1,kin= T2
km/sec/Mpc.
CMB?τ?2V2
bulk/c2, where TCMB= 2.725K. We adopt Ωtotal= 1,ΩΛ= 0.7,H0= 70h70
To improve upon the all-sky cluster catalogue of Kocevski & Ebeling (2006) used by
KABKE1,2, we have screened the ROSAT Bright-Source Catalogue (Voges et al. 1999) using
the same X-ray selection criteria (including a nominal flux limit of 1×10−12erg/sec, 0.1–2.4
keV) as employed during the Massive Cluster Survey (MACS, Ebeling et al. 2001), as well
as the same optical follow-up strategy. Unlike MACS, we apply neither a declination nor
a redshift limit though, thereby creating an all-sky list of cluster candidates that extends
to three times fainter X-ray fluxes than in KABKE1,2. Optical follow-up observations of
clusters identified in this manner and lacking spectroscopic redshifts in the literature (and
MACS) are well underway using telescopes on Mauna-Kea/Hawai‘i and La-Silla/Chile. As
a result, our interim all-sky cluster catalogue currently comprises in excess of 1,400 X-ray
selected clusters, all of them with spectroscopic redshifts. X-ray properties of all clusters
(most importantly total luminosities and central electron densities) are computed as before
(KABKE2). Within the same z-range (z ? 0.25) as our previous study, our new catalog
comprises 1,174 clusters outside the KP0 CMB mask. To eliminate low-mass galaxy groups
we require that clusters feature LX≥ 2×1043erg/sec; 985 systems meet this criterion. This
sample represents a significant improvement over the one in KABKE1,2 largely because of
the substantial increase (zmedian < 0.1 in KABKE1,2 vs zmedian ≃ 0.2 below) in median
cluster redshift and the higher fraction of intrinsically very X-ray luminous systems (Fig.
1a).
We applied this new cluster sample to the 5-year WMAP CMB data, processed as
described in detail in KABKE1,2. The all-sky dipole in the foreground-cleaned maps from
http://www.lambda.gsfc.nasa.gov was removed, and standard CMB masking was applied.
We also need to remove the primary CMB fluctuations, produced at last scattering, as they
are highly correlated and would contribute significantly to the measured dipole. To this

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end, all maps were filtered as in KABKE1,2 with a filter that minimizes ?(δT − δTΛCDM)2?.
The error budget associated with our filtering is discussed by Atrio-Barandela et al (2010,
hereafter AKEKE).
Measurement errors were computed as in KABKE1,2 with one important correction.
Although the filtering removes much of the CMB fluctuations, a residual component remains,
due to cosmic variance and imperfections of the theoretical model. Since this residual is
common to all WMAP bands, a component of the errors is correlated between the various
DA maps. We address this issue in the following manner. For each of the eight differential
assemblies (DAs) we simulate 4,000 realizations with Ncl =100–1,000 randomly selected
pseudo-clusters outside of the cluster pixels and the CMB mask. In each realization we
select the same pseudo-clusters for all DAs and evaluate the mean monopole and dipole
averaged over all DAs: ¯ a0,¯ a1m. For the 4,000 realizations at each Nclwe compute the mean
and dispersion of ¯ a0,¯ a1mover all the realizations. The distributions have zero mean and their
dispersion gives errors which scale as N−1/2
cl
. We find to good accuracy that the distribution
of the simulated dipoles (and monopoles) is Gaussian and the errors on each of the averaged
dipole components are σ1m ≃ 15?3/NclµK and on the monopole σ0 ≃ 15?1/NclµK as
explained in great detail in AKEKE; the errors of the x/z dipole component are slightly
larger/smaller because of the Galactic mask (Fig. 1b).
2.Results
We used the filtered maps to compute the dipole and monopole terms, ai
DA of the WMAP Q, V, W bands (i = 1,...,8) for clusters in cumulative redshift bins up to
a given z. The results were averaged to obtain the mean values over all eight DAs, ¯ a1m,¯ a0.
Since the volume probed out to low z is too small for meaningful measurements, Table 1 lists
results only for z-bins with sufficient signal-to-noise ratios (S/N). In KABKE1,2 we computed
the dipole in progressively increasing apertures but no larger than 30′to prevent geometric
biases from very nearby Coma-type clusters. To further reduce any selection effect related
to the apparent X-ray extent measured by ROSAT, we here impose a constant aperture for
all clusters (see Table 1) and compute the dipole component for each z-bin at the constant
aperture at which the monopole (initially negative because of the TSZ component) vanishes.
1m,ai
0for each
The improved cluster catalog allows us to extend our study to higher z, and to further
test the impact of systematics. We create LX-limited subsamples which achieves two impor-
tant objectives. 1) As the LX threshold is raised, fewer clusters remain and the statistical
uncertainty of the dipole increases (∝ 1/?Ncl(L > LX)). If, however, all clusters are part
of a bulk flow of a given velocity Vbulk, very X-ray luminous clusters will produce a larger

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CMB dipole (∝ τVbulk), an effect that might overcome the reduced number statistics, giving
a higher S/N in the measured dipole. 2) Since, as outlined under (1), the dipole signal
should increase with cluster luminosity, whereas systematic effects can be expected to be
independent of LX, an actual observation of such a correlation would lend strong support to
the validity of our measurement and the reality of the ”dark flow”.
Fig. 1a shows that the depth to which we probe the flow increases dramatically as
the LX-threshold is raised. Table 1 shows the results for each subsample. The monopole is
strongly negative in the smallest apertures due to the dominance of the TSZ component in
the central regions and the dipole is shown at the aperture where monopole vanishes. Of the
three dipole components, the y-component is best determined, its value always remaining
negative and its S/N increasing strongly with increasing LX. As shown in Fig. 1c the ampli-
tudes of the latter and of the monopole in the central parts are strongly, and approximately
linearly, correlated. This correlation provides strong evidence against unknown systematics
systematics - or primary CMB - causing our measurement.
Table 1 quantifies our finding of a statistically significant dipole out to the largest scales
probed (∼ 800h−1
produced by systematics; we briefly revisit the issue here: 1) At high statistical significance
the dipole originates only at cluster positions, and must thus originate from CMB photons
that passed through the hot intra-cluster gas. For the same reason the dipole can not be
due to a residual contribution from the all-sky CMB dipole. HEALPix ANAFAST routines
(Gorski et al 2005), employed in the analysis, further remove any all-sky dipole before the
filtered maps are produced. 2) Since the dipole is measured at zero monopole, the contribu-
tions from TSZ and other cluster emissions to the dipole are negligible. 3) The variations
in the final aperture where the dipole is measured were very small in KABKE1,2, and the
dipole signal remains in this work which uses a fixed aperture for all clusters. So the dipole
is not affected by the variations in cluster ΘX, which in any case is much smaller than the
final apertures in KABKE1,2. 4) The measured CMB quadrupole is significantly different
from that of the ΛCDM model, so a significant part of the CMB quadrupole is not removed
by our filter and could leak into other multipoles via the mask. However, we set the filter to
zero at ℓ ≤ 4 (KABKE2, AKEKE) for the final maps. More importantly, we have modified
the pipeline to remove the all-sky quadrupole from the original maps and find no notice-
able difference in the dipole computed at the cluster locations. This also removes the fully
relativistic components from the local motion vlocal, down to (vlocal/c)3corrections to the
octupole. (5) Finally, we demonstrate that more luminous clusters make a larger, and sta-
tistically more significant, contribution to the dipole, as is expected if all clusters participate
in the same flow, independent of LX. Note also that the intra-cluster medium motions from
cluster mergers have random directions and thus average down in large catalogs, contributing
70Mpc). In KABKE2 we discussed in detail why this dipole is unlikely to be