A direct empirical proof of the existence of dark matter

Abstract

We present new weak lensing observations of 1E0657-558 (z=0.296), a unique cluster merger, that enable a direct detection of dark matter, independent of assumptions regarding the nature of the gravitational force law. Due to the collision of two clusters, the dissipationless stellar component and the fluid-like X-ray emitting plasma are spatially segregated. By using both wide-field ground based images and HST/ACS images of the cluster cores, we create gravitational lensing maps which show that the gravitational potential does not trace the plasma distribution, the dominant baryonic mass component, but rather approximately traces the distribution of galaxies. An 8-sigma significance spatial offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained with an alteration of the gravitational force law, and thus proves that the majority of the matter in the system is unseen. Comment: Accepted for publication in ApJL

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arXiv:astro-ph/0608407v1 19 Aug 2006
ApJ Letters in press
Preprint typeset using LATEX style emulateapj v. 6/22/04
A DIRECT EMPIRICAL PROOF OF THE EXISTENCE OF DARK MATTER∗
Douglas Clowe1, Maruˇ sa Bradaˇ c2, Anthony H. Gonzalez3, Maxim Markevitch4,5, Scott W. Randall4,
Christine Jones4, and Dennis Zaritsky1
ApJ Letters in press
ABSTRACT
We present new weak lensing observations of 1E0657−558 (z = 0.296), a unique cluster merger,
that enable a direct detection of dark matter, independent of assumptions regarding the nature of the
gravitational force law. Due to the collision of two clusters, the dissipationless stellar component and
the fluid-like X-ray emitting plasma are spatially segregated. By using both wide-field ground based
images and HST/ACS images of the cluster cores, we create gravitational lensing maps which show
that the gravitational potential does not trace the plasma distribution, the dominant baryonic mass
component, but rather approximately traces the distribution of galaxies. An 8σ significance spatial
offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained
with an alteration of the gravitational force law, and thus proves that the majority of the matter in
the system is unseen.
Subject headings: Gravitational lensing – Galaxies: clusters: individual: 1E0657-558 – dark matter
1. INTRODUCTION
We have known since 1937 that the gravitational po-
tentials of galaxy clusters are too deep to be caused by
the detected baryonic mass and a Newtonian r−2gravita-
tional force law (Zwicky 1937). Proposed solutions either
invoke dominant quantities of non-luminous “dark mat-
ter” (Oort 1932) or alterations to either the gravitational
force law (Bekenstein 2004; Brownstein & Moffat 2006)
or the particles’ dynamical response to it (Milgrom 1983).
Previous works aimed at distinguishing between the
dark matter and alternative gravity hypotheses in galax-
ies (Buote et al. 2002; Hoekstra et al. 2004) or galaxy
clusters (Gavazzi 2002; Pointecouteau & Silk 2005) have
used objects in which the visible baryonic and hypoth-
esized dark matter are spatially coincident, as in most
of the Universe. These works favor the dark matter hy-
pothesis, but their conclusions were necessarily based on
non-trivial assumptions such as symmetry, the location
of the center of mass of the system, and/or hydrostatic
equilibrium, which left room for counterarguments. The
actual existence of dark matter can only be confirmed
∗BASED ON OBSERVATIONS MADE WITH THE NASA/ESA
HUBBLE SPACE TELESCOPE, OBTAINED AT THE SPACE
TELESCOPE SCIENCE INSTITUTE, WHICH IS OPERATED
BY THE ASSOCIATION OF UNIVERSITIES FOR RESEARCH
IN ASTRONOMY, INC., UNDER NASA CONTRACT NAS 5–
26555, UNDER PROGRAM 10200, THE 6.5 METER MAGEL-
LAN TELESCOPES LOCATED AT LAS CAMPANAS OBSER-
VATORY, CHILE, THE ESO TELESCOPES AT THE PARANAL
OBSERVATORIES UNDER PROGRAM IDS 72.A-0511, 60.A-
9203, AND 64.O-0332, AND WITH THE NASA CHANDRA X-
RAY OBSERVATORY, OPERATED BY THE SMITHSONIAN
ASTROPHYSICS OBSERVATORY UNDER CONTRACT TO
NASA.
Electronic address: dclowe@as.arizona.edu
1Steward Observatory, University of Arizona, 933 N Cherry
Ave, Tucson, AZ 85721
2Kavli Institute for Particle Astrophysics and Cosmology,
P.O. Box 20450, MS29, Stanford, CA 94309
3Department of Astronomy, University of Florida, 211 Bryant
Space Science Center, Gainesville, FL 32611
4Harvard-Smithsonian Center for Astrophysics, 60 Garden St.,
Cambridge, MA 02138
5Also Space Research Institute, Russian Acad. Sci., Profsoyuz-
naya 84/32, Moscow 117997, Russia
either by a laboratory detection or, in an astronomical
context, by the discovery of a system in which the ob-
served baryons and the inferred dark matter are spatially
segregated. An ongoing galaxy cluster merger is such a
system.
Given sufficient time, galaxies (whose stellar compo-
nent makes up ∼ 1 − 2% of the mass (Kochanek et al.
2003) under the assumption of Newtonian gravity),
plasma (∼ 5 − 15% of the mass (Allen et al. 2002;
Vikhlinin et al. 2006)), and any dark matter in a typical
cluster acquire similar, centrally-symmetric spatial dis-
tributions tracing the common gravitational potential.
However, during a merger of two clusters, galaxies be-
have as collisionless particles, while the fluid-like X-ray
emitting intracluster plasma experiences ram pressure.
Therefore, in the course of a cluster collision, galaxies
spatially decouple from the plasma. We clearly see this
effect in the unique cluster 1E0657−558 (Tucker et al.
1998).
The cluster has two primary galaxy concentrations sep-
arated by 0.72 Mpc on the sky, a less massive (T ∼ 6 keV)
western subcluster and a more massive (T ∼ 14 keV)
eastern main cluster (Markevitch et al. 2002). Both con-
centrations have associated X-ray emitting plasma off-
set from the galaxies toward the center of the system.
The X-ray image also shows a prominent bow shock on
the western side of the western plasma cloud, indicat-
ing that the subcluster is currently moving away from
the main cluster at ∼4700 km/s. As the line-of-sight ve-
locity difference between the components is only ∼ 600
km/s (Barrena et al. 2002), the merger must be occur-
ring nearly in the plane of the sky and the cores passed
through each other ∼ 100 Myr ago.
Two galaxy concentrations that correspond to the
main cluster and the smaller subcluster have moved
ahead of their respective plasma clouds that have been
slowed by ram pressure. This phenomenon provides an
excellent setup for our simple test. In the absence of
dark matter, the gravitational potential will trace the
dominant visible matter component, which is the X-ray
plasma. If, on the other hand, the mass is indeed domi-

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Fig. 1.— Shown above in the top panel is a color image from the Magellan images of the merging cluster 1E0657−558, with the white
bar indicating 200 kpc at the distance of the cluster. In the bottom panel is a 500 ks Chandra image of the cluster. Shown in green contours
in both panels are the weak lensing κ reconstruction with the outer contour level at κ = 0.16 and increasing in steps of 0.07. The white
contours show the errors on the positions of the κ peaks and correspond to 68.3%, 95.5%, and 99.7% confidence levels. The blue +s show
the location of the centers used to measure the masses of the plasma clouds in Table 2.
nated by collisionless dark matter, the potential will trace
the distribution of that component, which is expected
to be spatially coincident with the collisionless galax-
ies. Thus, by deriving a map of the gravitational po-
tential, one can discriminate between these possibilities.
We published an initial attempt at this using an archival
VLT image (Clowe et al. 2004); here we add three addi-
tional optical image sets which allows us to increase the
significance of the weak lensing results by more than a
factor of 3.
In this paper, we measure distances at the redshift of
the cluster, z = 0.296, by assuming an Ωm = 0.3,λ =
0.7,H0= 70km/s/Mpc cosmology which results in 4.413
kpc/′′plate-scale. None of the results of this paper are
dependent on this assumption; changing the assumed
cosmology will result in a change of the distances and
absolute masses measured, but the relative masses of
the various structures in each measurement remain un-
changed.
2. METHODOLOGY AND DATA
We construct a map of the gravitational poten-
tial using weak gravitational lensing (Mellier 1999;
Bartelmann & Schneider 2001), which measures the dis-
tortions of images of background galaxies caused by the
gravitational deflection of light by the cluster’s mass.
This deflection stretches the image of the galaxy pref-
erentially in the direction perpendicular to that of the
cluster’s center of mass. The imparted ellipticity is typi-
cally comparable to or smaller than that intrinsic to the
galaxy, and thus the distortion is only measurable statis-
tically with large numbers of background galaxies. To do
this measurement, we detect faint galaxies on deep op-
tical images and calculate an ellipticity from the second
moment of their surface brightness distribution, correct-
ing the ellipticity for smearing by the point spread func-
tion (corrections for both anisotropies and smearing are
obtained using an implementation of the KSB technique
(Kaiser et al. 1995) discussed in Clowe et al. (2006)).
The corrected ellipticities are a direct, but noisy, mea-
surement of the reduced shear ? g = ? γ/(1 − κ). The shear
? γ is the amount of anisotropic stretching of the galaxy
image. The convergence κ is the shape-independent in-
crease in the size of the galaxy image. In Newtonian
gravity, κ is equal to the surface mass density of the lens
divided by a scaling constant. In non-standard gravity
models, κ is no longer linearly related to the surface den-
sity but is instead a non-local function that scales as the
mass raised to a power less than one for a planar lens,
reaching the limit of one half for constant acceleration
(Mortlock & Turner 2001; Zhao et al. 2006). While one
can no longer directly obtain a map of the surface mass
density using the distribution of κ in non-standard grav-
ity models, the locations of the κ peaks, after adjusting
for the extended wings, correspond to the locations of
the surface mass density peaks.
Our goal is thus to obtain a map of κ. One can combine
derivatives of ? g to obtain (Schneider 1995; Kaiser 1995)
1
1 − g2
2
which is integrated over the data field and converted into
a two-dimensional map of κ. The observationally un-
constrained constant of integration, typically referred to
as the “mass-sheet degeneracy,” is effectively the true
mean of ln(1−κ) at the edge of the reconstruction. This
method does, however, systematically underestimate κ
in the cores of massive clusters. This results in a slight
increase to the centroiding errors of the peaks, and our
measurements of κ in the peaks of the components are
only lower bounds.
For 1E0657−558, we have accumulated an exception-
ally rich optical dataset, which we will use here to mea-
sure? g. It consists of the four sets of optical images shown
in Table 1 and the VLT image set used in Clowe et al.
(2004); the additional images significantly increase the
maximum resolution obtainable in the κ reconstructions
due to the increased number of background galaxies,
particularly in the area covered by the ACS images,
with which we measure the reduced shear. We reduce
each image set independently and create galaxy cata-
logs with 3 passband photometry. The one exception
is the single passband HST pointing of main cluster,
for which we measure colors from the Magellan images.
Because it is not feasible to measure redshifts for all
galaxies in the field, we select likely background galax-
ies using magnitude and color cuts (m814> 22 and not
in the rhombus defined by 0.5 < m606− m814 < 1.5,
∇ln(1−κ) =
1− g2
?1 + g1
g2
g2
1 − g1
??g1,1+ g2,2
g2,1− g1,2
?
,

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TABLE 1
Optical Imaging Sets
InstrumentDate of Obs. FoVPassbandtexp (s)mlim
nd(′−2) seeing
2.2m ESO/MPG
Wide Field Imager
01/2004
01/2004
01/2004
01/15/2004
01/15/2004
01/15/2004
10/21/2004
10/21/2004
10/21/2004
10/21/2004
34′× 34′
R
B
V
R
B
V
14100
6580
5640
10800
2700
2400
4944
2420
2336
2336
23.9 150.′′8
1.′′0
0.′′9
0.′′6
0.′′9
0.′′8
0.′′12
0.′′12
0.′′12
0.′′12
6.5m Magellan
IMACS
8′radius25.1 35
HST ACS
subcluster
3.′5×3.′5 F814W
F435W
F606W
F606W
27.6 87
main cluster3.′5×3.′5 26.154
Note. — Limiting magnitudes for completion are given for galaxies and measured by where the number counts depart from
a power law. All image sets had objects detected in the reddest passband available.
m435− m606> 1.5 ∗ (m606− m814) − 0.25, and m435−
m606< 1.6∗(m606−m814)+0.4 for the ACS images; sim-
ilar for the other image sets) that were calibrated with
photometric redshifts from the HDF-S (Fontana et al.
1999). Each galaxy has a statistical weight based on its
significance of detection in the image set (Clowe et al.
2006), and the weights are normalized among catalogs
by comparing the rms reduced shear measured in a re-
gion away from the cores of the cluster common to all five
data sets. To combine the catalogs, we adopt a weighted
average of the reduced shear measurements and appro-
priately increase the statistical weight of galaxies that
occur in more than one catalog.
3. ANALYSIS
We use the combined catalog to create a two-
dimensional κ reconstruction, the central portion of
which is shown in Fig. 1. Two major peaks are clearly
visible in the reconstruction, one centered 7.′′1 east and
6.′′5 north of the subcluster’s brightest cluster galaxy
(BCG) and detected at 8σ significance (as compared to
3σ in (Clowe et al. 2004)), and one centered 2.′′5 east
and 11.′′5 south of the northern BCG in the main clus-
ter (21.′′2 west and 17.′′7 north of the southern BCG)
detected at 12σ. We estimate centroid uncertainties by
repeating bootstrap samplings of the background galaxy
catalog, performing a κ reconstruction with the resam-
pled catalogs, and measuring the centroid of each peak.
Both peaks are offset from their respective BCG by ∼ 2σ,
but are within 1σ of the luminosity centroid of the re-
spective component’s galaxies (both BCGs are slightly
offset from the center of galaxy concentrations). Both
peaks are also offset at ∼ 8σ from the center of mass
of their respective plasma clouds.
toward the plasma clouds, which is expected because
the plasma contributes about 1/10th of the total clus-
ter mass (Allen et al. 2002; Vikhlinin et al. 2006) (and
a higher fraction in non-standard gravity models with-
out dark matter). The skew in each κ peak toward the
X-ray plasma is significant even after correcting for the
overlapping wings of the other peak, and the degree of
skewness is consistent with the X-ray plasma contribut-
ing 14%+16%
−14%of the observed κ in the main cluster and
10%+30%
−10%in the subcluster (see Table 2). Because of the
They are skewed
large size of the reconstruction (34′or 9 Mpc on a side),
the change in κ due to the mass-sheet degeneracy should
be less than 1% and any systematic effects on the cen-
troid and skewness of the peaks are much smaller than
the measured error bars.
The projected cluster galaxy stellar mass and plasma
mass within 100 kpc apertures centered on the BCGs
and X-ray plasma peaks are shown in Table 2.
aperture size was chosen as smaller apertures had sig-
nificantly higher kappa measurement errors and larger
apertures resulted in significant overlap of the apertures.
Plasma masses were computed from a multicomponent 3-
dimensional cluster model fit to the Chandra X-ray image
(details of this fit will be given elsewhere). The emission
in the Chandra energy band (mostly optically-thin ther-
mal bremsstrahlung) is proportional to the square of the
plasma density, with a small correction for the plasma
temperature (also measured from the X-ray spectra),
which gives the plasma mass. Because of the simplic-
ity of this cluster’s geometry, especially at the location
of the subcluster, this mass estimate is quite robust (to
a 10% accuracy).
Stellar masses are calculated from the I-band lumi-
nosity of all galaxies equal in brightness or fainter than
the component BCG. The luminosities were converted
into mass assuming (Kauffmann et al. 2003) M/LI= 2.
The assumed mass-to-light ratio is highly uncertain (can
vary between 0.5 and 3) and depends on the history of
recent star formation of the galaxies in the apertures;
however even in the case of an extreme deviation, the X-
ray plasma is still the dominant baryonic component in
all of the apertures. The quoted errors are only the errors
on measuring the luminosity and do not include the un-
certainty in the assumed mass-to-light ratio. Because we
did not apply a color selection to the galaxies, these mea-
surements are an upper limit on the stellar mass as they
include contributions from galaxies not affiliated with the
cluster.
The mean κ at each BCG was calculated by fitting a
two peak model, each peak circularly symmetric, to the
reconstruction and subtracting the contribution of the
other peak at that distance. The mean κ for each plasma
cloud is the excess κ after subtracting off the values for
both peaks.
This

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TABLE 2
Component Masses
Component RA (J2000)Dec (J2000)MX(1012M⊙)M∗(1012M⊙)¯ κ
Main cluster BCG
Main cluster plasma
Subcluster BCG
Subcluster plasma
06 : 58 : 35.3
06 : 58 : 30.2
06 : 58 : 16.0
06 : 58 : 21.2
−55 : 56 : 56.3
−55 : 56 : 35.9
−55 : 56 : 35.1
−55 : 56 : 30.0
5.5 ± 0.6
6.6 ± 0.7
2.7 ± 0.3
5.8 ± 0.6
0.54 ± 0.08
0.23 ± 0.02
0.58 ± 0.09
0.12 ± 0.01
0.36 ± 0.06
0.05 ± 0.06
0.20 ± 0.05
0.02 ± 0.06
Note. — All values are calculated by averaging over an aperture of 100 kpc radius around the given position (marked with
blue +s for the centers of the plasma clouds in Fig 1). ¯ κ measurements for the plasma clouds are the residual left over after
subtraction of circularly symmetric profiles centered on the BCGs.
The total of the two visible mass components of the
subcluster is greater by a factor of 2 at the plasma peak
than at the BCG; however, the center of the lensing mass
is located near the BCG. The difference of the baryonic
mass between these two positions would be even greater
if we excluded a contribution of the non-peaked plasma
component between the shock front and the subcluster.
For the main cluster, we see the same effect, although
the baryonic mass difference is smaller. Note that both
the plasma mass and the stellar mass are determined
directly from the X-ray and optical images, respectively,
independently of any gravity or dark matter models.
4. DISCUSSION
A key limitation of the gravitational lensing method-
ology is that it only produces a two-dimensional map of
κ, and hence raises the possibility that structures seen in
the map are caused by physically unrelated masses along
the line-of-sight. Because the background galaxies reside
at a mean z ∼ 1, structures capable of providing a signifi-
cance amount of κ must lie at z ? 0.8. By comparing the
measured shear for galaxies divided into crude redshift
bins using photometric redshifts (Wittman et al. 2003),
we further limit the redshift of the lensing objects to
0.18 < z < 0.39. This range is consistent with the clus-
ter redshift, but corresponds to a large volume in which
a structure unassociated with the cluster could exist and
be projected onto the lensing map. However, the num-
ber density of structures with these lensing strengths in
blank field surveys is ∼ 10−3arcmin−2for the subcluster
(Wittman et al. 2006), and an order of magnitude less
for the main cluster, resulting in a ∼ 10−7probability of
having two structures within a square arcminute of the
observed cluster cores. Further, all such lenses observed
in these cosmic shear surveys are clusters with enough
plasma and galaxies to be easily observable. There is
no evidence, however, in our deep imaging for additional
cluster sized concentrations of galaxies or of plasma hot-
ter than T ∼ 0.5 keV (the lower bound of the Chandra
energy band) near the observed lensing structures.
Another alternate explanation of the lensing signal is
related to the fact that clusters form at the intersections
of matter filaments (Bond et al. 1996). In principle, one
could imagine two line-of-sight filaments of intergalactic
gas (too cool to be visible with Chandra and too dif-
fuse to have cooled into stars) extending from the clus-
ter at the locations of the weak lensing peaks. To ex-
plain the measured surface mass density, such filaments
would have to be several Megaparsecs long, very nar-
row, and oriented exactly along the line of sight. The
probability of such an orientation for two such filaments
in the field is ∼ 10−6. Further, because the two clus-
ter components are moving at a relative transverse ve-
locity of 4700 km/s compared to the typical peculiar
velocities in the CMB frame of a few hundred km/s,
the filaments could coincide so exactly with each of the
BCGs only by chance. This is an additional factor of
∼ 10−5reduction in probability. While such projections
become more important in non-standard gravity mod-
els because in such models the thin lens approximation
breaks down (Mortlock & Turner 2001) and structures
with a given surface density produce a greater amount
of lensing the more they are extended along the line-of-
sight, two such projections would still have a ≪ 10−8
probability. Finally, we mention that two other merg-
ing clusters, MS1054−03 (Jee et al. 2005) and A520 (in
preparation), exhibit similar offsets between the peaks of
the lensing and baryonic mass, although based on lens-
ing reconstructions with lower spatial resolution and less
clear-cut cluster geometry.
A final possibility is that some alternative gravity mod-
els may be able to suppress the lensing potential of the
central peak in a multiple-peak system, as in Angus et al.
(2006). That work used a model of a gas disk located be-
tween two symmetric mass concentrations representing
the galaxy subclusters. In their κ map, derived in the
TeVeS framework (Bekenstein 2004), the relative signal
from this disk may be suppressed, but would still be eas-
ily visible with the noise levels of our reconstruction. Our
κ map, however, has no evidence of any mass concentra-
tion between the two galaxy subclusters other than the
small perturbations consistent with the gas mass contri-
bution in Newtonian gravity. Furthermore, such a sup-
pression has also only been shown to work for symmetric
systems which have the central peak directly between
the two outer peaks. In 1E0657−558, however, the X-
ray plasma, which would provide the central peak, lies
north of the line connecting the two κ peaks. Further, the
absolute κ levels of the peaks observed in 1E0657−558
are in good agreement with those in systems with sim-
ilar velocity dispersions and X-ray temperatures (e.g.
Clowe & Schneider 2002) which have the gas and the
galaxies coincident. The κ-to-light ratios are also con-
sistent with those in normal clusters with coincident gas
and galaxies. Therefore one would need to not only sup-
press the inner peak in the κ map relative to the two
outer peaks in this system, but also enhance the strength

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5
of the outer peaks to make up for the missing plasma
mass.
Any non-standard gravitational force that scales with
baryonic mass will fail to reproduce these observations.
The lensing peaks require unseen matter concentrations
that are more massive than and offset from the plasma.
While the existence of dark matter removes the pri-
mary motivation for alternative gravity models, it does
not preclude non-standard gravity. The scaling relation
between κ and surface mass density, however, has im-
portant consequences for models that mix dark matter
with non-Newtonian gravity: to achieve the ∼ 7 : 1
ratio in κ between the dark matter + galaxy compo-
nent and the plasma component (Table 2), the true ra-
tio of mass would be even higher (as high as 49:1 for a
constant acceleration model; although MOND (Milgrom
1983) would not reach this ratio as the dark matter
density would become high enough to shift the accel-
eration into the quasi-Newtonian regime), making the
need for dark matter even more acute. Such high con-
centrations of dark matter, however, are extremely un-
likely based on the measured X-ray plasma temperatures
(Markevitch et al. 2002) and cluster galaxy velocity dis-
persions (Barrena et al. 2002).
The spatial separation of the dominant baryonic com-
ponent in a galaxy cluster from the hypothesized dark
matter produced during a cluster merger has enabled
us to directly compare the dark matter hypothesis to
one with only visible matter but a modified law of grav-
ity. The observed displacement between the bulk of the
baryons and the gravitational potential proves the pres-
ence of dark matter for the most general assumptions
regarding the behavior of gravity.
We wish to thank Bhuvnesh Jain, Hongsheng Zhao,
and Peter Schneider for useful discussions. This work
was supported by NASA through grant number LTSA04-
0000-0041 (DC and DZ). Support for program 10200 was
provided by NASA through grant GO-10200.01 from the
Space Telescope Science Institute, which is operated by
the Association of Universities for Research in Astron-
omy, Inc., under NASA contract NAS 5-26555. MB ac-
knowledges support from the NSF grant AST-0206286.
MM acknowledges support from Chandra grant GO4-
5152X.
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