Understanding the Physics and Observational Effects of Collisions
between Galaxy Clusters
Daniel R. Wik1
Advisor: Craig L. Sarazin1
1
Department of Astronomy, University of Virginia, Charlottesville, VA, 22904
[email protected]
ABSTRACT
Galaxy clusters, the largest gravitationally bound objects in the universe, form over time
from collisions and mergers between clusters and between clusters and smaller galaxy groups.
The results of these collisions can be detected in a variety of ways. In one case, I have found that
clusters which have recently undergone a merger will have an enhanced Sunyaev-Zel’dovich (SZ)
Effect. The SZ signal from thousands of clusters will soon be measured in order to constrain the
dark matter and dark energy content of the universe. However, I have shown that while observations of the central SZ effect, which is more sensitive to merger enhancements, will hopelessly
bias these estimates, the integrated SZ signal will not and should be the quantity extracted from
SZ surveys. Another result of cluster mergers is the acceleration of relativistic particles, which
produce non-thermal emission that should be observable in X-rays. In the Coma cluster, the
brightest merging cluster in the sky, detections of this emission have been claimed, though these
findings are controversial. Using observations of Coma with the Hard X-ray Detector onboard
Suzaku, I find no conclusive non-thermal emission and derive an upper limit on the emission that
excludes the most recent previous detection.
Introduction
Over the past decade, the history, age, and
likely future evolution of the universe have been
reliably uncovered for the first time, prompting
some to call our time the golden age of cosmology.
While past advances have come from observations
of the afterglow of the Big Bang and of supernovae
in distant galaxies, it will soon be possible to study
the largest scales of the cosmos with the largest
and most massive objects in the universe, clusters of galaxies. These tightly bound collections
of thousands of galaxies grow by pulling in galaxies, groups of galaxies, and even other clusters,
which they attract with their immense gravity.
When 2 galaxy clusters merge, they release enormous amounts of energy, up to 1057 Joules, making cluster mergers the most energetic events since
the Big Bang itself. Part of this energy is used to
heat up intracluster gas – the atmospheres of clusters filling up the space in between the galaxies –
through shock waves and turbulence. In addition
to heating up the gas, shocks and turbulence act
to accelerate particles traveling near the speed of
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light, which can emit light in the form of radio
waves and X-rays. The existence of this light indicates that a cluster has recently or is currently
undergoing a merger, an often difficult conclusion
to draw from the optical light alone, and it can tell
us about the dynamics and history of the merger,
along with the specific physics necessary to produce that light.
As well as studying individual clusters undergoing mergers, we can apply what we learn from
these observations to understand how mergers affect large samples of galaxy clusters. Over the
history of the universe, the nearby galaxy clusters
we see now formed from many merger events, so
if we observed one of these clusters in the past,
it would hold fewer galaxies, smaller amounts of
colder gas, and would overall contain less mass.
The number of clusters at a given mass changes
over time, and how the number evolves can tell us
how much “stuff” is in the universe, namely the
total amount of mass and dark energy – the mysterious substance that appears to be accelerating
the expansion of the universe. In a cluster that
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has reached equilibrium, the intracluster gas is in
balance with the cluster’s gravity, so the energy
in the particles of this gas directly corresponds to
the mass of the cluster, which is the source of its
gravity. This gas is very energetic and hot because
the gravity in clusters is so strong, so we can observe its emission at X-rays energies. Also, the hot
intracluster gas will distort the Cosmic Microwave
Background (CMB), the relic radiation left over
from the Big Bang, via the Sunyaev-Zel’dovich
(SZ) effect. The amount of change in the CMB
spectrum is also directly related to the energy in
the cluster gas, and so can be used to measure the
total mass of the cluster. From measurements of
the X-ray temperature or SZ signal of many galaxy
clusters, we can use their inferred masses to constrain the dark matter and dark energy content of
the universe.
However, the mass you derive is only valid if
the cluster gas is in equilibrium and is energetically the dominant component. During violent
cluster mergers, the gas is not in equilibrium but
is transiently heated, which temporarily “boosts”
the SZ signal. If a cluster is observed while it is
undergoing a boost, the inferred mass will be incorrect. Also, the mass that is inferred assumes
nearly all the energy in the cluster is in the thermal, hot gas particles. While this is a reasonable
assumption, it is known that clusters contain nonthermal particles as well, in the form of relativistic electrons traveling near the speed of light. The
precise amount of energy in these particles and another relativistic quantity, the magnetic field, has
so far yet to be decisively measured, though both
are required to explain the presence cluster-wide
structures seen at radio frequencies, called radio
halos and radio relics, that happen to be found
only in merging clusters. The existence of this
emission directly implies the presence of Inverse
Compton (IC) emission at high X-ray energies,
which if observed would uniquely determine the
energetic contribution of relativistic electrons and
magnetic fields to the intracluster gas. Thus, if
clusters are to be used as cosmological probes, the
physics taking place during cluster mergers must
be well understood.
Cluster Mergers and the SZ Effect
To assess the effect of mergers on measurements
of the SZ effect in galaxy clusters, we used a small
suite of binary cluster merger simulations from
Ricker & Sarazin (2001). These simulations include mergers between clusters with various mass
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Fig. 1.— Images of the SZ parameter y from 3D
snapshots of the 1:3 mass ratio, 2 rs impact parameter merger simulation. The image are viewed
from a line-of-sight which is rotated 45◦ from the
merger axis and 45◦ azimuthally from the merger
plane 386 Myr before first core crossing.
Fig. 2.— Same as Figure 1, but at 114 Myr after
first core crossing.
ratios (M< : M> = 1 : 1, 1 : 3, 1 : 6.5) and impact
parameters (head-on to glancing impacts), totaling 8 unique simulations. From these we calculated the SZ observable y at each time step for
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which data was saved. Sample images of y from
the 1:3 mass ratio merger are provided in Figures 1
and 2.
In practice, only one characteristic value for the
SZ signal will be extracted for an individual cluster
in a large sample. Generally in the literature, this
value is taken to be either the central (or equivalently the maximum) value of y, ymax , or y is
integrated over the entire cluster, usually denoted
by Y . Though it is not immediately clear from the
figures, note that the scale of Figure 2 is twice that
of Figure 1, indicating that after the cluster centers have collided for the first time, the value of y
increases or experiences a “boost.” These boosts,
which appear in both Y and ymax , show up as a
peak when the SZ parameter is plotted as a funciton of time. We present the evolution of Y and
ymax over time during a merger event for the 1:1
mass ratio case in Figures 3 and 4, respectively.
In Figure 3, the peak is always less than a factor of two of the initial value of Y , and appears to
be less than the final value of Y , once the clusters
have merged completely and have reached equilibrium. This is an excellent feature of Y regarding
its use as a mass estimate for clusters, as it means
that if a cluster is observed during a merger event,
the inferred mass will not be overestimated since
Y ∝ M 2 . In fact, catching the merger at its peak
would give a more accurate mass estimate than observing it 1 Gyr later, when the mass would be underestimated slightly. However, for ymax the transient boost is much larger, though shorter lived.
The ymax parameter is boosted by nearly a factor
of 10 (see Figure 4), and though it is less likely a
cluster will be observed during this shorter boost
phase, if it is observed the inferred mass will be
significantly larger than its actual mass.
From these results, we need to determine
whether enough clusters in a survey are affected
by these transient boosts to bias the cosmological studies that typically would not take merger
events into account. Because of the computational
power required in simulating a large portion of the
universe over billions of years, we instead use a
semi-analytic method to approximate the growth
of galaxy clusters, called the extended PressSchechter formalism (Press & Schechter 1974;
Lacey & Cole 1993). This method allows us to
follow the merger history of a present-day cluster
back in time, so we know when mergers happen
and what the mass ratio of the merger was. The
only other parameter we need is the impact parameter, which can be taken from the probability
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Fig. 3.— Evolution of Y during the 1:1 mass ratio
mergers. The different curves are for different values of the merger impact parameter: b = 0 (solid,
black line), 2 rs (dashed,red line), and 5 rs (dotted, blue line). The b = 2rs simulation run is
offset downward by 0.15 and the 5rs run is offset
downward by 0.3 for clarity.
Fig. 4.— Same as Figure 3, but for ymax and with
no artifical offset between the curves.
distribution of likely values of b (Sarazin 2002;
Bullock et al. 2001). By characterizing the nature
of the boosts as a function of mass ratio and impact parameter, the observed value of Y and ymax
can be found for clusters today or at any time in
the past. This is the type of information surveys
will get, so we can now find whether the surveys
would be biased by neglecting merger effects since
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we know the true masses of the clusters along with
the inferred masses derived from either Y or ymax .
A qualitative understanding of our findings can
be inferred directly from Figures 5 and 6. In these
figures, the value of Y or ymax is shown as a function of mass for 10,000 present-day clusters. The
majority of clusters are not currently undergoing
a boost, and so they lie along the equilibrium SZ–
M relation, which shows up as a solid line. In
the case of Y , almost all of the clusters lie along
this relation, and only a few lie below it, indicating that the mass would be underestimated as
Figure 3 suggested. In fact, the effect of merger
boosts on Y is so slight that cosmological parameters such as the amount of mass in the universe
and the nature of dark energy are determined to
within ∼ 1%. This accuracy is well-within the typical uncertainties of the surveys themselves, making mergers an unimportant factor if Y is used to
estimate cluster masses.
In the case of ymax , on the other hand, there is
a large number of clusters that are boosted from
the equilibrium relation, as illustrated in Figure 6.
The parameter ymax is preferentially boosted to
larger values, which leads to a larger implied mass
for those clusters. Even though the boost period
for a given cluster is short, making it more difficult
to catch a cluster during one of these periods, it is
still long and strong enough to affect quite a few
clusters. The implied masses lead to significantly
biased cosmological parameter estimates, with the
total mass of the universe being underestimated by
15-45% and the value of the dark energy equation
of state parameter w to be similarly misestimated.
In conclusion, it is clear that when these surveys get going in earnest, the SZ parameter that
best returns the cluster mass, and that should be
used to derive cosmological parameters, is the integrated parameter Y .
Fig. 5.— Integrated Comptonization parameter Y
versus total mass. The apparent solid line is the
result of many individual clusters at or near their
equilibrium values of Y .
Fig. 6.— Same as Figure 5, but for ymax .
The Search for Non-thermal Emission
in the Coma Cluster
While cluster mergers themselves can confuse
cosmological studies that depend on the galaxy
cluster mass distribution, mergers can also be exploited to census another component coincident
with the gas – relativistic particles and magnetic
fields. If these relativistic components contain a
significant amount of energy relative to the thermal gas, then they would modify the equilibrium
state of the gas upon which conversions between
observables, such as Y , ymax , and X-ray tempera-
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ture, and cluster mass are based. It is thought
that relativistic particles are accelerated across
shock fronts and turbulence induced by mergers
(Sarazin 1999, 2002), which may explain why radio halos and relics are observed exclusively in
clusters currently or recently undergoing a merger
event (Feretti & Giovannini 2007). The radio
emission is produced by relativistic electrons spiralling around magnetic field lines, so we know
both of these relativistic components exist. However, the strength of this emission depends on both
the number of electrons and the strength of the
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magnetic field, so from the radio data alone these
components cannot be disentangled. Certain assumptions, arrived at through equipartition arguments, lead to estimates of the number of relativistic particles and magnetic field strengths that
do not contribute significant amounts of energy
relative to the thermal gas. This would not remain true if the value of the average magnetic
field in clusters was about 10 times larger than
its equipartition value, as suggested by Faraday
RM measurements from which the magnetic field
can be derived along particular lines of sight.
The relativistic electrons that produce the radio
halos and relics also produce IC emission through
interactions with the CMB, and this emission
should be observable at hard X-ray energies. If
emission is seen at both radio and X-ray frequencies, then the magnetic field can be directly determined. However, the IC X-ray emission has been
difficult to observe with past instruments, generally leading to weak or non-detections (Nevalainen
et al. 2004). The most recent observatory with
hard X-ray capabilities, the Suzaku X-ray Observatory, should be ∼ 3× more sensitive where IC
emission is expected to be detected. We report
here an observation with the Suzaku Hard X-ray
Detector (HXD) of the Coma cluster, which hosts
the brightest radio halo in the sky. Coma was
observed for over 160,000 seconds, or for about 2
days.
The greatest difficulty in detecting IC emission
from clusters like Coma is that they tend to be
hot because they are so massive – massive clusters
undergo more mergers typically and are thus more
likely to host radio halos or relics. The hotter the
gas in a cluster, the more thermal emission there
is at higher energies, which is where we are looking for the IC emission. So, in order to confidently
detect an IC signal, the thermal emission must be
well characterized. To accomplish this goal, we extract complimentary data at lower energies, where
the thermal emission is completely dominant, from
a mosaic observation of Coma with the XMMNewton Observatory (Schuecker et al. 2004). For
this data, we spatially weight the X-rays according to the spatial sensitivity of the HXD (since
it is a non-imaging instrument while XMM is) to
create a spectrum that exactly corresponds to the
spectrum obtained from the Suzaku HXD observation. With these two spectra, we now have a
long enough lever arm to accurately characterize
the thermal emission and see whether there is evidence for IC emission as well. Our best model fit
for these spectra is given in Figure 7.
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Considering only statistical errors, we detect a
non-thermal component to the total emission from
Coma at the 3.4σ level. When systematic errors
are also included, however, this non-thermal signal is no longer robustly detected. The main uncertainty lies in the precise determination of the
non-X-ray background in the instrument, which
is known to an accuracy of 3%. Since the flux
of the IC emission is very similar to 3% of the
background flux, if the background is actually
3% higher than we have assumed, then the nonthermal component is not needed. We determine
an upper limit for IC emission instead, by setting quantities with systematic errors to the limit
that would favor an IC detection. For the background level, we set it to be 3% lower than originally set, for example. We find an upper limit
on the IC emission of 7.8 × 10−15 W/m2 . This
value is 2× lower than the most recent detections
of IC emission in Coma, with the RXTE observatory (Rephaeli & Gruber 2002) and the BeppoSAX observatory (Fusco-Femiano et al. 2004).
This result is not entirely surprising, especially
given that the BeppoSAX detection was controversial. Rossetti & Molendi (2004) analyzed the
same data as Fusco-Femiano et al. (2004) and due
to a different background determination, they only
found an upper limit consistent with our result.
The lack of a non-thermal component is also
bolstered by a more detailed analysis of the lower
energy X-ray data from XMM. In reality, the
thermal component in Coma consists of a multiple temperature gas, and even a small amount of
higher-than-average temperature gas can mimic a
non-thermal signal at high energies. We divided
the XMM data into spatial regions and found the
temperature of the gas in each region, and then
we created a multi-temperature model which was
extrapolated to higher energies. In other words,
if all the emission is due to thermal sources, then
the fits we derive at low energies should also work
at higher energies. If not, and there is an excess
of emission at higher energies, then the existence
of IC emission is supported. We found that our
multi-temperature model more successfully fit the
data than the model that included a non-thermal
component. This result is consistent with recent
findings from the INTEGRAL observatory that
also detected hard X-ray photons from Coma that
was entirely consistent with only thermal emission
(Renaud et al. 2006; Eckert et al. 2007).
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Fig. 7.— The photon detection rate as a function of energy in kilo-electron volts. The black data points are
from XMM and the red points are from the Suzaku HXD. The bottom panel reports the residuals compared
to the best-fit model, relative to the size of the error on the data points. The various histograms represent
the contribution of thermal emission (the line almost overlapping with the data, deviating more at higher
energies), the Cosmic X-ray background (line only in red), the Inverse Compton emission (line second from
the bottom, close to the CXB line) and emission from point sources (line closest to bottom).
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6
Future Work
Upper limits on the flux of IC emission in clusters with radio halos or relics provide a lower limit
on the magnetic field strength, which sets a lower
limit on the amount of energy in relativistic components in galaxy clusters. Even if no IC emission
is detected, the derived lower limit could still indicate that a non-negligible amount of energy resides in relativistic components, which would modify observable quantity-mass relations necessary to
use clusters to study cosmology. Because cluster
surveys, both in X-rays and in the SZ effect, are
achieving senstitivity to cosmological parameters,
it is critical that merger effects are allowed for and
that we fully understand the energetics of the intracluster gas. To that end, I plan to repeat my
analysis of Suzaku HXD data on the Coma cluster
for all the clusters so far observed with Suzaku, in
order to produce a uniform analysis of their hard
X-ray emission. This work will allow a better determination of the relativistic energy contribution
in clusters, which will address the usefulness of
current observable quantity-mass relations as well
as probe the physical processes that occur during
cluster mergers.
Sarazin, C. L. 2002, The Physics of Cluster Mergers (ASSL Vol. 272: Merging Processes in
Galaxy Clusters), 1–38
Schuecker, P., Finoguenov, A., Miniati, F.,
Böhringer, H., & Briel, U. G. 2004, A&A, 426,
387
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