Measuring Dark Matter Flows in
Merging Clusters of Galaxies
J.A. Rubiño-Martín, C. Hernández-Monteagudo, T.A. Enßlin
Max-Planck-Institut für Astrophysik, Postfach 1317, D-85748 Garching, Germany
Abstract: The Rees-Sciama effect produced in mergers of galaxy clusters is discussed, and an analytical approximation
to compute this effect from numerical simulations is given. Using this approximation and a novel toy model describing
the physics of the merger, we characterize the spatial properties and symmetries of the Rees-Sciama signal. Based on
these properties, we propose a method to extract the physical parameters of the merger, which relies on the computation
of the quadrupole moment of the observed brightness distribution on the sky.
The relationships between the quadrupole coefficients and the physical parameters of the merger (physical separation,
projection angle on the sky and angular momentum) are discussed. Finally, we propose a method to co-add coherently
the RS signals from a sample of cluster mergers, in order to achieve an statistical detection of the effect for those cases
where individual signals are masked by the kinetic SZ effect, the primordial CMB components, and by observational
noise.
Introduction
The Rees-Sciama effect associated to the regime of moving single
galaxy clusters was already examined by Birkinshaw & Gull (1983);
Aghanim et al. (1998); Molnar & Birkinshaw (2000;2003) and
Cooray (2002). However, clusters reach the largest velocities during
mergers, so we will consider here the peculiarities of this case.
Formalism
The CMB temperature change in a line-of-sight direction caused by
the Rees-Sciama (RS) effect can be written as (e.g. MartinezGonzalez et al. 1990)
Using the Newtonian approximation to the gravitational potential,
and neglecting the intrinsic variation of the cluster potential while
the photon is passing through it , we can show that the RS signal
can be computed as:
The RS effect measures the convergence of the projected
perpendicular velocity.
Morphology of the effect
For a pair of merging clusters with opposite momenta, the RS
signal has a peculiar quadrupole morphology. In addition, and
because of its gravitational nature, it is much more extended than
the Sunyaev-Zel'dovich effect.
Toy model
We use two NFW dark matter profiles filled with isothermal
hydrostatic gas. The cluster velocities are computed as free-falling
velocities, and the total momentum of the system is assumed to be
zero. Hydrodynamical interactions of the gas are neglected.
We show the result for a major merger of two clusters with masses
1015 Msun and 5 ·1014 Msun, and with physical separation of 1 Mpc.
Left: without angular momentum, practically face-on merger.
Right: considering angular momentum, and projection angle 45° .
Signal extraction
The figure on the right illustrates the order
of magnitude of the RS signal when
compared to the kinetic SZ effect. The kSZ
contribution has been derived using our toy
model, for the case of a projection angle
î=80° and the same previous parameters.
Although the RS effect is much smaller, its
morphology may allow to separate it.
Thus, we propose to quantify the RS effect using the quadrupole moment of the
observed intensity map. In our paper, we have adopted the following definition
To extract the RS information, we proceed as follows:
1. Observations at frequencies far from 217 Ghz will show us the spatial
distribution of the gas. This information is used to determine the centre of light
point (to compute the quadrupole) and to built a filter to enhance the RS signal.
2. Observations at 217 Ghz will provide us a map with only RS and kSZ (and
CMB) components.
The quadrupole components are related to the physical parameters of the cluster.
In the left figure we show the dependence of Qxx on the projection angle, using
and not using a taper for the kSZ emission built from the tSZ map; in the right
figure, we show the change of Qxx with the physical separation.
In both cases, the total angular momentum is zero. In opposite case, it can be
shown that Qxy is proportional to the projected angular momentum.
Conclusions
We have presented a formalism to predict the Rees-Sciama effect in a merging
system of clusters of galaxies, that can be easily incorporated to N-body
simulation codes. The RS signature detection is discussed using the quadrupole
moments of the observed map. The relationship of these quadrupole coefficients
with the physical parameters of the merger is also shown.
References:
[1] Rubiño-Martín J.A., Hernández-Monteagudo C. & Enßlin T.A., 2004, A&A,
419, 439.
[2] Birkinshaw & Gull, 1983, Nature, 302, 315.
[3] Cooray A., 2002, Phys. Rev. D, 65, 83518.
[4] Martinez-Gonzalez E., Sanz J.L. & Silk J.,1990, ApJ, 355, 5.
[5] Molnar S.M. & Birkinshaw M., 2000, ApJ, 537, 542.
[6] Molnar S.M. & Birkinshaw M., 2003, ApJ, 586, 731.