and Cosmology

6.3 X-Ray Radiation from Clusters of Galaxies
bitrarily long times. To decide whether this gas cooling
is important for the dynamics of the system, the cooling
time-scale needs to be considered. This cooling time
turns out to be very long,
249
t cool := u ɛ ff
(
≈ 8.5 × 10 10 n
) ( )
e
−1
1/2
Tg
yr
10 −3 cm −3 10 8 ,
K
(6.43)
where u = (3/2)nk B T g is the energy density of the gas
and n e the electron density. Hence, the cooling time is
longer than the Hubble time nearly everywhere in the
cluster, which allows a hydrostatic equilibrium to be
established. In the centers of clusters, however, the density
may be sufficiently large to yield t cool t 0 ∼ H −1
0 .
Here, the gas can cool quite efficiently, by which its
pressure decreases. This then implies that, at least close
to the center, the hydrostatic equilibrium can no longer
be maintained. To re-establish pressure equilibrium, gas
needs to flow inwards and is thus compressed. Hence,
an inward-directed mass flow should establish itself.
The corresponding density increase will further accelerate
the cooling process. Since the emissivity (6.32)
of a relatively cool gas increases with decreasing temperature,
this process should then very quickly lead to
a strong compression and cooling of the gas in the centers
of dense clusters. In parallel to this increase in
density, the X-ray emission will strongly increase, because
ɛ ff ∝ n 2 e . As a result of this process, a radial density
and temperature distribution should be established with
a nearly unchanged pressure distribution. In Fig. 6.18,
the cooler gas in the center of the Centaurus cluster is
clearly visible.
These so-called cooling flows have indeed been observed
in the centers of massive clusters, in the form of
a sharp central peak in I(R). However, we need to stress
that, as yet, no inwards flows have been measured. Such
a measurement would be very difficult, though, due to
the small expected velocities. The amount of cooling gas
can be considerable, with models predicting values of
up to several 100M ⊙ /yr. However, after spectroscopic
observations by XMM-Newton became available, we
have learned that these very high cooling rates implied
by the models were significantly overestimated.
Fig. 6.18. Chandra image of the Centaurus cluster; the size of
the field is 3 ′ ×3 ′ . Owing to the excellent angular resolution of
the Chandra satellite, the complexity of the morphology in the
X-ray emission of clusters can be analyzed. Colors indicate
photon energies, from low to high in red, yellow, green, and
blue. The relatively cool inner region might be the result of
a cooling flow
The Fate of the Cooling Gas. The gas cooling in this
way will accumulate in the center of the cluster, but
despite the expected high mass of cold gas, no clear
evidence has been found for it. In clusters harboring
a cD galaxy, the cooled gas may, over a Hubble time,
contribute a considerable fraction of the mass of this galaxy.
Hence, the question arises whether cD galaxies may
have formed by accretion in cooling flows. In this scenario,
the gas would be transformed into stars in the cD
galaxy. However, the star-formation rate in these central
galaxies is much lower than the rate by which cluster
gas cools, according to the “old” cooling flow models.
The sensitivity and spectral resolution achieved with
XMM-Newton have strongly modified our view of cooling
flows. In the standard model of cooling flows, the
gas cools from the cluster temperature down to temperatures
significantly below 1 keV. In this process many
atomic lines are emitted, produced by various ionization
stages, e.g., of iron, which change with decreasing
temperature. Figure 6.19 (top panel) shows the expected
spectrum of a cooling flow in which the gas cools down