and Cosmology

6. Clusters and Groups of Galaxies
246
Fig. 6.17. Surface brightness contours of the X-ray emission
for four different groups or clusters of galaxies. Upper
left: the galaxy group NGC 5044, at redshift z = 0.009, with
an X-ray temperature of T ≈ 1.07 keV and a virial mass of
M 200 ≈ 0.32h −1 ×10 14 M ⊙ . Upper right: the group MKW4, at
z = 0.02, with T ≈ 1.71 keV and M 200 ≈ 0.5h −1 × 10 14 M ⊙ .
Lower left: the cluster of galaxies A 0754, at z = 0.053, with
T ≈ 9.5keVandM 200 ≈ 13.1h −1 ×10 14 M ⊙ . Lower right: the
cluster of galaxies A 3667, at z = 0.056, with T ≈ 7.0keVand
M 200 ≈ 5.6h −1 × 10 14 M ⊙ . The X-ray data were obtained by
ROSAT, and the optical images were taken from the Digitized
Sky Survey. These clusters are part of the HIFLUGCS Survey,
which we will discuss more thoroughly in Sect. 6.3.5
6.3.2 Models of the X-Ray Emission
Hydrostatic Assumption. To draw conclusions about
the properties of the intergalactic (intracluster) medium
from the observed X-ray radiation and about the distribution
of mass in the cluster, the gas distribution needs
to be modeled. For this, we first consider the speed of
sound in the cluster gas,
c s ≈
√
P
ρ g
=
√
nk B T
ρ g
=
√
k B T
μ m p
∼ 1000 km s −1 ,
where P denotes the gas pressure, ρ g the gas density,
and n the number density of gas particles. Then, the
average molecular mass is defined as the average mass
of a gas particle in units of the proton mass,
μ := 〈m〉 . (6.33)
m p
so that ρ g = n 〈m〉 = nμm p . For a gas of fully ionized
hydrogen, one gets μ = 1/2 because in this case one has
one proton and one electron per ∼proton mass. Since the
cluster gas also contains helium and heavier elements,
one obtains μ ∼ 0.63. The sound-crossing time for the
cluster is
t sc = 2R A
c s
∼ 7 × 10 8 yr ,