and Cosmology

6. Clusters and Groups of Galaxies
258
Fig. 6.27. For the clusters of galaxies from the extended HI-
FLUGCS sample (see Sect. 6.3.5), the mass within a mean
overdensity of 500 is plotted as a function of X-ray temperature,
where a dimensionless Hubble constant of h = 0.5
has been assumed. In the left-hand panel, the mass was determined
by applying an isothermal β-model, while in the
right-hand panel, the radial temperature profile T(r) was
used to determine the mass, by means of (6.36). Most of
the temperature measurements are from observations by the
ASCA satellite. The solid and dash-dotted curves in the
left-hand panel show the best fit to the data, where for the
latter only the clusters from the original HIFLUGCS sample
were used. In the right-hand panel, the dotted line is a fit
to all the data in the plot, while the solid line takes into
account only clusters with a mass ≥ 5 × 10 13 M ⊙ . In both
panels, the upper dotted line shows the mass–temperature
relation that was obtained from a simulation using simplified
gas dynamics – the slope agrees with that found
from the observations, but the amplitude is significantly too
high
This relation can now be tested using clusters for which
the mass has been determined using the X-ray method,
and for which the velocity dispersion of the cluster
galaxies has been measured. Alternatively, the relation
T ∝ σv 2 can be tested. One finds that these relations are
essentially satisfied for the observed clusters. However,
the relation between σ v and M is not as tight as the M–T
relation. Furthermore, numerous clusters exist which
strongly deviate from this relation. These are clusters
of galaxies that are not relaxed, as can be deduced from
the velocity distribution of the cluster galaxies (which
strongly deviates from a Maxwell distribution in these
cases) or from a bimodal or even more complex galaxy
distribution in the cluster. These outliers need to
be identified, and removed, if one intends to apply the
scaling relation between mass and velocity dispersion.
6.4.3 Mass–Luminosity Relation
The total X-ray luminosity that is emitted via bremsstrahlung
is proportional to the squared gas density and
the gas volume, hence it should behave as
L X ∝ ρg 2 T 1/2 rvir 3 ∝ ρ2 g T 1/2 M vir . (6.52)
Estimating the gas density through ρ g ∼ M g rvir −3 =
f g M vir rvir −3,
where f g = M g /M vir denotes the gas fraction
with respect to the total mass of the cluster, and
using (6.48), we obtain
L X ∝ fg 2 M4/3 vir . (6.53)
This relation needs to be modified if the X-ray luminosity
is measured within a fixed energy interval.
Particularly for observations with ROSAT, which could
only measure low-energy photons (below 2.4 keV), the
received photons typically had E γ < k B T, so that the
measured X-ray luminosity becomes independent of T.
Hence, one expects a modified scaling relation between
the X-ray luminosity measured by ROSAT L