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3.5. The Relation between Gas and Galaxies
The hot intracluster gas in rich clusters appears to trace reasonably well the galaxies in the clusters, and - with larger uncertainty - also the cluster mass.
Velocity-Temperature relation
The galaxy velocity dispersion in clusters is well correlated with the
temperature of the intracluster gas; it is observed
(Fig. 1) that
2r
kT/µmp
(Lubin and Bahcall 1993).
The best-fit
-T relation is
listed in
Section 3.7. The observed correlation
indicates that, on average,
the energy per unit mass in the gas and in the galaxies is the same.
Figure 1 shows that, unlike previous
expectations, the
galaxy velocities (and therefore the implied cluster mass) are not
biased low with respect to the gas (and, by indirect implications,
with respect to the cluster mass; see also
Section 3.4). Results
from gravitational lensing by clusters also suggest that no
significant velocity bias exists in clusters, and that the gas,
galaxies, and mass provide consistent tracers of the clusters.
Cosmological simulations of clusters
(Lubin et al. 1996)
produce
-T
correlations that match well the data in
Figure 1.
![]() |
Figure 1. Cluster radial velocity dispersion
( |
Density Profiles The gas density profile in clusters follows
![]() | (36) |
with core radii in the range Rc
0.1-0.3h-1 Mpc
(Section 3.2). This implies
gas(r)
r-2
for Rc < r
1.5h-1 Mpc.
The galaxy density profile in clusters follows approximately (Section 2.6)
![]() | (37) |
with core radii
Rc
0.1 - 0.25h-1 Mpc
(Section 2.7).
The mass density profile in clusters is less well established, but
initial results from gravitational lensing distortions of background
galaxies by foreground clusters suggest that the mass profile is
consistent with the galaxy density profile
(Tyson and Fischer 1996).
In the small central core regions of some clusters (r
100
kpc), the mass distribution may be more compact than the gas or
galaxies, with a small mass core radius of Rc(m)
50h-1 kpc. The results for the overall cluster,
however, suggest
that the distributions of gas, galaxies, and mass are similar (with
the gas distribution possibly somewhat more extended than
the galaxies, as seen by the mean density slopes above).
Beta-Discrepancy The mean
spec
2r /
kT/µmp
1
result discussed above, combined with the similarity of the gas and
galaxy density profile slopes (that yields
fit
0.85 ± 0.1;
Section 3.3) show that the long claimed
-discrepancy
for clusters (where Bspec >
fit
was claimed) has been resolved
(Bahcall and Lubin 1994).
The gas and galaxies trace
each other both in their spatial density distribution and in their
energies, as expected for a quasi-hydrostatic equilibrium.
Gas Mass Fraction The ratio of the mass of gas in clusters to the total virial cluster mass (within ~ 1.5h-1 Mpc) is observed to be in the range
![]() | (38) |
with a median value of
![]() | (39) |
(Jones and Forman 1992;
White et al. 1993;
White and Fabian 1995;
Lubin et al. 1996).
The implications of this result, which shows a
high fraction of baryons in clusters, is discussed in
Section 4.
The total gas mass in clusters, ~ 1013-1014
h-2.5
M, is
generally larger than the total mass of the
luminous parts of the galaxies (especially for low values of h).
With so much gas mass, it is most likely that a large fraction of the
intracluster gas is of cosmological origin (rather than all the cluster gas
being stripped out of galaxies). Additional optical-X-ray
correlations of clusters are summarized in
Section 3.7.