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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 sigma2r appeq kT/µmp (Lubin and Bahcall 1993). The best-fit sigma-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 sigma-T correlations that match well the data in Figure 1.

Figure 1

Figure 1. Cluster radial velocity dispersion (sigmar) vs. gas temperature (kT) for 41 clusters (Lubin and Bahcall 1993). The best-fit beta ident sigma2r / (kT/µmp) lines are shown by the solid and dotted curves, with beta appeq 1. The beta appeq 0.5 line previously proposed for a velocity bias in clusters is shown by the dashed curve; the velocity bias is inconsistent with the data.

Density Profiles     The gas density profile in clusters follows

Equation 36 (36)

with core radii in the range Rc appeq 0.1-0.3h-1 Mpc (Section 3.2). This implies rhogas(r) propto r-2 for Rc < r ltapprox 1.5h-1 Mpc.

The galaxy density profile in clusters follows approximately (Section 2.6)

Equation 37 (37)

with core radii Rc appeq 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 ltapprox 100 kpc), the mass distribution may be more compact than the gas or galaxies, with a small mass core radius of Rc(m) ltapprox 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 betaspec ident sigma2r / kT/µmp appeq 1 result discussed above, combined with the similarity of the gas and galaxy density profile slopes (that yields betafit appeq 0.85 ± 0.1; Section 3.3) show that the long claimed beta-discrepancy for clusters (where Bspec > betafit 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

Equation 38 (38)

with a median value of

Equation 39 (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 Modot, 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.

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