5.4.6. Convection and mixing
The diffusive transport processes discussed so far tend to cause the gas in a cluster to be isothermal, tend to damp out fluid motions, and tend to cause heavy elements to settle to the cluster center. On the other hand, mixing processes due to turbulent motions of the intracluster gas tend to make the specific entropy (the entropy per atom) equal within the cluster, tend to make the composition of the gas homogeneous, and drive fluid motions. It is conventional to describe a gas in which the entropy per atom is constant as an 'adiabatic' gas. If mixing occurs on a time scale that is rapid compared to the age of the cluster or the time scale for diffusive transport, the resulting intracluster gas distribution will tend to be adiabatic and to have constant heavy element abundances.
One possible source of mixing motions in the gas is convection. If the intracluster gas were hydrostatic but had a steep temperature gradient
it would be unstable to convective mixing. If the temperature gradient in equation (5.52) were exceeded by a significant amount, mixing would occur within several sound crossing times in the cluster. Since this is a rather short time (equation 5.54 below), it is reasonable to assume that the temperature gradient is smaller than that in equation (5.52).
Motions of galaxies through the intracluster gas may mix the gas. This process has not been treated in any great detail in the literature. It might be reasonable to assume that each galaxy mixes the gas within a wake of radius RW. Very roughly, the gas within the whole cluster would be mixed on a time scale given by
where ngal is the number density of galaxies, r is their velocity dispersion, and rc is the cluster core radius. Depending on whether the galaxy contained any interstellar medium or not, the wake radius might be 10 kpc, or only as large as the accretion radius (Section 5.3.4). The resulting value of tmix is generally much longer than 1011 yr for any reasonable values of the cluster parameters, and mixing due to galaxy motions is probably not very important. Nepveu (1981b) discussed the mixing of gas ejected from cluster galaxies and showed that the mixing was not effective unless the galaxy motions were highly subsonic, which is not the case. His calculations indicated that the gas remained inhomogeneous on both small and large scales.
Large scale hydrodynamic motions during the formation of the cluster may be effective in mixing the intracluster gas. Similarly, mixing may occur when subclusters merge within the cluster.