**5.3. Heating and cooling of the intracluster gas**

In this section, processes that heat or cool the intracluster gas are reviewed. Only processes that affect the total energy of the gas are considered here, while processes (such as heat conduction or mixing) that redistribute the gas energy are discussed in Section 5.4.

The primary cooling process for intracluster gas is the emission of
radiation by the processes discussed in
Section 5.2.2 above.
At temperatures *T*_{g}
3 ×
10^{7} K,
the main emission mechanism is thermal bremsstrahlung, for which the total
emissivity is

(5.21) |

where is the integrated
Gaunt factor, and *z*_{i} and *n*_{i} are the
charge and number
density of various ions *i*. The second equation follows from
assuming solar abundances and
= 1.1 in a fully ionized
plasma. For *T*_{g}
3 ×
10^{7} K, line cooling becomes very important.
Raymond *et al.*
(1976)
give the cooling rate at lower temperatures; a very crude approximation is
(McKee and Cowie,
1977)

(5.22) |

In assessing the role of cooling in the intracluster gas, it is useful
to define a cooling time scale as *t*_{cool}
(*d* ln
*T*_{g} / *dt*)^{-1}. For the temperatures
that apply for
the intracluster gas in most clusters, equation (5.21) gives a reasonable
approximation to the X-ray emission. If the gas cools isobarically, the
cooling time is

(5.23) |

which is longer in most clusters than the Hubble time (age of the universe). Thus cooling is not very important in these cases. However, at the centers of some clusters the cooling time is shorter than the Hubble time, and these clusters are believed to have cooling flows (Section 5.7).