Cooling is a crucial ingredient of galaxy formation. Depending on temperature and density, a variety of cooling processes can affect gas. In massive halos, where the virial temperature 
, gas is fully collisionally ionized and cools mainly through bremsstrahlung emission from free electrons. In the temperature range 
, a number of excitation and de-excitation mechanisms can play a role. Electrons can recombine with ions, emitting a photon, or atoms (neutral or partially ionized) can be excited by a collision with another particle, thereafter decaying radiatively to the ground state. Since different atomic species have different excitation energies, the cooling rates depend strongly on the chemical composition of the gas. In halos with 
, gas is predicted to be almost completely neutral. This strongly suppresses the cooling processes mentioned above. However, if heavy elements and/or molecules are present, cooling is still possible through the collisional excitation/de-excitation of fine and hyperfine structure lines (for heavy elements) or rotational and/or vibrational lines (for molecules). Finally, at high redshifts (z ∼ > 6), inverse Compton scattering of cosmic microwave background photons by electrons in hot halo gas can also be an effective cooling channel. Chapter 8 will discuss these cooling processes in more detail.
Except for inverse Compton scattering, all these cooling mechanisms involve two particles. Consequently, cooling is generally more effective in higher density regions. After nonlinear gravitational collapse, the shocked gas in virialized halos may be dense enough for cooling to be effective. If cooling times are short, the gas never comes to hydrostatic equilibrium, but rather accretes directly onto the central protogalaxy. Even if cooling is slow enough for a hydrostatic atmosphere to develop, it may still cause the denser inner regions of the atmosphere to lose pressure support and to flow onto the central object. The net effect of cooling is thus that the baryonic material segregates from the dark matter, and accumulates as dense, cold gas in a protogalaxy at the center of the dark matter halo.
...dark matter halos, as well as the baryonic material associated with them, typically have a small amount of angular momentum. If this angular momentum is conserved during cooling, the gas will spin up as it flows inwards, settling in a cold disk in centrifugal equilibrium at the center of the halo. This is the standard paradigm for the formation of disk galaxies, ...
