In hierarchical models, structure grows by gravitational collapse
of succesively larger structures. The emergence
of galaxies as separate entities within this hierarchy depends
on the ability of baryons within a given overdense region to
cool and form stars before being subsumed into the next higher level
of the hierarchy.
Cooling of gas in protogalaxies is thought to be a runaway
process. As soon as gas is able to cool in a galaxy halo it
contracts, whereupon the cooling becomes more efficient, leading
to more cooling and contraction until something (e.g. star formation)
is able to put a halt the process.
The virial temperatures (k Tvir 
µ
mH 
2,
where µ mH is the mean molecular weight of
the gas) of collapsing protogalaxies are high enough
that the associated gas will be collisionally ionized and
cool radiatively. In the absence of other energy sources or
sources of ionization, the cooling time at radius r can be written as
where
For dwarf galaxy halos collapsing at z 
(T) is the
cooling rate due to bremsstrahlung,
recombination, and collisionally excited line emission, and
(r) is the
density at r (e.g.
White and Frenk
1991;
Cole et al. 1994).
3-10, the cooling
time is short compared to the free-fall time, so cooling
should be efficient. Unless this cooling is suppressed, most
of the baryonic material in the universe would collapse into
dwarf-galaxy size objects. This is the ``overcooling problem''
noted by
Cole (1991)
and others. As dwarf galaxies do not appear to be so overwhelming abundant,
some mechanism to counteract cooling is needed. Plausible
mechanisms involve both internal and external agents.