  Cosmological simulations of the low-density intergalactic medium exhibit a
strikingly tight power-law relation between temperature and density that holds
over two decades in density. It is found that this relation should roughly
apply Delta z ~ 1-2 after a reionization event, and this limiting behavior has
motivated the power-law parameterizations used in most analyses of the Ly-alpha
forest. This relation has been explained by using equations linearized in the
baryonic overdensity (which does not address why a tight power-law relation
holds over two decades in density) or by equating the photoheating rate with
the cooling rate from cosmological expansion (which we show is incorrect).
Previous explanations also did not address why recombination cooling and
Compton cooling off of the cosmic microwave background, which are never
negligible, do not alter the character of this relation. We provide an
understanding for why a tight power-law relation arises for unshocked gas at
all densities for which collisional cooling is unimportant. We also use our
results to comment on (1) how quickly fluctuations in temperature redshift away
after reionization processes, (2) how much shock heating occurs in the
low-density intergalactic medium, and (3) how the temperatures of collapsing
gas parcels evolve.
