We present models for temperature and ionization structure of low, uniform-density (n ~ 0.3 cm^-3) interstellar gas in a galactic disk which is exposed to soft X-rays from supernova outbursts occurring randomly in space and time. The structure was calculated by computing the time record of temperature and ionization at a given point by Monte Carlo simulation. The calculation yields probability distribution functions for ionized fraction x, temperature T, and their various observable moments. These time-dependent models predict a bimodal temperature distribution of the gas with structure in x, T that agrees with various observations. Cold regions in the low-density gas may have the appearance of clouds in 21-cm absorption. The time-dependent model, in contrast to the steady-state model, predicts large fluctuations in ionization rate and the existence of cold (T ~ 30° K), ionized (x ~ 0.1) regions.
Gerola, H., Kafatos, M., McCray, R. (1974) Statistical Time-Dependent Model for the Interstellar Gas, Astrophysical Journal, 189: 55-66. doi: 10.1086/152768