background gas, cooling is turned off whenever the background gas exceeds a volume fraction of 0.5, as measured by the relative amounts of the two tracers initially placed within the cloud and background. Cooling is also not allowed whenever the temperature of a cell exceeds 0.2 times the initial temperature of the background gas.

The models with polytropic equations of state permit the use of dimensionless numbers, as used here, to scale the results to a wide range of systems. The presence of cooling in Model 3, however, introduces some dimensions into the problem. In that model, we take $T_h=10^6$ K, and $T_w=10^4$ K, appropriate, as discussed above, for an L$_\ast$ galaxy. The corresponding sound speeds are $C_h=130$ km s$^{-1}$, and $C_w=13$ km s$^{-1}$ (assuming ionized gas). The initial density of the cloud, $n_w=6$ cm$^{-3}$. A length dimension is not explicitly imposed upon the problem, because the heating and cooling are strictly local processes. Typical values can, however, be computed. For an isothermal potential, $g=V_c^2/R$, where $V_c$ is the circular speed and $R$ is the galactocentric radius. Taking $V_c=220$ km s$^{-1}$, the physical scale height of the gas $$R_h={{C_h^2}\over g}={130\over220}R=350~R_{kpc}{\ \rm pc},$$ where $R_{kpc}$ is the galactocentric radius in kpc. 