The validity of 21 cm spin temperature as a kinetic temperature indicator in atomic and molecular gas

The gas kinetic temperature ($T_K$) of various interstellar environments is often inferred from observations that can deduce level populations of atoms, ions, or molecules using spectral line observations; H I 21 cm is perhaps the most widely used with a long history. Usually the H I 21 cm line is assumed to be in thermal equilibrium and the populations are given by the Boltzmann distribution. A variety of processes, many involving Lyman alpha ($Ly\alpha$), can affect the 21 cm line. Here we show how this is treated in the spectral simulation code Cloudy, and present numerical simulations of environments where this temperature indicator is used, with a detailed treatment of the physical processes that determine level populations within $H^0$. We discuss situations where this temperature indicator traces $T_K$, cases where they fail, as well as the effects of $Ly\alpha$ pumping on the 21 cm spin temperature. We also show that the $Ly\alpha$ excitation temperature rarely traces the gas kinetic temperature.