Modeling molecular hyperfine line emission
  In this paper we discuss two approximate methods previously suggested for
modeling hyperfine spectral line emission for molecules whose collisional
transitions rates between hyperfine levels are unknown. Hyperfine structure is
seen in the rotational spectra of many commonly observed molecules such as HCN,
HNC, NH3, N2H+, and C17O. The intensities of these spectral lines can be
modeled by numerical techniques such as Lambda-iteration that alternately solve
the equations of statistical equilibrium and the equation of radiative
transfer. However, these calculations require knowledge of both the radiative
and collisional rates for all transitions. For most commonly observed radio
frequency spectral lines, only the net collisional rates between rotational
levels are known. For such cases, two approximate methods have been suggested.
The first method, hyperfine statistical equilibrium (HSE), distributes the
hyperfine level populations according to their statistical weight, but allows
the population of the rotational states to depart from local thermodynamic
equilibrium (LTE). The second method, the proportional method approximates the
collision rates between the hyperfine levels as fractions of the net rotational
rate apportioned according to the statistical degeneracy of the final hyperfine
levels. The second method is able to model non-LTE hyperfine emission. We
compare simulations of N2H+ hyperfine lines made with approximate and more
exact rates and find that satisfactory results are obtained.
