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Description
In this paper, we discuss two approximate methods previously suggested for modeling hyperfine spectral line emission for molecules whose collisional transition rates between hyperfine levels are unknown. Hyperfine structure is seen in the rotational spectra of many commonly observed molecules such as HCN, HNC, NH_3_, N_2_H^+^, and C^17^O. 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, distributes the hyperfine level populations according to their statistical weight, but allows the population of the rotational states to depart from local thermal equilibrium (LTE). The second method, the proportional method, approximates the collision rates between the hyperfine levels as fractions of the net rotational rates 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 N_2_H^+^ hyperfine lines made with approximate and more exact rates and find that satisfactory results are obtained.
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