Modeling molecular hyperfine line emission

TL;DR

This paper evaluates two approximate methods for modeling hyperfine spectral line emission in molecules, enabling more practical simulations when detailed collisional data are unavailable, and compares their effectiveness against exact calculations.

Contribution

It introduces and compares two approximate methods, HSE and the proportional method, for modeling hyperfine line emission without detailed collisional rates.

Findings

The proportional method can model non-LTE hyperfine emission effectively.

Simulations of N2H+ hyperfine lines show satisfactory results with approximate methods.

The methods provide practical alternatives when detailed collisional data are missing.

Abstract

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.