The impact of collisional rate coefficients on molecular hyperfine selective excitation

Abstract

Nuclei with non-zero spin induce hyperfine splittings in the rotational spectrum of many commonly observed interstellar molecules. Radiative transfer modelling of such species requires in general a good knowledge of hyperfine selective collisional rate coefficients. We investigate in this work the impact of collisional rate coefficients on the molecular hyperfine excitation. The approximate sudden and statistical (proportional) methods are first compared to the almost exact recoupling approach. Rate coefficients are presented for a large number of CN and HCN transitions, with para-H2(j = 0) as a collider. The sudden approximation and the recoupling approach, which both predict the propensity rule Δj = ΔF, are found to agree within a factor of 3 or better. Radiative transfer calculations are then performed using the large velocity gradient approximation. At low and moderate total optical depths (τ ≲ 10), where the relative hyperfine populations are close to the statistical weights, both the sudden and the statistical approximations are shown to provide accurate alternatives to the recoupling approach. At higher total opacities, however, the hyperfine propensity rule appears to matter and the sudden method is found to be significantly superior to the statistical approach. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.