Impact of nonconvergence and various approximations of the partition function on the molecular column densities in the interstellar medium

TL;DR

This paper investigates how different approximations of the partition function impact the accuracy of molecular column density estimates in interstellar medium observations, emphasizing the importance of using a converged partition function.

Contribution

It demonstrates the significant effect of various partition function approximations on molecular density calculations in astronomical data analysis.

Findings

Partition function approximation causes 9-43% variation in column densities.

Using a converged partition function reduces uncertainty in molecular density estimates.

The study applies the analysis to observations of N-bearing molecules in NGC7538-IRS1.

Abstract

We emphasize that the completeness of the partition function, that is, the use of a converged partition function at the typical temperature range of the survey, is very important to decrease the uncertainty on this quantity and thus to derive reliable interstellar molecular densities. In that context, we show how the use of different approximations for the rovibrational partition function together with some interpolation and/or extrapolation procedures may affect the estimate of the interstellar molecular column density. For that purpose, we apply the partition function calculations to astronomical observations performed with the IRAM-30m telescope towards the NGC7538-IRS1 source of two N-bearing molecules: isocyanic acid (HNCO, a quasilinear molecule) and methyl cyanide (CH$_3$CN, a symmetric top molecule). The case of methyl formate (HCOOCH$_3$), which is an asymmetric top O-bearing molecule containing an internal rotor is also discussed. Our analysis shows that the use of different partition function approximations leads to relative differences in the resulting column densities in the range 9 to 43\%. Thus, we expect this work to be relevant for surveys of sources with temperatures higher than 300~K and to observations in the infrared.