Understanding spatially unresolved measurements of molecular line emission

¹ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université Paul Sabatier, Toulouse cedex 4, France
² IRAM, 300 rue de la Piscine, 38406 Saint Martin d’Hères, France
³ LUX, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 75014 Paris, France
⁴ Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-Lab, Grenoble 38000, France
⁵ Univ. Lille, CNRS, Centrale Lille, UMR 9189 – CRIStAL, 59651 Villeneuve d’Ascq, France
⁶ LUX, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁷ Department of Astronomy, University of Florida, PO Box 112055, Gainesville, FL 32611, USA
⁸ Instituto de Física Fundamental (CSIC). Calle Serrano 121, 28006, Madrid, Spain
⁹ Université de Toulon, Aix Marseille Univ, CNRS, IM2NP, Toulon, France
¹⁰ Department of Earth, Environment, and Physics, Worcester State University, Worcester, MA 01602, USA
¹¹ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
¹² Department of Physics, University of Connecticut, Storrs, CT 06269, USA
¹³ Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Allee Geoffroy Saint-Hilaire, 33615 Pessac, France
¹⁴ Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile
¹⁵ Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Sorbonne Paris Cité, Paris, France
¹⁶ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
¹⁷ National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
¹⁸ Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium
¹⁹ School of Physics and Astronomy, Cardiff University, Queen’s buildings, Cardiff CF24 3AA, UK

^★ Corresponding author; azakardjian@irap.omp.eu

Received: 13 June 2024
Accepted: 10 February 2025

Abstract

Context. Observations of molecular emission lines are commonly used to derive the physical properties of cold molecular gas clouds. In external galaxies, these measurements suffer from limited spatial resolution, typically averaging a complex position–position– velocity distribution of emission over several tens of parsecs.

Aims. We aim to quantify the variability in the basic parameters (peak brightness and line width) of spatially unresolved (>20 pc) line profiles that can be attributed to beam averaging. We focus on the commonly observed low-J transitions of CO isotopologues, HCN, HNC, HCO⁺, CS, SO and N₂H⁺.

Methods. We generated a sample of 1000 toy molecular cloud observations by resampling high-resolution (<0.05 pc) multiline Galactic observations of the Orion B molecular cloud. In the construction of our toy clouds, we imposed a range of density and velocity fields, characterised by their statistics and power spectra. These high-resolution molecular cloud observations were then averaged to single spatially unresolved spectra. We examined the resulting distribution of line profile parameters, and searched for potential correlations among line profile parameters and the underlying sub-beam density and velocity fields.

Results. We find that unresolved line profiles’ parameters can vary significantly because of the sub-beam distribution of the emission. Emission lines that tend to be excited at higher densities show the most variability, up to a factor of two for N₂H⁺ (J = 1 0). This variability in an emission line profile is related to the emission line’s covering fraction. As the spectral index of the velocity field increases, unresolved emission lines’ profiles increasingly diverge from a Gaussian shape.

Conclusions. Line profile parameters exhibit non-negligible variability solely due to the sub-beam position-position-velocity distribution of the emission. This variability may exceed calibration and noise-related uncertainties.