Understanding spatially unresolved measurements of molecular line emission

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 N_{2H+.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.}}