A Model for Protostellar Cluster Luminosities and the Impact on the CO-H$_2$ Conversion Factor

TL;DR

This paper develops a semi-analytic model to assess how FUV radiation from embedded protostars influences gas chemistry and the CO-H$_2$ conversion factor, revealing dependence on cluster size and star formation efficiency.

Contribution

It introduces a combined model using the Protostellar Luminosity Function and astrochemistry simulations to quantify FUV effects on $X_{CO}$ in star-forming regions.

Findings

$X_{CO}$ weakly depends on FUV in large clusters due to optical depth.

In smaller, efficient clusters, $X_{CO}$ increases to Milky Way levels.

Cloud structure and chemistry are significantly altered by embedded FUV radiation.

Abstract

We construct a semi-analytic model to study the effect of far-ultraviolet (FUV) radiation on gas chemistry from embedded protostars. We use the Protostellar Luminosity Function (PLF) formalism of Offner & McKee (2011) to calculate the total, FUV, and ionizing cluster luminosity for various protostellar accretion histories and cluster sizes. We compare the model predictions with surveys of Gould Belt star-forming regions and find the Tapered Turbulent Core model matches best the mean luminosities and the spread in the data. We combine the cluster model with the photo-dissociation region astrochemistry code, {\sc 3d-pdr}, to compute the impact of the FUV luminosity from embedded protostars on the CO to H$_2$ conversion factor, $X_{\rm CO}$, as a function of cluster size, gas mass and star formation efficiency. We find that $X_{\rm CO}$ has a weak dependence on the FUV radiation from embedded sources for large clusters due to high cloud optical depths. In smaller and more efficient clusters the embedded FUV increases X$_{\rm CO}$ to levels consistent with the average Milky Way values. The internal physical and chemical structure of the cloud are significantly altered, and $X_{\rm CO}$ depends strongly on the protostellar cluster mass for small efficient clouds.