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 H2 conversion factor, XCO, as a function of cluster size, gas mass and star formation efficiency. We find that XCO 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 XCO to levels consistent with the average Milky Way values. The internal physical and chemical structure of the cloud are significantly altered, and XCO depends strongly on the protostellar cluster mass for small efficient clouds.
@article{arxiv.1801.08555,
title = {A Model for Protostellar Cluster Luminosities and the Impact on the CO-H$_2$ Conversion Factor},
author = {Brandt A. L. Gaches and Stella S. R. Offner},
journal= {arXiv preprint arXiv:1801.08555},
year = {2018}
}