A Probabilistic Model to Estimate Number Densities from Column Densities in Molecular Clouds

Abstract: Constraining the physical and chemical evolution of molecular clouds is essential to our understanding of star formation. These investigations often necessitate knowledge of some local representative number density of the gas along the line of sight. However, constraining the number density is a difficult endeavor. Robust constraints of the number density often require line observations of specific molecules along with radiation transfer modeling, which provides densities traced by that specific molecule. Column density maps of molecular clouds are more readily available, with many high-fidelity maps calculated from dust emission and extinction, in particular from surveys conducted with the Herschel Space Observatory. We introduce a new probabilistic model which is based on the assumption that the total hydrogen nuclei column density along a line of sight can be decomposed into a turbulent component and a gravitationally-dominated component. Therefore, for each pixel in a column density map, the line of sight is decomposed into characteristic diffuse (dubbed turbulent'') and dense (dubbedgravitational'') gas number densities from column density maps. The method thus exploits a physical model of turbulence to decouple the random turbulent column from gas in dense bound structures empirically using the observed column density maps. We find the model produces reasonable turbulent and gravitational densities in the Taurus L1495/B213 and Polaris Flare clouds. The model can also be used to infer an effective attenuating column density into the cloud, which is useful for astrochemical models of the clouds. We conclude by demonstrating an application of this method by predicting the emission of the [C II], [C I], and CO (J = 1-0) lines across the Taurus L1495/B213 region at the native resolution of the column density map utilizing a grid of photodissociation-region models.