I successfully fit the Sternberg model to the vs. relationship. I assumed that our case is a two-sided irradiation by an isotropic field, where they predict an threshold given by

where the variables are described in the previous post.

I am fitting the / ratio as a function of total gas surface density, = where and are the and gas fraction to the total. I solve for as a function of with

Below are the fits to Taurus cores. Where only the and parameters were allowed to vary in the Sternberg+14 and Krumholz+09 models, respectively. A metallicity of was assumed. I also assumed for the S+14 model, and for the K+09 model.

Below are Taurus fits. Find the locations of the cores in this post

Below are Perseus fits