This post adresses two questions: Are the simulations converged for mass evolution? How does the initial density contrast affect the mass evolution?
I attempt to answer the first question with the following plot, which shows the mass evolution as a function of cloud crushing time for the sphere simulation at 3 different resolutions: 16, 32, and 64 cells / . The mass fraction is calculated as the amount of material above a given density threshold (in this case ) as compared to the intial mass of the cloud.
From this plot, I don’t know if we’re converged. The lines certainly aren’t lying on top of one another, nor are they approaching a common solution.
I can make the same plot using different density thresholds to measure the cloud mass, but that doesn’t change the convergence much. In the plot above, the solid line represents a threshold of 1/20th the initial cloud density, while the dashed and dot-dash lines represent 1/10th and 1/3rd, respectively.
To address the second question, I plot below the mass evolution for simulations with different intial density contrasts.
As expected, the evolution of the sphere falls between the and cases. Watching a movie of the simulation (here), we see that the cloud cools more effectively than the cloud, but it loses significantly more of its initial mass than the case. To me, it looks like about half the cloud follows the adiabatic track, as indicated by the initial steep dropoff a , and the other half gets dense enough to cool and follow the radiative track.