Meeting update

Here is the working paper figure for the pressure approximation,

As you can see, 1/10 case (light blue line - accidentally not on legend) is no longer a valid approximation with this method. This makes sense when we consider the Jeans length of the ambient — the ambient is Jeans unstable, and so the ambient in this case collapses more like a uniform sphere. When I do a similar approximation for the pressure, only using the solutions given by uniform collapse, I get this,

From this plot, we see the same value of the 1/10 case as in the previous approximation, which seems to indicate this is some boundary case between the dense and light approximations — ambients equal and denser than 1/10 are better approximated by the uniform collapse. We also see the same grouping up of the lighter cases that we do in the sparse approximation, but they are grouped up around a different value. This indicates that the trend is robust — settling of the atmosphere leads to some external pressure threshold needed to induce collapse.

Here is a wiki page on the 2 different approximation methods I used to make these plots -

​http://astrobear.pas.rochester.edu/trac/astrobear/wiki/u/SurfacePressureApprox

In running out the 1/100 case longer, did not get collapse. This may have to do with the scale height for this case extending beyond the box..?

I added the sparse approximation description to the paper, and worked on finishing up the appendices on self-gravity. Here is a completed paper draft,

​http://www.pas.rochester.edu/~erica/BEsphere_EK_09.20.13.pdf

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