Stability Tests --

Sphere only stable for ~ 1/2 of theoretical expectation. mBE is drastically smaller than mass of sphere... why?

**Update, 8/8/11

I re-did the calculation for mass in the ambient and the sphere. I found the following useful information:

So it seems that using an ambient medium that is 1/10 the density of the outer rim of the sphere is sufficient for smaller xi. As xi increases, the sphere becomes inherently less stable and so the ambient medium must be far less massive than the sphere in order for the sphere to support itself against the weight around it. Initializing the grid with a lighter medium (1/100 of rho outter) leads to a stable sphere. Ideally, the mass in the ambient should go to zero to minimize the effects of material outside the Bonner Ebert sphere. This however would result in higher velocities in the ambient (Cs^2 ~ P/rho) since lower densities there will increase Cs. This will slow simulations. 

I am still looking into the discrepancy between Mbe and the mass function I am using for my sphere...

Also, the change in the density profile should throw the sphere out of perfect hydrostatic equilibrium around the boundary... As seen below, the line out for densities with higher and higher weights flattens at the sphere's boundary, away from the solution. This must have to do with smoothing of the density function in the clumps object. Here is what it looks like for xi= 6.3:

I am curious how these two compare. To convert the top to this graph, I have to alter the radial dimension in Visit by the factor: Lscale*gravo_thermal, where gravo_thermal is a constant that scales r to xi. I could then also divide rho by rho_center and plot that before doing the line-out..