update

For a planar HSE atmosphere, with differential equation,

,

the solution is an exponential with given scale height,

where

Assuming the force is given by,

and Matm is the mass of the accumulated atmosphere, gravitationally attracted to the BE sphere through freefall,

(where rff is found by inverting the tff for r for 2 point masses)we get the expression for P = F/A at the surface (after plugging in the variables),

Using this expression gives the following results,

Vertical lines indicate when a sink formed for the corresponding run. The horizontal line is the initial external pressure on the BE sphere, which since the sphere is a critical BE sphere, equals the critical pressure.

We see that as eta = rho(Rbe)/rho(amb) increases (i.e. the ambient gets sparser), it takes longer for the pressure to grow at the surface of the sphere, inducing collapse.

Plotting denser ambient mediums skews the graph, as they increase much more rapidly on the y-axis.

Here is a table of the runs summary,

Things for me to consider:

Is this an adequate description of the problem, does it give good results?

How does box size come into play?

Should we do a different approximation for the dense cases?

Does this explain the qualitative results in the table?

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Comments

1. Jonathan -- 11 years ago

Are you sure Pext and P(t) are in the same units when you add them? I'm surprised that a .1 % change in pressure is enough to cause a particle to form.