Update

Hypotheses,

  1. As the box becomes more and more jeans stable (i.e., the density is low enough that the major forces acting on the particles in the ambient is the gravitational acceleration by the sphere - i.e. Bondi flow), for a fixed volume of the ambient the sphere will go unstable on a timescale given by the bondi flow (such that an appreciable amount of matter has been accreted by sphere). In order to test this, need a time scale for which the sphere goes unstable (how to define this?). Then, compare to simulations. For this limit, the amount of mass in the box is also a strong factor in stability of the sphere, so varying the box volume changes the stability of the sphere.
  1. As the box becomes more jeans unstable (i.e., density is high enough that the box is well approximated by a uniform sphere and collapses as such), the amount of mass in the box, over some length scale, becomes less important given the ambient collapses on its own. This case leads to strong compression waves on the sphere.

Questions to address

What is the appropriate 'collapse time' of a BE sphere? A's - 1) time it takes for the BP case to collapse to sink, 2) Average free-fall time, 3) dynamical time

Is the collapse time a constant? That is, once the BE sphere goes unstable, does it always collapse in the same amount of time?

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