Studying the gravitational potential of the BE sphere/ambient system

What should the global gravitational potential, phi, of the BE sphere/ambient system look like in a) a "light" ambient medium and b) a "matched" ambient medium?

To answer this question, first some preliminaries:

1) How massive is the critical BE sphere in my simulations compared to the ambient medium?

• A) The BE sphere is 150 solar masses. The mass of the ambient medium then is given by the equation:

4\over3