Big Picture

A Bonnor Ebert sphere is just a clump "object" with a Bonnor Ebert density profile. The Bonnor Ebert density profile is coded into astrobear using an approximate analytic solution to the Lane-Emden equation. This function solves for the density contrast of the sphere from center to outer edge, as a function of the non-dimensional radius,xi, where xi is given by:

xi ~=~ (\frac{4 \pi G \rho_c}{C_s^2})^\frac{1}{2}~r

and r is the dimensional radius of the sphere, Cs is the isothermal sound speed of the sphere (function of the temperature), and rho_c is the central density of the sphere. Once the user specifies r, rho_c, and xi for the sphere (see next section), astrobear sets both a) the temperature of the sphere using the above equation, and b) the outer density of the sphere. One can then use the ideal EOS in physics.data with a gamma = 1.0001 to approximate the grid as isothermal. Given P = nKT, the pressure of the sphere then drops away from the center of the sphere with the same gradient as rho.

Now, that (^{) all explains the clump object itself, but there is an additional "object" in the BE problem module that controls the ambient medium in which the clump resides. This ambient object is by default set to have a uniform density, equal to the density at the sphere's outer most edge, rho(Rbe). Additionally, it is also in pressure equilibrium with the sphere. That is, Pamb=P(Rbe). Now, since the simulation is isothermal, this condition means the temperature is discontinuous at the sphere-ambient interface, given by P/n = KT, where n is the number-density of the gas.}

To summarize, the BE sphere is a clump object that is intialized with the BE density profile. It is placed in an ambient medium object. How to control the different parameters of these objects is described next.

Problem.data

The BE module requires the following 3 parameters to set up a BE sphere on the grid:

1. central density of the sphere (central_rho),
2. non-dimensional radius (xi),
3. dimensional radius (clump_rad).

These 3 parameters uniquely and completely specify a sphere in hydrostatic equilibrium as given by the Lane Emden equation (see). They are user-specified in problem.data.

Now, to recap, the BE sphere is actually a clump object. It is completely controlled external to problem.f90 by the input parameters in physics.data that all explains the initiation of the BE sphere, or clump object.

Units