Bondi accretion module mods

I'll be implementing two changes to the Bondi Accretion module. The first will be a flag which will force sink particles to only accrete the *radial* momentum of gas (see previous blog post for motivation). The second is a check that the accretion volume does not contain any cells that violate the Jeans condition following Bondi accretion. If so, the excess gas will be removed.

Radial momentum accretion fix: description and equations

Here is a diagram defining the relevant variables. Note, in what follows primes (') will denote accreted quantities.

The momentum vector of each cell in the accretion volume is decomposed into its radial and transverse components (relative to the location of the sink particle):

Following accretion, only the radial component of the momentum will be accreted:

where

and

(i.e. fm = the fraction of mass to be left in the cell following accretion; the radial momentum will be accreted proportionally to mass).

Subtracting the first two equations gives us an equation for the update of the momentum vector:

which in cartesian coordinates is:

This last equation gives the accreted momentum in each cell within the accretion volume, for the case of radial momentum accretion.

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