1. Sink particles ● Introduce sink particles whenever the density in a cell violates the Jeans criterion or and set the mass of the sink particle to: so that the host cell is left with gas density

2. Accretion rate ● If the particle's Bondi-Hoyle radius is much greater than the cell spacing... then the flow is supersonic and the exact pressure determined by the accretion rate is not very important. Mass will continue to flow in and create sink particles that will merge. ● If the particle's Bondi-Hoyle radius is smaller than the cell spacing, then pressure is the dominant force on the scales of interest and one has the classical Bondi-Hoyle-Lyttleton problem with an approximate accretion rate given by: where and are based on the host cell's temperature and relative velocity and is based on an analytic solution to Bondi accretion using a weighted mean density for the accretion region. where and

3. Angular Momentum ● We then set the amount of material accreted from each cell as ● The actual amount of mass accreted from each cell is then modified by calculating the fraction of each cell whose distance of closest approach ● The accreted mass from each cell takes with it a corresponding fraction of the cell's radial momentum and internal energy, leaving the transverse momentum behind.

4. Particle-gas gravitational interactions ● The self-gravity of the gas is calculated as usual, while the gas/particle(s) interactions are done by summing the pairwise gravitational force between each cell and each sink particle with a softening length of ● The particle-particle interactions are also calculated pairwise, however there is no softening length and the integration is done by a higher order method.

5. Basic Flow chart ● For all levels: – Hydro step w/ poisson solve – Source term update of gas and existing sink particles using N-body type calculation with softening length. Accumulate forces for each particle where the cell has no children. – Set flags based on Jean's criteria ● At the finest level – Update of sink particle locations from inter-particle interactions – Find new sink particles – Get grid data around each sink particle – Update grids around sink particles using accretion rate etc... – Use friend of friend to merge sink particles – Set error flags around existing sink particles ● repeat/restrict etc...