Plots:

Each run was carried out until a sink particle formed (except the Light ambient case, for which the run was carried out for 5 crossing times to check stability during which time no sink particle was formed). The plots for q(r) then sampled 5 evenly spaced times during the simulation between t=0 and t=tfinal, where tfinal was the time when a sink particle formed.

• 1. rho - the average number density over successive shells inside the BE sphere out to r=1.5Rbe.
• 2. vrad - the average radial velocity over successive shells inside the BE sphere out to r=1.5 Rbe, normalized to the local sound speed.
• 3. M(t) - 2 plots showing the Total_Mass(t) for a) a thin shell on top of the BE sphere of thickness dr=0.1Rbe (this is ~ 3 cells wide in the mesh), b) a sphere of r=Rbe, c) a sphere of r=1.1Rbe. This plot was designed to track the amount of mass falling on top of the BE sphere, and compare it to the critical mass of the initial BE sphere, Mcrit. Mcrit=M(Rbe, t=0).
• 4. M(r)

Stability Case:

BP Case:

Matched Case:

3 Intermediate cases, log spaced between the Matched and Light cases:

rho_ambient = rho(Rbe)/3.162:

rho_ambient = rho(Rbe)/10:

rho_ambient = rho(Rbe)/31.62: