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 and of r=1.1Rbe. These plots were 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=M(Rbe, t=0).
• 4. M(r) - tracks the total mass within a given radius for r=0.06 to r=1.5Rbe compared to the Mcrit. This plot was designed to track at what radius does the total mass exceed Mcrit.
• 5. Pressure ratios - this is a plot of the ratio of Pthermal/Pram, Ptherm/Pcrit, Pram/Pcrit in a thin shell on top of the BE sphere.

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: