| 30 | | The same wave of inward moving material is seen in each of these plots, except that the sphere in the lighter medium is more resilient to allowing the wave to pass through the boundary, whereas in the matched case there seems to be no boundary and the wave passes freely through Rbe. Thus it seems that in the light ambient case, while there is inward moving material, there is little momentum being imparted to the sphere's boundary and thus, the velocity of the material inside doesn't acquire the shape of the velocity outside of the sphere. The inward moving material in the matched case must have a greater momentum, allowing the flow of energy to enter into the sphere resulting in a continuous wave across the boundary. |
| | 30 | The same wave of inward moving material is seen in each of these plots, except that the sphere in the lighter medium is more resilient to allowing the wave to pass through the boundary, whereas in the matched case there seems to be no boundary and the wave passes freely through Rbe. Thus it seems that in the light ambient case, while there is inward moving material, there is little momentum being imparted to the sphere's boundary and so, the velocity of the material inside doesn't acquire the general shape of the velocity curve outside of the sphere. The inward moving material in the matched case must have a greater momentum, allowing the flow of energy to enter into the sphere resulting in a continuous wave across the boundary. |
| 36 | | It is interesting to compare these plots to those of a similar collapse study in which the critical BE sphere in a light medium (same density and homogeneity as in the light ambient of this study) was triggered to collapse with a density enhancement above equilibrium values [https://clover.pas.rochester.edu/trac/astrobear/wiki/u/BonnorEbert#Collapse (click here)]. |
| | 36 | In the light ambient case, there is no shell of infalling matter building up on the boundary of the BE sphere. However, the density profile inside of the sphere is decreasing uniformly with time as it is "breathing" around its equilibrium values. Over time, these curves would increase back up to initial values. |
| | 37 | |
| | 38 | In contrast, the matched ambient case shows a definite build up of material at the boundary, and by t=3.07 myrs, the sphere is no longer a BE sphere, with a density profile that markedly differs from the earlier density profiles. Additionally, while density is increasing at the boundary, it is not simply piling up at the sphere's initial surface (Rbe), rather material has caused the sphere to contract, building up further inside Rbe as t progresses. |
| | 39 | |
| | 40 | By t=tc~2.3 myr, my [https://clover.pas.rochester.edu/trac/astrobear/attachment/wiki/u/BonnorEbertMatched/ApproxSphereWriteUp.pdf calculations] predicted a density to be of order rho~2.3x10^-21^g/cm^3^. This is |
| | 41 | |
| | 42 | It is interesting to compare these plots to those of a similar collapse study in which the critical BE sphere in a light medium (same density and homogeneity as in the light ambient of this study) was triggered to collapse with a density enhancement above equilibrium values [https://clover.pas.rochester.edu/trac/astrobear/wiki/u/BonnorEbert#Collapse (click here)] -- <<put a comparison between the times seen in these plots and the times seen there>>. |
