Changes between Version 40 and Version 41 of u/BonnorEbertMatched
- Timestamp:
- 06/18/12 14:05:37 (12 years ago)
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u/BonnorEbertMatched
v40 v41 38 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 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 is40 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^. While this is off by ~ 2, it also should be noted that my calculation was considering a shell of mass piling up at the initial Rbe. Since by 2.3 myrs, material has passed within the initial Rbe, my calculation would presumably be larger than observed here. 41 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>>. 42 It may be 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>>. 43 44 '''Pressure Plots''' 45 46 The horizontal line in the following plots is the value of Pcrit, where Pcrit~1.14 Cs^8^/G^3^*M^2^ and characterizes the maximum external pressure a critical BE sphere can withstand before collapsing. Note that both the thermal and ram pressure at the Bonnor Ebert surface, Rbe, is BELOW the threshold under light ambient medium conditions, whereas in the "matched" ambient medium case both of these pressures EXCEED the threshold. 43 47 44 48 '''''Thermal Pressure-''''' 45 49 46 The horizontal line in the following plots is the value of Pcrit, where Pcrit~1.14 Cs^8^/G^3^*M^2^ and characterizes the maximum external pressure a critical BE sphere can withstand before collapsing. Note that both the thermal and ram pressure at the Bonnor Ebert surface, Rbe, is BELOW the threshold under light ambient medium conditions, whereas in the "matched" ambient medium case both of these pressures EXCEED the threshold.47 50 48 51 :[[Image(ThermalP.png, 40%)]] [[Image(thermalPM.png, 36%)]] 52 53 As the EOS used was effectively isothermal, the curves here are of the same shape as the density curves above. The x-axis is scaled as in the above plots, however, the y-axis is in computational units (CU's). To put into scaled units, one can multiply y-values by Pscale in the table above in the Scales section. 54 55 Of interest here is that in the light ambient case, the pressure at the sphere's edge (RBE), never exceeds Pcrit, which lies along the external pressure of the ambient material. However, as soon as the density exceeds equilibrium values as shown in above plot and proportional to these curves here, Pthermal>Pcrit. Thus the BE sphere is very early on UNSTABLE to collapse. 49 56 50 57 '''''Ram Pressure-''''' 51 58 52 59 :[[Image(RamP.png, 40%)]] [[Image(ramPM.2.png, 42%)]] 60 61 The ram pressure in the light ambient case does not build up outside of the sphere at all, which is in accordance with the above statement that the material in the ambient, while moving inward, is carrying no momentum. Inside the ram pressure is fluctuating in a manner that coincides with the radial velocity and density plots in this region. At all times, the ram pressure is well below the critical value. 62 63 In the matched ambient case, however, Pram>Pcrit only after t~2.3 myrs. By t =3 myrs, the Pram profile has taken on a very unique cowboy hat appearance. 53 64 54 65 … … 72 83 '''Discussion''' 73 84 85 -The ram pressure does not seem to be as dominant a factor in inducing collapse, rather the thermal pressure almost immediately exceeds Pcrit.. Thus it may be better to approximate tc as much earlier on. 74 86 -size differences, computational difficulties, etc. 75 87 -[https://clover.pas.rochester.edu/trac/astrobear/wiki/u/BEmoviesLonger here]
