Changes between Version 50 and Version 51 of u/BonnorEbertMatched
- Timestamp:
- 06/19/12 11:45:58 (12 years ago)
Legend:
- Unmodified
- Added
- Removed
- Modified
-
u/BonnorEbertMatched
v50 v51 1 '''Observing the effects of different background media on the critical Bonnor Ebert sphere''' 2 3 4 1 5 [[PageOutline]] 2 6 3 '''Observing the effects of different background media on the critical Bonnor Ebert sphere''' 7 8 9 4 10 5 11 This page describes the effects of placing a marginally stable Bonnor Ebert sphere in different ambient media. Two ambient mediums and their effects on BE spheres were measured - a) a uniform light ambient medium (rho=rho(Rbe)/100), and b) an ambient medium with density that matches the density at the sphere's outer edge (rho=rho(Rbe)). The aim was to see if the effect of the "matched" ambient would be induced collapse of the sphere, triggered by the ram pressure of the infalling ambient material gravitationally accelerated by the BE sphere. The ram pressure was calculated at the sphere's outer edge and indeed exceeded the critical threshold of external pressure on the BE sphere. However, Pram>Pcrit long after Pthermal>Pcrit, thus it seems the increase in thermal pressure was the primary trigger for collapse. In contrast, the sphere in the light ambient medium remained dynamically stable, oscillating slowly about its equilibrium values for ~ 5 crossing times. 6 12 7 13 8 '''Parameters:'''14 === Parameters:''' 9 15 10 16 11 17 :[[Image(lightparams.png, 27%)]], :[[Image(domainParamsMatched.png, 28%)]] 12 18 13 '''Computational Scales:''' 19 === Computational Scales:=== 14 20 15 21 :[[Image(sCALESmatched.png, 23%)]] 16 22 17 23 18 '''Approximations'''24 === Approximations''' 19 25 20 26 … … 22 28 23 29 24 '''Results:'''30 === Results:''' 25 31 26 32 Note the line marking 'dx' denotes the size of the smallest cells in the grid, those within the BE sphere's center most regions (dx~0.1 pc). The cells outside a radius of 150% Rbe (radius of BE sphere), however, made up the coarsest level grid (see below movies of the mesh) and had dx~1.62 pc for smaller grid and dx~3 pc for larger grid. The last time frame of data included in these plots and the movies below is the time before the collapse was no longer resolved adequately with the refinement criteria used. Since the aim of this study was to look at the initialization of the collapse, the refinement used here was sufficient. The time in which the sphere's Pram(Rbe) > Pcrit was between 2.3<tc<3 myr, ~ 67%<tff<88% (see calculation in approximations section). 27 33 28 '''''Radial Velocity-'''''34 ==== Radial Velocity-''''' 29 35 30 36 :[[Image(vrad.png, 37%)]] [[Image(VradM.png, 40%)]] … … 32 38 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. 33 39 34 '''''Density-'''''40 ==== Density-''''' 35 41 36 42 :[[Image(rho.png, 36%)]] [[Image(rhoM.png, 36%)]] … … 48 54 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. 49 55 50 '''''Thermal Pressure-'''''56 ==== Thermal Pressure-''''' 51 57 52 58 … … 57 63 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. 58 64 59 '''''Ram Pressure-'''''65 ==== Ram Pressure-''''' 60 66 61 67 :[[Image(RamP.png, 40%)]] [[Image(ramPM.2.png, 42%)]] … … 66 72 67 73 68 '''Discussion'''74 === Discussion''' 69 75 70 76 -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. … … 76 82 77 83 78 '''Movies'''84 === Movies''' 79 85 80 86 Left panel is sphere in the light ambient, right is the matched ambient.
