Observing the effects of different background media on the critical Bonnor Ebert sphere

This page describes the effects of placing a marginally stable Bonnor Ebert sphere in different ambient mediums. 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, resulting in collapse. The sphere in the light ambient medium, however, remained dynamically stable, oscillating slowly about its equilibrium values for ~ 5 crossing times.

Parameters:

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Computational Scales:

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Approximations

I have made a pdf of my calculations on the expected density and ram pressure at Rbe. Please see the attached pdf ​here. The results I have found were namely a predicted density at r=Rbe, rho(Rbe) = 2.315*10^-21 g/cm³, and ram pressure Pram(Rbe)= 5.52 (CU- computational units). The free fall time associated with the approximated uniform sphere was found to be tff=3.4 myrs.

Results:

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~0.06). 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 2.3<tc<3 myr, ~ 67%<tff<88% (see below calculation in approximations section).

Radial Velocity-

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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.

Density-

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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 ​(click here).

Thermal Pressure-

The horizontal line in the following plots is the value of Pcrit, where Pcrit~1.14 Cs⁸/G³*M² 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.

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Ram Pressure-

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Movies

Left panel is sphere in the light ambient, right is the matched ambient.

Mesh-

The movies shown below are just of the time frames up until the collapse in the matched case became poorly resolved. To see extended version of the sphere in the light ambient, follow the link below.

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Density-

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The BE sphere in the light ambient was stable for 5 crossing times, to see a longer clip see ​here.

Discussion

-size differences, computational difficulties, etc. -​here