| 3 | | Various properties of the “Bonnor-Ebert” (BE) sphere, a hydrostatic sphere in pressure equilibrium with its ambient environment, make it a good candidate for numerical modeling of protostellar collapse. First, as a candidate star forming structure is envisaged as gravitationally bound and unstable, it is easy to imagine a protostar evolving from an initially hydrostatic configuration. Indeed, spherical clumps have been observed in or near hydrostatic equilibrium, such as the Bok Globule, B68 (Myers). Second, the stability criterion against gravitational collapse has been worked out analytically. Third, pushing the sphere out of the stability regime with various physical perturbations illuminate collapse characteristics. Such features of the collapse may help advance single star formation theory as well as provide clues to observational astronomers in identifying potential star forming sites. |
| | 3 | Various properties of the “Bonnor-Ebert” (BE) sphere, a hydrostatic sphere in pressure equilibrium with its ambient environment, make it a good candidate for numerical modeling of protostellar collapse. First, as a candidate star forming structure is envisaged as gravitationally bound and unstable, it is easy to imagine a protostar evolving from an initially hydrostatic configuration. Indeed, spherical clumps have been observed in or near hydrostatic equilibrium, such as the Bok Globule, B68 (Myers). Second, the stability criterion against gravitational collapse has been worked out analytically. Third, pushing the sphere out of the stability regime with various physical perturbations illuminate collapse characteristics. Such features of the collapse may help advance single star formation theory as well as provide clues to observational astronomers in identifying potential star forming sites. |
| 7 | | Shu’s model, the other models, F&C even went far with the different xis - still no inside out. But while this was helpful, the next step needed to be taken. (And were taken - review Myers and Hannabelle) That was the aim of this paper. We have found that the collapse acquires a “crushing solution”, in the matched ambient limit. In contrast, when the limit of light ambient material (on the order of previous studies) was approached, the outside-in collapse was recovered. The difference in these collapses can be understood in terms of an accretion time -scale. In a light ambient, the material accretes, and the sphere re-equilibrates, until it can’t hold itself up anymore under the “weight”. In a higher density ambient, the accretion time is < equilibration time, so the sphere doesn’t have time to equilibrate. Thus the sphere succumbs to a compression induced collapse. |
| | 7 | The collapse of a BE sphere was originally anticipated to be an inside-out process, a characteristic feature of Frank Shu’s similarity solution for the Singular Isothermal Sphere (SIS). In his (1977) pivotal paper, Shu speculated that the collapse of any hydrostatic isothermal sphere, including Bonnor Ebert spheres, would approach the SIS through a subsonic adjustment to 1/r^2 density distribution. The classic inside-out collapse of the SIS was then, as Shu proposed, a general feature of collapse, applicable to any hydrostatic isothermal sphere, unstable or not. |
| | 8 | Simulations of stable, flat-topped BE spheres in low density ambient environments, however, proved the contrary. In 1994 Foster and Chevalier explored the collapse of BE spheres of varying truncation radii embedded in ambient backgrounds of uniform rho = 0.01 rho(RBE), where Rbe is the BE sphere’s truncation radius. Their set ups showed that despite initial perturbation methods, as well as whether the sphere was initially in a stable or unstable hydrostatic regime, the collapse proceeded much differently than the SIS. Instead of an inside-out collapse, the collapse of a flat-topped BE sphere was outside-in. Further, the collapse was not subsonic, rather supersonic. This directly refuted Shu’s proposal that the collapse is generally inside-out. (note - the sink formation in the flat-topped studies may more closely resemble the collapse of the SIS... perhaps this is what he was talking about?). Studies of the collapse with more sophisticated fluid dynamic codes have provided further support of outside-in collapse of the BE sphere (B&P). |
