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Here is a link to the pdf ApJ pre-print here

## Abstract

This paper describes a series of 3D hydrodynamic simulations that explored the effects of placing a marginally stable Bonnor Ebert sphere in different ambient media. Various uniform density media were initialized that were in pressure equilibrium with the Bonnor Ebert sphere. These densities ranged from a traditional light ambient (rho=0.01rho(Rbe)) to an ambient with density that matched that at the sphere’s outermost edge (rho=rho(Rbe)). The main aims were to a) discern whether a massive ambient medium would be sufficient to induce collapse of the sphere, b) whether this collapse would be triggered by the ram pressure of infalling ambient material gravitationally accelerated by the BE sphere, and c) how this collapse would compare with the classic cases of outside-in and inside-out collapse of previous models. [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. These results are qualitatively different than those found previously by authors such as who found a very nice outside-in collapse.

## Introduction

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.

While the collapse of a BE sphere has been studied extensively over the years, the literature reveals studies of the BE sphere in precarious and unphysical conditions. The BE sphere has largely been modeled as residing in low density ambient mediums (cite), seemingly to isolate the collapse of the sphere from the ambient environment. In this way, previous models have been physically unrealistic; any actual collapsing cloud of gas would not be discontinuous from the ambient medium. However, modeling the cloud in this way did reveal a feature of the collapse that was unexpected.

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.

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).

Now, although these early models illuminated unique and unexpected features of the BE collapse, they were physically unrealistic given the discontinuous jump in density across the BE sphere/ambient boundary. If the BE sphere might be considered as a initial structure of star formation, it should be examined in a more physically plausible setting. Such a simulation would more accurately describe astrophysical situations that resemble collapsing hydrostatic structures.

Preliminary studies that have begun to address this need were supplied by:. In this one, that, and in that one, that. But the field has not been studied simply enough. A

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- BEsphere.2.tex (14.9 KB ) - added by 12 years ago.
- BEsphere.3.tex (22.0 KB ) - added by 12 years ago.
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- BEsphere.pdf (2.5 MB ) - added by 12 years ago.

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