SPHERICALLY SYMMETRIC, COLD COLLAPSE: The EXACT SOLUTIONS and A COMPARISON with SELF-SIMILAR SOLUTIONS

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1 Scopus citations

Abstract

We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston's solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities - potentially generated by such turbulence - as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.

Original languageEnglish (US)
Article number40
JournalAstrophysical Journal
Volume835
Issue number1
DOIs
StatePublished - Jan 20 2017
Externally publishedYes

Keywords

  • formation
  • gravitation
  • magnetohydrodynamics (MHD)
  • methods: analytical
  • stars: formation

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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