Criticality and convergence in Newtonian collapse

Abstract

We study through numerical simulation the spherical collapse of isothermal gas in Newtonian gravity. We observe a critical behavior which occurs at the threshold of gravitational instability leading to core formation. For a given initial density profile, we find a critical temperature, which is of the same order as the virial temperature of the initial configuration. For the exact critical temperature, the collapse converges to a self-similar form, the first member in Hunter's family of self-similar solutions. For a temperature close to the critical value, the collapse first approaches this critical solution. Later on, in the supercritical case, the collapse converges to another self-similar solution, which is called the Larson-Penston solution. In the subcritical case, the gas bounces and disperses to infinity. We find two scaling laws: one for the collapsed mass in the supercritical case and the other for the maximum density reached before dispersal in the subcritical case. The value of the critical exponent is measured to be $\simeq 0.11$ in the supercritical case, which agrees well with the predicted value $\simeq 0.10567$. These critical properties are quite similar to those observed in the collapse of a radiation fluid in general relativity. We study the response of the system to temperature fluctuation and discuss astrophysical implications for the insterstellar medium structure and for the star formation process. Newtonian critical behavior is important not only because it provides a simple model for general relativity but also because it is relevant for astrophysical systems such as molecular clouds.

15 pages, 8 figures, accepted for publication in PRD, figures 1 and 3 at lower resolution than in journal version, typos corrected

References in corpus (4)

• Physical Processes in Naked Singularity Formation
• Convergence to a self-similar solution in general relativistic gravitational collapse
• Stability criterion for self-similar solutions with perfect fluids in general relativity
• Critical phenomena in Newtonian gravity

Cited by in corpus (10)

• Critical phenomena in gravitational collapse
• Envelope Expansion with Core Collapse. I. Spherical Isothermal Similarity Solutions
• The Similarity Hypothesis in General Relativity
• Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity
• Spherical Isothermal Self-Similar Shock Flows
• Envelope Expansion with Core Collapse II. Quasi-Spherical Self-Similar Solutions for an Isothermal Magnetofluid
• Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions
• Self-similar motion of a Nambu-Goto string
• Power-laws from critical gravitational collapse: The mass distribution of subsolar objects
• Universality of the subsolar mass distribution from critical gravitational collapse