Critical phenomena in Newtonian gravity

Hideki Maeda and Tomohiro Harada
Phys. Rev. D 64, 124024 – Published 28 November 2001
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Abstract

We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse solution has an analytic unstable mode. Since the homogeneous collapse solution is known to suffer the kink instability, the present result and recent numerical simulations strongly support a proposition that the Larson-Penston solution will be realized in astrophysical situations. It is also found that the Hunter (A) solution has a single unstable mode, which implies that it is a critical solution associated with some critical phenomena which are analogous to those in general relativity. The critical exponent γ is calculated as γ0.10567. In contrast with the general relativistic case, the order parameter will be the collapsed mass. In order to obtain a complete picture of the Newtonian critical phenomena, full numerical simulations will be needed.

  • Received 1 August 2001

DOI:https://doi.org/10.1103/PhysRevD.64.124024

©2001 American Physical Society

Authors & Affiliations

Hideki Maeda* and Tomohiro Harada

  • Department of Physics, Waseda University, Shinjuku, Tokyo 169-8555, Japan

  • *Electronic address: hideki@gravity.phys.waseda.ac.jp
  • Electronic address: harada@gravity.phys.waseda.ac.jp

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Issue

Vol. 64, Iss. 12 — 15 December 2001

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