Shell instability of a collapsing dense core

¹ Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp – CNRS – Université Paris Diderot, 91191 Gif-sur-Yvette Cedex, France
e-mail: eva.ntormousi@cea.fr
² LERMA, UMR CNRS 8112, École Normale Supérieure, 75231 Paris Cedex, France

Received: 29 July 2014
Accepted: 7 November 2014

Abstract

Aims. Understanding the formation of binary and multiple stellar systems largely comes down to studying the circumstances under which a condensing core fragments (or not) during the first stages of the collapse. However, both the probability of fragmentation and the number of fragments seem to be determined to a large degree by the initial conditions. In this work we explore this dependence by studying the fate of the linear perturbations of a homogeneous gas sphere, both analytically and numerically.

Methods. In particular, we investigate the stability of the well-known homologous solution that describes the collapse of a uniform spherical cloud. One problem that arises in such treatments is the mathematical singularity in the perturbation equations, which corresponds to the location of the sonic point of the flow. This difficulty is surpassed here by explicitly introducing a weak shock next to the sonic point as a natural way of connecting the subsonic to the supersonic regimes. In parallel, we perform adaptive mesh refinement (AMR) numerical simulations of the linear stages of the collapse and compare the growth rates obtained by each method.

Results. With this combination of analytical and numerical tools, we explore the behavior of both axisymmetric and non-axisymmetric perturbations. The numerical experiments provide the linear growth rates as a function of the core’s initial virial parameter and as a function of the azimuthal wave number of the perturbation. The overlapping regime of the numerical experiments and the analytical predictions is the situation of a cold and large cloud, and in this regime the analytically calculated growth rates agree very well with the ones obtained from the simulations.

Conclusions. The use of a weak shock as part of the perturbation allows us to find physically acceptable solutions to the equations for a continuous range of growth rates. The numerical simulations agree very well with the analytical prediction for the most unstable cores, while they impose a limit of a virial parameter of 0.1 for core fragmentation in the absence of rotation.