Gravitational Instability of Shocked Interstellar Gas Layers
Abstract
In this paper we investigate gravitational instability of shocked gas layers using linear analysis. An unperturbed state is a selfgravitating isothermal layer which grows with time by the accretion of gas through shock fronts due to a cloudcloud collision. Since the unperturbed state is not static, and cannot be described by a selfsimilar solution, we numerically solved the perturbation equations and directly integrated them over time. We took account of the distribution of physical quantities across the thickness. Linearized RankineHugoniot relations were imposed at shock fronts as boundary conditions. The following results are found from our unsteady linear analysis: the perturbation initially evolves in oscillatory mode, and begins to grow at a certain epoch. The wavenumber of the fastest growing mode is given by k=2√{2π Gρ_{E} M}/c_{s}, where ρ_{E},c_{s} and M are the density of the parent clouds, the sound velocity and the Mach number of the collision velocity, respectively. For this mode, the transition epoch from oscillatory to growing mode is given by t_{g} = 1.2/√{2π Gρ_{E}M}. The epoch at which the fastest growing mode becomes nonlinear is given by 2.4δ_{0}^{0.1}/√{2π G ρ_{E}M}, where δ_{0} is the initial amplitude of the perturbation of the column density. As an application of our linear analysis, we investigated criteria for collisioninduced fragmentation. Collisioninduced fragmentation will occur only when parent clouds are cold, or α_{0} = 5c_{s}^{2} R/2GM < 1, where R and M are the radius and the mass of parent clouds, respectively.
 Publication:

Publications of the Astronomical Society of Japan
 Pub Date:
 February 2008
 DOI:
 10.1093/pasj/60.1.125
 arXiv:
 arXiv:0802.0917
 Bibcode:
 2008PASJ...60..125I
 Keywords:

 Hydrodynamics;
 Instabilities;
 ISM: clouds;
 Stars: formation;
 Astrophysics
 EPrint:
 12 pages, 21 figures, accepted for publication in PASJ