Fragmentation of a dynamically condensing radiative layer

In this paper, the stability of a dynamically condensing radiative gas layer is investigated by linear analysis. Our own time-dependent, self-similar solutions describing a dynamical condensing radiative gas layer are used as an unperturbed state. We consider perturbations that are both perpendicular and parallel to the direction of condensation. The transverse wave number of the perturbation is defined by $k$. For $k=0$, it is found that the condensing gas layer is unstable. However, the growth rate is too low to become nonlinear during dynamical condensation. For $k\ne0$, in general, perturbation equations for constant wave number cannot be reduced to an eigenvalue problem due to the unsteady unperturbed state. Therefore, direct numerical integration of the perturbation equations is performed. For comparison, an eigenvalue problem neglecting the time evolution of the unperturbed state is also solved and both results agree well. The gas layer is unstable for all wave numbers, and the growth rate depends a little on wave number. The behaviour of the perturbation is specified by $kL_\mathrm{cool}$ at the centre, where the cooling length, $L_\mathrm{cool}$, represents the length that a sound wave can travel during the cooling time. For $kL_\mathrm{cool}\gg1$, the perturbation grows isobarically. For $kL_\mathrm{cool}\ll1$, the perturbation grows because each part has a different collapse time without interaction. Since the growth rate is sufficiently high, it is not long before the perturbations become nonlinear during the dynamical condensation. Therefore, according to the linear analysis, the cooling layer is expected to split into fragments with various scales.Comment: 12 pages, 10 figures, accepted for publication in Astronomy & Astrophysic

Self-Sustained Turbulence without Dynamical Forcing: A Two-Dimensional Study of a Bistable Interstellar Medium

In this paper, the nonlinear evolution of a bistable interstellar medium is investigated using two-dimensional simulations with a realistic cooling rate, thermal conduction, and physical viscosity. The calculations are performed using periodic boundary conditions without any external dynamical forcing. As the initial condition, a spatially uniform unstable gas under thermal equilibrium is considered. At the initial stage, the unstable gas quickly segregates into two phases, or cold neutral medium (CNM) and warm neutral medium (WNM). Then, self-sustained turbulence with velocity dispersion of $0.1-0.2\;\mathrm{km\;s^{-1}}$ is observed in which the CNM moves around in the WNM. We find that the interfacial medium (IFM) between the CNM and WNM plays an important role in sustaining the turbulence. The self-sustaining mechanism can be divided into two steps. First, thermal conduction drives fast flows streaming into concave CNM surfaces towards the WNM. The kinetic energy of the fast flows in the IFM is incorporated into that of the CNM through the phase transition. Second, turbulence inside the CNM deforms interfaces and forms other concave CNM surfaces, leading to fast flows in the IFM. This drives the first step again and a cycle is established by which turbulent motions are self-sustained.Comment: 14 pages, 15 figures, accepted by The Astrophysical Journa

Gravitational Fragmentation of Expanding Shells. I. Linear Analysis

We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the density profile across the thickness. It is found that the time evolution of the density profile can be divided into three evolutionary phases, deceleration-dominated, intermediate, and self-gravity-dominated phases. The density peak moves relatively from the shock front to the contact discontinuity as the shell expands. We perform a linear analysis taking into account the asymmetric density profile obtained by the semi-analytic method, and imposing the boundary conditions for the shock front and the contact discontinuity while the evolutionary effect of the shell is neglected. It is found that the growth rate is enhanced compared with the previous studies based on the thin-shell approximation. This is due to the boundary effect of the contact discontinuity and asymmetric density profile that were not taken into account in previous works.Comment: 13 pages, 13 figures, to be published in the Astrophysical Journa

Gravitational Instability of Shocked Interstellar Gas Layers

In this paper we investigate gravitational instability of shocked gas layers using linear analysis. An unperturbed state is a self-gravitating isothermal layer which grows with time by the accretion of gas through shock fronts due to a cloud-cloud collision. Since the unperturbed state is not static, and cannot be described by a self-similar 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 Rankine-Hugoniot 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\sqrt{2\pi G\rho_\mathrm{E} {\cal M\mit}}/c_\mathrm{s}, where $\rho_\mathrm{E}, c_\mathrm{s}$ and \cal M\mit are the density of 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/\sqrt{2\pi G\rho_\mathrm{E} {\cal M\mit}}. The epoch at which the fastest growing mode becomes non-linear is given by 2.4\delta_0^{-0.1}/\sqrt{2\pi G \rho_\mathrm{E}{\cal M\mit}}, where $\delta_0$ is the initial amplitude of the perturbation of the column density. As an application of our linear analysis, we investigate criteria for collision-induced fragmentation. Collision-induced fragmentation will occur only when parent clouds are cold, or $\alpha_0=5c_\mathrm{s}^2 R/2G M < 1$, where $R$ and $M$ are the radius and the mass of parent clouds, respectively.Comment: 12 pages, 21 figures, accepted for publication in PAS