Analysis of the Relaxation Process using Non-Relativistic Kinetic Equation

We study the linearized kinetic equation of relaxation model which was proposed by Bhatnagar, Gross and Krook (also called BGK model) and solve the dispersion relation. Using the solution of the dispersion relation, we analyze the relaxation of the macroscopic mode and kinetic mode. Since BGK model is not based on the expansion in the mean free path in contrast to the Chapman-Enskog expansion, the solution can describe accurate relaxation of initial disturbance with any wavelength. This non-relativistic analysis gives suggestions for our next work of relativistic analysis of relaxation.Comment: 18 pages, 14 figures, accepted for publication in Prog. Theor. Phys

Evolutionary Conditions in the Dissipative MHD System Revisited

The evolutionary conditions for the dissipative continuous magnetohydrodynamic (MHD) shocks are studied. We modify Hada's approach in the stability analysis of the MHD shock waves. The matching conditions between perturbed shock structure and asymptotic wave modes shows that all types of the MHD shocks, including the intermediate shocks, are evolutionary and perturbed solutions are uniquely defined. We also adopt our formalism to the MHD shocks in the system with resistivity without viscosity, which is often used in numerical simulation, and show that all types of shocks that are found in the system satisfy the evolutionary condition and perturbed solutions are uniquely defined. These results suggest that the intermediate shocks may appear in reality.Comment: 13 pages, 4 figures, accepted for publication in Prog. Theor. Phy

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