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The propagation of a shock wave into an interstellar medium is investigated by two-dimensional numerical hydrodynamic calculation with cooling, heating and thermal conduction. We present results of the high-resolution two-dimensional calculations to follow the fragmentation due to the thermal instability in a shock-compressed layer. We find that geometrically thin cooling layer behind the shock front fragments into small cloudlets. The cloudlets have supersonic velocity dispersion in the warm neutral medium in which the fragments are embedded as cold condensations. The fragments tend to coalesce and become larger clouds.Comment: 4 pages, 2 figures. ApJL accepte

Recent studies of the nearest star-forming clouds of the Galaxy at submillimeter wavelengths with the Herschel Space Observatory have provided us with unprecedented images of the initial and boundary conditions of the star formation process. The Herschel results emphasize the role of interstellar filaments in the star formation process and connect remarkably well with nearly a decade's worth of numerical simulations and theory that have consistently shown that the ISM should be highly filamentary on all scales and star formation is intimately related to self-gravitating filaments. In this review, we trace how the apparent complexity of cloud structure and star formation is governed by relatively simple universal processes -from filamentary clumps to galactic scales. We emphasize two crucial and complementary aspects: (i) the key observational results obtained with Herschel over the past three years, along with relevant new results obtained from the ground on the kinematics of interstellar structures, and (ii) the key existing theoretical models and the many numerical simulations of interstellar cloud structure and star formation. We then synthesize a comprehensive physical picture that arises from the confrontation of these observations and simulations.

The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard disk model. From our numerical experiments we find that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength and is unaffected by ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly isothermal calculations, where pressure varies little with time. Over the entire region of parameter space explored, turbulence driven by the MRI has many characteristic ratios such as that of the Maxwell stress to the magnetic pressure. We also find that the amplitudes of the spatial fluctuations in density and the time variability in the stress are characterized by the ratio of magnetic pressure to gas pressure in the nonlinear regime. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of nonsteady magnetic reconnection.

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We investigate the propagation of a shock wave into a warm neutral medium and cold neutral medium by one-dimensional hydrodynamic calculations with detailed treatment of thermal and chemical processes. Our main result shows that thermal instability inside the shock-compressed layer produces a geometrically thin, dense layer in which a large amount of hydrogen molecules is formed. Linear stability analysis suggests that this thermally-collapsed layer will fragment into small molecular cloudlets. We expect that frequent compression due to supernova explosions, stellar winds, spiral density waves, etc., in the galaxy make the interstellar medium occupied by these small molecular cloudlets.

Using three-dimensional magnetohydrodynamics simulations, we investigate general properties of a blast wave shock interacting with interstellar clouds. The pre-shock cloudy medium is generated as a natural consequence of the thermal instability that simulates realistic clumpy interstellar clouds and their diffuse surrounding. The shock wave that sweeps the cloudy medium generates a turbulent shell through the vorticity generations that are induced by shock-cloud interactions. In the turbulent shell, the magnetic field is amplified as a result of turbulent dynamo action. The energy density of the amplified magnetic field can locally grow comparable to the thermal energy density, particularly at the transition layers between clouds and the diffuse surrounding. In the case of a young supernova remnant (SNR) with a shock velocity 10 3 km s −1 , the corresponding strength of the magnetic field is approximately 1 mG. The propagation speed of the shock wave is significantly stalled in the clouds because of the high density, while the shock maintains a high velocity in the diffuse surrounding. In addition, when the shock wave hits the clouds, reflection shock waves are generated that propagate back into the shocked shell. From these simulation results, many observational characteristics of a young SNR RX J1713.7−3946 that is suggested to be interacting with molecular clouds, can be explained as follows: The reflection shocks can accelerate particles in the turbulent downstream region where the magnetic field strength reaches 1mG, which causes short-time variability of synchrotron X-rays. Since the shock velocity is stalled locally in the clouds, the temperature in the shocked cloud is suppressed far below 1 keV. Thus, thermal Xray line emission would be faint even if the SNR is interacting with molecular clouds. We also find that the photon index of the π 0 -decay gamma rays generated by cosmic-ray protons can be 1.5 (corresponding energy flux is νF ν ∝ ν 0.5 ), because the penetration depth of high-energy particles into the clumpy clouds depends on their energy. This suggests that, if we rely only on the spectral study, the hadronic gamma-ray emission is indistinguishable from the leptonic inverse Compton emission. We propose that the spatial correlation of the gamma-ray, X-ray, and CO line emission regions can be conclusively used to understand the origin of gamma rays from RX J1713.7−3946.

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