Abstract:
In this paper we numerically study the behavior of the density power spectrum in turbulent thermally bistable flows. We analyze a set of five three-dimensional simulations where turbulence is randomly driven in Fourier space at a fixed wave-number and with different Mach numbers M (with respect to the warm medium) ranging from 0.2 to 4.5. The density power spectrum becomes shallower as M increases and the same is true for the column density power spectrum. This trend is interpreted as a consequence of the simultaneous turbulent compressions, thermal instability generated density fluctuations, and the weakening of thermal pressure force in diffuse gas. This behavior is consistent with the fact that observationally determined spectra exhibit different slopes in different regions. The values of the spectral indexes resulting from our simulations are consistent with observational values. We do also explore the behavior of the velocity power spectrum, which becomes steeper as M increases. The spectral index goes from a value much shallower than the Kolmogorov one for M=0.2 to a value steeper than the Kolmogorov one for M=4.5.

Abstract:
We performed a numerical experiment designed for core formation in a self-gravitating, magnetically supercritical, supersonically turbulent, isothermal cloud. A density probability distribution function (PDF) averaged over a converged turbulent state before turning self-gravity on is well-fitted with a lognormal distribution. However, after turning self-gravity on, the volume fractions of density PDFs at a high density tail, compared with the lognormal distribution, increase as time goes on. In order to see the effect of self-gravity on core formation rates, we compared the core formation rate per free-fall time (CFR$_{\rm ff}$) from the theory based on the lognormal distribution and the one from our numerical experiment. For our fiducial value of a critical density, 100, normalised with an initial value, the latter CFR$_{\rm ff}$ is about 30 times larger the former one. Therefore, self-gravity plays an important role in significantly increasing CFR$_{\rm ff}$. This result implies that core (star) formation rates or core (stellar) mass functions predicted from theories based on the lognormal density PDF need some modifications. Our result of the increased volume fraction of density PDFs after turning self-gravity on is consistent with power-law like tails commonly observed at higher ends of visual extinction PDFs of active star-forming clouds.

Abstract:
We numerically study the volume density probability distribution function (n-PDF) and the column density probability distribution function (Sigma-PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional hydrodynamic models in periodic boxes of 100pc by side, where turbulence is driven in the Fourier space at a wavenumber corresponding to 50pc. At low densities (n <= 0.6cm^-3) the n-PDF, is well described by a lognormal distribution for average local Mach number ranging from ~0.2 to ~5.5. As a consequence of the non linear development of thermal instability (TI), the logarithmic variance of the distribution for the diffuse gas increases with M faster than in the well known isothermal case. The average local Mach number for the dense gas (n >= 7.1cm^-3) goes from ~1.1 to ~16.9 and the shape of the high density zone of the n-PDF changes from a power-law at low Mach numbers to a lognormal at high M values. In the latter case the width of the distribution is smaller than in the isothermal case and grows slower with M. At high column densities the Sigma-PDF is well described by a lognormal for all the Mach numbers we consider and, due to the presence of TI, the width of the distribution is systematically larger than in the isothermal case but follows a qualitatively similar behavior as M increases. Although a relationship between the width of the distribution and M can be found for each one of the cases mentioned above, these relations are different form those of the isothermal case.

Abstract:
The Parker instability is considered to play important roles in the evolution of the interstellar medium. Most studies on the development of the instability so far have been based on an initial equilibrium system with a uniform magnetic field. However, the Galactic magnetic field possesses a random component in addition to the mean uniform component, with comparable strength of the two components. Parker and Jokipii have recently suggested that the random component can suppress the growth of small wavelength perturbations. Here, we extend their analysis by including gas pressure which was ignored in their work, and study the stabilizing effect of the random component in the interstellar gas with finite pressure. Following Parker and Jokipii, the magnetic field is modeled as a mean azimuthal component, $B(z)$, plus a random radial component, $\epsilon(z) B(z)$, where $\epsilon(z)$ is a random function of height from the equatorial plane. We show that for the observationally suggested values of $<\epsilon^2>^{1/2}$, the tension due to the random component becomes important, so that the growth of the instability is either significantly reduced or completely suppressed. When the instability still works, the radial wavenumber of the most unstable mode is found to be zero. That is, the instability is reduced to be effectively two-dimensional. We discuss briefly the implications of our finding.

Abstract:
To examine how non-uniform nature of the Galactic gravity might affect length and time scales of the Parker instability, we took three models of gravity, uniform, linear and realistic ones. To make comparisons of the three gravity models on a common basis, we first fixed the ratio of magnetic pressure to gas pressure at $\alpha$ = 0.25, that of cosmic-ray pressure at $\beta$ = 0.4, and the rms velocity of interstellar clouds at $a_s$ = 6.4 km s$^{-1}$, and then adjusted parameters of the gravity models in such a way that the resulting density scale heights for the three models may all have the same value of 160 pc. Performing linear stability analyses onto equilibrium states under the three models with the typical ISM conditions, we calculate the maximum growth rate and corresponding length scale for each of the gravity models. Under the uniform gravity the Parker instability has the growth time of 1.2$\times10^{8}$ years and the length scale of 1.6 kpc for symmetric mode. Under the realistic gravity it grows in 1.8$\times10^{7}$ years for both symmetric and antisymmetric modes, and develops density condensations at intervals of 400 pc for the symmetric mode and 200 pc for the antisymmetric one. A simple change of the gravity model has thus reduced the growth time by almost an order of magnitude and its length scale by factors of four to eight. These results suggest that an onset of the Parker instability in the ISM may not necessarily be confined to the regions of high $\alpha$ and $\beta$.

Abstract:
Investigamos, mediante simulaciones de alta resoluci on, los efectos no lineales de la rotaci on uniforme en la inestabilidad de Parker para un disco estrati cado exponencialmente. Durante la etapa lineal, la velocidad del gas es subs onica y la evoluci on es similar al caso sin rotaci on. Esto es debido a que la fuerza de Coriolis es peque~na. Durante la etapa no lineal, los ujos supers onicos que se mueven en direcciones opuestas cerca de los valles magn eticos sienten la fuerza de Coriolis en sentido invertido y enrollan las l neas de campo en esos lugares. Las l aminas de gas formadas, que quedan inclinadas respecto a la direcci on inicial del campo, tienen una densidad columnar 1.5 veces mayor al valor inicial. Aunque cuando la rotaci on no tiene mucha in uencia sobre el aumento en densidad, genera campos con enrollamiento helicoidal que pueden dar soporte adicional a las nubes resultantes.

Abstract:
We calculate the evolution of molecular line profiles of HCO$^+$ and C$^{18}$O toward a dense core thatis forming inside a magnetized turbulent molecular cloud. Features of the profiles can be affected more significantly by coupled velocity and abundance structures in the outer region than those in the inner dense part of the core. The velocity structure at large radii is dominated by a turbulent flow nearby and accretion shocks onto the core, which resulting in the variation between inward and outward motions during the evolution of the core. The chemical abundance structure is significantly affected by the depletion of molecules in the central region with high density and low temperature. During the evolution of the core, the asymmetry of line profiles easily changes from blue to red, and vice versa. According to our study, the observed reversed (red) asymmetry toward some starless cores could be interpreted as an intrinsic result of outward motion in the outer region of a dense core, which is embedded in a turbulent environment and still grows in density at the center.

Abstract:
A linear stability analysis has been done to a magnetized disk under a linear gravity. We have reduced the linearized perturbation equations to a second-order differential equation which resembles the Schr\"{o}dinger equation with the potential of a harmonic oscillator. Depending on the signs of energy and potential terms, eigensolutions can be classified into ``continuum'' and ``discrete'' families. When magnetic field is ignored, the continuum family is identified as the convective mode, while the discrete family as acoustic-gravity waves. If the effective adiabatic index $\gamma$ is less than unity, the former develops into the convective instability. When a magnetic field is included, the continuum and discrete families further branch into several solutions with different characters. The continuum family is divided into two modes: one is the original Parker mode, which is a slow MHD mode modulated by the gravity, and the other is a stable Alfv\'en mode. The Parker modes can be either stable or unstable depending on $\gamma$. When $\gamma$ is smaller than a critical value $\gamma_{cr}$, the Parker mode becomes unstable. The discrete family is divided into three modes: a stable fast MHD mode modulated by the gravity, a stable slow MHD mode modulated by the gravity, and an unstable mode which is also attributed to a slow MHD mode. The unstable discrete mode does not always exist. Even though the unstable discrete mode exists, the Parker mode dominates it if the Parker mode is unstable. However, if $\gamma \ge \gamma_{cr}$, the discrete mode could be the only unstable one. When $\gamma$ is equal $\gamma_{cr}$, the minimum growth time of the unstable discrete mode is $1.3 \times 10^8$ years with a corresponding length scale of 2.4 kpc. It is suggestive that the corrugatory features seen in the Galaxy and external galaxies are related to the unstable discrete mode.

Abstract:
We investigate the nonlinear effects of uniform rotation on the Parker instability in an exponentially-stratified disk through high-resolution simulations. During the linear stage, the speed of gas motion is subsonic and the evolution with the rotation is not much different from that without the rotation. This is because the Coriolis force is small. During the nonlinear stage, oppositely-directed supersonic flows near a magnetic valley are under the influence of the Coriolis force with different directions, resulting in twisted magnetic field lines near the valley. Sheet-like structures, which are tilted with respect to the initial field direction, are formed with an 1.5 enhancement of column density with respect to its initial value. Even though uniform rotation doesn't give much impact on density enhancement, it generates helically twisted field lines, which may become an additional support mechanism of clouds.

Abstract:
Wu et al. (2009) suggested an empirical relation between the magnetic field strength along the line of sight (LOS) and the dispersion of Faraday rotation measure (RM) distribution in turbulent media with root-mean-square sonic Mach number $M_s \simeq 1$. In this paper, we extend the work by incorporating the Mach number dependence. Media with $\sim 0.5 < M_s < \sim 2$ are considered to cover the Mach number range of the warm ionized medium (WIM) of our Galaxy. Three-dimensional, magnetohydrodynamic isothermal turbulence simulations with solenoidal forcing are used. We suggest a new relation among the LOS magnetic field strength, the dispersion of RM distribution, and the Mach number, which approximately represents the relation for Alfv\'enic perturbations. In addition, we suggest a relation between the Mach number and the dispersion of log-normal distribution of emission measure (EM), which is basically the relation for the Mach number and the density dispersion. The relations could be used for a quick and rough estimation of the LOS magnetic field strength in the turbulent WIM.