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The objective of this paper is to help shedding some light on the nature and the properties of the cold structures formed via thermal instability in the magnetized atomic interstellar medium. To this end, we searched for clumps formed in forced (magneto)hydrodynamic simulations with an initial magnetic field ranging from 0 to 8.3$\mu$G. We statistically analyzed, through the use of Kernel Density Estimations, the physical and the morphological properties of a sample containing $\sim 1500$ clumps, as well as the relative alignments between the main direction of clumps and the internal velocity and magnetic field. The density ($n\sim 50-200$cm$^{-3}$), the thermal pressure ($P_{th}/k\sim 4.9\times 10^3-10^4$K cm$^{-3}$), the mean magnetic field ($\sim 3-11$$\mu$G ), and the sonic Mach number of the selected clumps have values comparable to those reported in observations. We find, however, that the cloud sample can not be described by a single regime concerning their pressure balance and their Alf\'enic Mach number. We measured the morphological properties of clumps mainly through the asphericity and the prolatness, which appear to be more sensitive than the aspect ratios. From this analysis we find that the presence of magnetic field, even if it is weak, does qualitatively affect the morphology of the clumps by increasing the probability of having highly aspherical and highly plolate clumps by a factor of two, that is by producing more filamentary clumps. Finally, we find that the angle between the main direction of the clumps and the local magnetic field lies between $\sim\pi/4-\pi/2$ and shifts to more perpendicular alignments as the intensity of this field increases, while the relative direction between the local density structure and the local magnetic field transits from parallel to perpendicular., Comment: Accepted for publication in MNRAS

We present numerical experiments aimed to study the correlation between the magnetic field strength, $B$, and the density, $n$, in the cold atomic interstellar medium (CNM). We analyze 24 magneto-hydrodynamic models with different initial magnetic field intensities ($B_0=$0.4, 2.1, 4.2, and 8.3 $\mu$G) and/or mean densities (2, 3, and 4 cm$^{-3}$), in the presence of driven and decaying turbulence, with and without self-gravity, in a cubic computational domain with 100 pc by side. Our main findings are: i) For forced simulations, which reproduce the main observed physical conditions of the CNM in the Solar neighborhood, a positive correlation between $B$ and $n$ develops for all the $B_0$ values. ii) The density at which this correlation becomes significant ($\lesssim 30$ cm$^{-3}$) depends on $B_0$ but is not sensitive to the presence of self-gravity. iii) The effect of self-gravity, when noticeable, consists of producing a shallower correlation at high densities, suggesting that, in the studied regime, self-gravity induces motions along the field lines. iv) Self-gravitating decaying models where the CNM is subsonic and sub-Alfv\'enic with $\beta\lesssim 1$ develop a high density positive correlation whose slopes are consistent with a constant $\beta(n)$. v) Decaying models where the low density CNM is subsonic and sub-Alfv\'enic with $\beta>1$ show a negative correlation at intermediate densities, followed by a high density positive correlation., Comment: Accepted for publication in MNRAS, 10 pages, 11 figures

It has been recently shown that molecular clouds do not exhibit a unique shape for the column density probability distribution function (Npdf). Instead, clouds without star formation seem to possess a lognormal distribution, while clouds with active star formation develope a power-law tail at high column densities. The lognormal behavior of the Npdf has been interpreted in terms of turbulent motions dominating the dynamics of the clouds, while the power-law behavior occurs when the cloud is dominated by gravity. In the present contribution we use thermally bi-stable numerical simulations of cloud formation and evolution to show that, indeed, these two regimes can be understood in terms of the formation and evolution of molecular clouds: a very narrow lognormal regime appears when the cloud is being assembled. However, as the global gravitational contraction occurs, the initial density fluctuations are enhanced, resulting, first, in a wider lognormal Npdf, and later, in a power-law Npdf. We thus suggest that the observed Npdf of molecular clouds are a manifestation of their global gravitationally contracting state. We also show that, contrary to recent suggestions, the exact value of the power-law slope is not unique, as it depends on the projection in which the cloud is being observed.

We present results from a two-dimensional numerical study of the effects of turbulent velocity fluctuations on the thermal and magnetic pressure distribution of a magnetized thermally bistable flow in a 100 × 100 pc2 box. We analyze simulations with a uniform initial magnetic field whose intensity, B 0, varies from 2.5 to 10 μG and in which the turbulent forcing is driven at scales ranging from 6.25 to 50 pc and with Mach numbers, with respect to the gas at 104 K M, ranging from 0.5 to 3.0. We find that the response of the thermal pressure distribution to variations on the forcing scale and Mach number follows the same trends as in the nonmagnetic case, which is consistent with a reduction of the ratio between the turbulent crossing time and the cooling time produced when the Mach number is increased or when the forcing scale is decreased. In the magnetic case, however, the thermal pressure distribution develops a low-pressure tail and does not develop a power-law shape. We interpret this fact as a consequence of the magnetic pressure acting as a random force instead of as a restoring force. On the other hand, the magnetic pressure distribution is very sensitive to the Mach number which in fact determines the maximum value of the magnetic pressure independently of B 0. For low-density gas, less than 80 cm–3, we do not observe any correlation between the density and the magnetic field strength but the densest gas in our simulations shows magnetic pressures equal to or above the pressure at B 0 and thermal pressures equal to or above the value given by the mean density in thermal equilibrium. The high thermal pressure of this gas suggests that it has a dynamical origin.

(Abridged) We discuss the nonlinear development of the isobaric mode of thermal instability (TI) in the context of the atomic interstellar medium (ISM), in order to assess the ability of TI to establish a well-segregated multi-phase structure in the turbulent ISM. The key parameter is the ratio of the cooling time to the dynamical crossing time $\eta$. The isobaric density perturbations of sizes $\gtrsim 15$ pc in media with mean density $\sim 1$ cm$^{-3}$ develop inflow motions with Mach number larger than 0.5 and a shock that propagates outwards from the condensation and brings the surrounding medium out of thermal equilibrium. The time for the dynamical transient state to subside ranges from 4 to 30 Myr for initial density perturbations of 20% and sizes 3 to 75 pc. By the time the condensations have formed, a substantial fraction of the mass is still traversing the unstable range and, therefore, clouds formed by TI should be bounded by accreting gas traversing the unstable range, rather than by sharp transitions to the stable warm phase. In the presence of random velocity forcing the condensation process can be suppressed for arbitrarily long times if the forcing causes a moderate rms Mach number ($\gtrsim 0.3$) and extends to small enough scales that $\eta>1$. We suggest that these mechanisms may be at the origin of the relatively large amounts of gas mass in the unstable regime. We remark that in the (stable) warm diffuse medium, $\eta>1$ for velocity perturbations of scales up to several pc. The flow's response to them is thus nearly adiabatic, and relatively weakly compressible, consistent with observations that suggest a nearly Kolmogorov power spectrum in this medium.

We investigate the scale dependence of fluctuations inside a realistic model of an evolving turbulent HII region and to what extent these may be studied observationally. We find that the multiple scales of energy injection from champagne flows and the photoionization of clumps and filaments leads to a flatter spectrum of fluctuations than would be expected from top-down turbulence driven at the largest scales. The traditional structure function approach to the observational study of velocity fluctuations is shown to be incapable of reliably determining the velocity power spectrum of our simulation. We find that a more promising approach is the Velocity Channel Analysis technique of Lazarian & Pogosyan (2000), which, despite being intrinsically limited by thermal broadening, can successfully recover the logarithmic slope of the velocity power spectrum to a precision of +-0.1 from high resolution optical emission line spectroscopy., 20 pages, 19 figures, accepted by MNRAS

We discuss the temperature distribution in a two-dimensional, thermally unstable numerical simulation of the warm and cold gas in the Galactic disk, including the magnetic field, self-gravity, the Coriolis force, stellar energy injection and a realistic cooling function. We find that ~50% of the turbulent gas mass has temperatures in what would be the thermally unstable range if thermal instability were to be considered alone. This appears to be a consequence of there being many other forces at play than just thermal pressure. We also point out that a bimodal temperature pdf is a simple consequence of the form of the interstellar cooling function and is not necessarily a signature of discontinuous phase transitions., video address has been updated

We investigate numerically the role of thermal instability (TI) as a generator of density structures in the interstellar medium (ISM), both by itself and in the context of a globally turbulent medium. Simulations of the instability alone show that the condenstion process which forms a dense phase (``clouds'') is highly dynamical, and that the boundaries of the clouds are accretion shocks, rather than static density discontinuities. The density histograms (PDFs) of these runs exhibit either bimodal shapes or a single peak at low densities plus a slope change at high densities. Final static situations may be established, but the equilibrium is very fragile: small density fluctuations in the warm phase require large variations in the density of the cold phase, probably inducing shocks into the clouds. This result suggests that such configurations are highly unlikely. Simulations including turbulent forcing show that large- scale forcing is incapable of erasing the signature of the TI in the density PDFs, but small-scale, stellar-like forcing causes erasure of the signature of the instability. However, these simulations do not reach stationary regimes, TI driving an ever-increasing star formation rate. Simulations including magnetic fields, self-gravity and the Coriolis force show no significant difference between the PDFs of stable and unstable cases, and reach stationary regimes, suggesting that the combination of the stellar forcing and the extra effective pressure provided by the magnetic field and the Coriolis force overwhelm TI as a density-structure generator in the ISM. We emphasize that a multi-modal temperature PDF is not necessarily an indication of a multi-phase medium, which must contain clearly distinct thermal equilibrium phases., 18 pages, 11 figures. Submitted to ApJ

We study the effects of projection of three-dimensional (3D) data onto the plane of the sky by means of numerical simulations of turbulence in the interstellar medium including the magnetic field, parameterized cooling and diffuse and stellar heating, self-gravity and rotation. We compare the physical-space density and velocity distributions with their representation in position-position-velocity (PPV) space (``channel maps''), noting that the latter can be interpreted in two ways: either as maps of the column density's spatial distribution (at a given line-of-sight (LOS) velocity), or as maps of the spatial distribution of a given value of the LOS velocity (weighted by density). This ambivalence appears related to the fact that the spatial and PPV representations of the data give significantly different views. First, the morphology in the channel maps more closely resembles that of the spatial distribution of the LOS velocity component than that of the density field, as measured by pixel-to-pixel correlations between images. Second, the channel maps contain more small-scale structure than 3D slices of the density and velocity fields, a fact evident both in subjective appearance and in the power spectra of the images. This effect may be due to a pseudo-random sampling (along the LOS) of the gas contributing to the structure in a channel map: the positions sampled along the LOS (chosen by their LOS velocity) may vary significantly from one position in the channel map to the next., Comment: 6 figures. To appear in the March 20th volume in ApJ

In this paper, we study the role of superbubbles in the evolution of the large-scale interstellar medium, within the context of numerical simulations that incorporate most of the relevant physical parameters. Our previous model has been completed by the addition of supernova (SN) explosions and the effect on the gravitational potential of the density stratification in the direction perpendicular to the Galactic disk, and by the inclusion of the three velocity and magnetic-field components in the Galactic midplane dynamics. The explosions of many Type II SNe in dense clouds lead to the creation of a hot ( K) and tenuous (n ≈ 10-3) phase that expands in the intercloud medium, creating supershells that fragment under the effect of magnetohydrodynamical instabilities. One conspicuous effect is the formation of dense, roundish clouds in regions where the magnetic field, aligned perpendicular to the direction of the expansion, undergoes a strong bending and where the Lorentz force is thus directed inward. The magnetic-field component perpendicular to the Galactic plane contributes significantly to the pressure inside the shells, thus opposing their collapse. This model, which has a very limited number of ad hoc assumptions, also allows us to monitor the star formation (SF) cycle and to study its dependence on the environmental parameters. The rate of SN explosions per unit surface, which is not imposed but is determined by the dynamics, is consistent with recent estimates in the solar neighborhood. We also find that the presence of superbubbles leads to a more intermittent cycle and a globally increased SF rate. When the strength of the uniform component of the magnetic field increases, the SF rate increases, while the size of individual bubbles decreases, resulting in a more complex influence on the hot gas filling factor. The latter can reach 20% for isolated bubbles, but on average it does not exceeds a few percent.

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 = 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., 23 pages and 7 figures. Accepted for publication in ApJ

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., Comment: 16 pages, 11 figures. Accepted for publication in ApJ

We present three numerical simulations of randomly driven, isothermal, non-magnetic, self-gravitating turbulence with different rms Mach numbers Ms and physical sizes L, but approximately the same value of the virial parameter, alpha approx 1.2. We obtain the following results: a) We test the hypothesis that the collapsing centers originate from locally Jeans-unstable ("super-Jeans"), subsonic fragments; we find no such structures. b) We find that the fraction of small-scale super-Jeans structures is larger in the presence of self-gravity. c) The velocity divergence of subregions of the simulations exhibits a negative correlation with their mean density. d) The density probability density function (PDF) deviates from a lognormal in the presence of self-gravity. e) Turbulence alone in the large-scale simulation does not produce regions with the same size and mean density as those of the small-scale simulation. Items (b)-(e) suggest that self-gravity is not only involved in causing the collapse of Jeans-unstable density fluctuations produced by the turbulence, but also in their {it formation}. We also measure the star formation rate per free-fall time, as a function of Ms for the three runs, and compare with the predictions of recent semi-analytical models. We find marginal agreement to within the uncertainties of the measurements. However, the hypotheses of those models neglect the net negative divergence of dense regions we find in our simulations. We conclude that a) part of the observed velocity dispersion in clumps must arise from clump-scale inwards motions, and b) analytical models of clump and star formation need to take into account this dynamical connection with the external flow and the fact that, in the presence of self-gravity, the density PDF may deviate from a lognormal., Comment: 10 pages. Accepted by MNRAS. Replacement matches accepted version. Six new figure panels, extended discussion, conclusions unchanged. Abstract abridged

We present a systematic numerical study of the effect of turbulent velocity fluctuations on the thermal pressure distribution in thermally bistable flows. The simulations employ a random turbulent driving generated in Fourier space rather than star-like heating. The turbulent fluctuations are characterized by their rms Mach number M and the energy injection wavenumber, k_for. Our results are consistent with the picture that as either of these parameters is increased, the local ratio of turbulent crossing time to cooling time decreases, causing transient structures in which the effective behavior is intermediate between the thermal-equilibrium and adiabatic regimes. As a result, the effective polytropic exponent gamma_ef ranges between ~0.2 to ~1.1. The fraction of high-density zones with P>10^4 Kcm^-3 increases from roughly 0.1% at k_for=2 and M=0.5 to roughly 70% for k_for=16 and M=1.25. A preliminary comparison with the pressure measurements of Jenkins (2004) favors our case with M=0.5 and k_for=2. In all cases, the dynamic range of the pressure summed over the entire density range, typically spans 3-4 orders of magnitude. The total pressure histogram widens as the Mach number is increased, and develops near-power-law tails at high (resp.low) pressures when gamma_ef~ 1), which occurs at k_for=2 (resp.k_for=16) in our simulations. The opposite side of the pressure histogram decays rapidly, in an approx. lognormal form. Our results show that turbulent advection alone can generate large pressure scatters, with power-law high-P tails for large-scale driving, and provide validation for approaches attempting to derive the shape of the pressure histogram through a change of variable from the known form of the density histogram, such as that performed by MacLow et al.(2004)., Comment: to be published in ApJ

We investigate the core mass distribution (CMD) resulting from numerical models of turbulent fragmentation of molecular clouds. In particular we study its dependence on the sonic root-mean-square Mach number $\Ms$. We analyze simulations with $\Ms$ ranging from 1 to 15 to show that, as $\Ms$ increases, the number of cores increases as well while their average mass decreases. This stems from the fact that high-Mach number flows produce many and strong shocks on intermediate to small spatial scales, leading to a highly-fragmented density structure. We also show that the CMD from purely turbulent fragmentation does not follow a single power-law, but it may be described by a function that changes continuously its shape, probably more similar to a log-normal function. The CMD in supersonic turbulent flows does not have a universal slope, and as consequence, cast some doubt on attempts to directly relate the CMD to a universal Initial Mass Function., Comment: 21 pages, 8 figures. Accepted for publication in The Astrophysical Journal

We discuss numerical simulations (and issues) of the atomic ISM tailored to investigate the possible existence of significant amounts of gas in the temperature range between the warm and cold stable phases. We attribute the presence of this gas to two facts: the enhanced stability of moderate, adiabatic-like velocity fluctuations occurring when the ratio of the cooling to the dynamical crossing time is large, and the recycling of gas from the dense to the diffuse phase by stellar energy injection. We conclude by suggesting that the gas with unstable temperatures can be observationally distinguished through simultaneous determination of two of its thermodynamic variables.

This paper is devoted to the study of the gravitational instability of a medium permeated by a uniform magnetic field along which a circularly polarized Alfven wave propagates. We concentrate on the case of perturbations purely transverse to the ambient field by means of direct numerical simulations of the MHD equations and of a linear stability analysis performed on a moderate amplitude asymptotic model. The Alfven wave provides an extra stabilizing pressure when the scale of perturbations is sufficiently large or small compared with the Jeans length $L_J$. However, there is a band of scales around $L_J$ for which the Alfven wave is found to have a destabilizing effect. In particular, when the medium is stable in absence of waves, the gravitational instability can develop when the wave amplitude lies in an appropriate range. This effect appears to be a consequence of the coupling between Alfven and magnetosonic waves. The prediction based on a WKB approach that the Alfven wave pressure tensor is isotropic and thus opposes gravity in all directions is only recovered for large amplitude waves for which the coupling between the different MHD modes is negligible., submitted to A&A

We review recent results on the nonlinear development of thermal instability (TI) in the context of the turbulent atomic interstellar medium (ISM), in which correlated density and velocity fluctuations are present, as well as forces other than the thermal pressure gradient. First, we present a brief summary of the linear theory, remarking that, in the atomic ISM, the condensation mode is unstable but the wave mode is stable at small scales. Next, we revisit the growth of isolated entropy perturbations in initially unstable gas, as a function of the ratio of the cooling to the dynamical crossing times η. The time for the dynamical transient state to subside ranges from 4 to 30 Myr for initial density perturbations of 20% and sizes 3 to 75 pc. When η≪ 1, the condensation produces locally supersonic motions and a shock propagates off the condensation, bringing the surrounding medium out of thermal equilibrium. Third, we consider the evolution of velocity perturbations, maintained by a random forcing, representing turbulent energy injection to the ISM from stellar sources. These perturbations correspond to the wave mode, and are stable at moderate amplitudes and small scales, as confirmed numerically. We then consider the behavior of magnetic pressure in turbulent regimes. Various observational and numerical results suggest that the magnetic pressure does not correlate well with density at low and intermediate densities. We propose that this is a consequence of the slow and fast modes of nonlinear MHD waves being characterized by different scalings of the magnetic field strength versus density. This lack of correlation suggests that, in fully turbulent regimes, the magnetic field may not be a very efficient source of pressure, and that polytropic descriptions of magnetic pressure are probably not adequate. Finally, we discuss simulations of the ISM (and resolution issues) tailored to investigate the possible existence of significant amounts of gas in the “lukewarm” temperature range between the warm and cold stable phases. The mass fraction in this range increases, and the phase segregation decreases, as smaller scales are considered. We attribute this to two facts: the enhanced stability of moderate, adiabatic-like velocity fluctuations with η≫ 1 and the recycling of gas from the dense to the diffuse phase by stellar energy injection. Moreover, the magnetic field is not strongly turbulent there, possibly providing additional stability. We conclude by suggesting that the gas with unstable temperatures can be observationally distinguished through simultaneous determination of two of its thermodynamic variables.

We numerically study the thermal pressure distribution in a gas with thermal properties similar to those of the cold neutral interstellar gas by analyzing three-dimensional hydrodynamic models in boxes with sides of 100 pc with turbulent compressible forcing at 50 pc and different Mach numbers. We find that at high pressures and for large Mach numbers, both the volume-weighted and the density-weighted distributions can be appropriately described by a log-normal distribution, whereas for small Mach numbers they are better described by a power law. Thermal pressure distributions resulting from similar simulations but with self-gravity differ only for low Mach numbers; in this case, they develop a high pressure tail.

We present numerical results concerning the behavior of the density and the velocity power spectrum in turbulent thermally bistable flows for different Mach numbers.

We present a numerical study on the behavior of the density power spectrum resulting from compressible hydrodynamic, thermally unstable simulations with different rms Mach numbers M rms . We find that the spectrum becomes shallower as M increases and that spectral index values that are consistent with those reported from observations.