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We explain the large variety of star formation laws in terms of one single, simple law that can be inferred from the definition of the star formation rate and basic algebra. The resulting equation, $\SFR = \eff\ \Mcollapsing/\tauff$, although it has been presented elsewhere, is interpreted in terms of clouds undergoing collapse { rather than being turbulence-supported, an idea that different groups have pursued this century}. Under such assumption, one can explain the constancy of $\eff$, the different intra-cloud correlations observed in Milky Way's molecular clouds, as well as the resolved and unresolved extragalactic relationships between SFR and a measurement of the mass in CO, HCN, and CO+HI. We also explain why the slope of the correlation changes when the orbital time $\tauorb$ is considered instead of the free-fall time, and why estimations of the free-fall time from extragalactic observations skew the correlation, providing a false sublinear correlation. We furthermore show that the apparent nearly linear correlation between the star formation rate and the dynamical equilibrium pressure in the midplane of the galaxies, $\PDE$, is just a consequence of $\PDE$ values being dominated by the variation of the column density of molecular gas. All in all, we argue that the star formation law is driven by the collapse of cold, dense gas, which happens to be primarily molecular in the present Universe, and that the role of stellar feedback is just to shut down the star formation process, not to shape the star formation law., Comment: 17 pages, one figure. Accepted by MNRAS

Recent works have proposed the idea of a tidal screening scenario, in which tidal forces determine the mass that a protostar can accrete to explain the IMF. In this scenario, gravitationally unstable fragments will compete for the gas reservoir in a star-forming clump. In this contribution, we propose to properly include the action of an external gravitational potential in the Jeans linear instability analysis as previously proposed by Jog. We have found that an external gravitational potential can reduce the critical mass required for the perturbation to collapse if the tidal force produced is compressive or increase it if it is disruptive. Our analytical treatment provides (a) new mass and length collapse conditions; (b) a simple equation for observers to check whether their observed fragments can collapse; and (c) a simple equation to compute whether collapse-induced turbulence can produce the levels of observed fragmentation. Our results suggest that, given envelopes with similar mass and density, the flatter ones should produce more stars than the steeper ones. If the density profile is a power-law, the corresponding power-law index separating these two regimes should be about 1.5. We finally applied our formalism to 160 fragments identified within 18 massive star-forming cores of previous works. We found that considering tides, 49% of the sample may be gravitationally unstable and that it is unlikely that turbulence acting at the moment of collapse has produced the fragmentation of these cores. Instead, these fragments should have formed earlier when the parent core was substantially flatter., Comment: Accepted MNRAS, 18 pages, 5 figures

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

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

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., Comment: 9 pages, 4 figures. MNRAS, accepted

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 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 molecular cloud formation by large-scale supersonic compressions in the diffuse warm neutral medium (WNM). Initially, a shocked layer forms, and within it, a thin cold layer. An analytical model and high-resolution 1D simulations predict the thermodynamic conditions in the cold layer. After $\sim 1$ Myr of evolution, the layer has column density $\sim 2.5 \times 10^{19} \psc$, thickness $\sim 0.03$ pc, temperature $\sim 25$ K and pressure $\sim 6650$ K $\pcc$. These conditions are strongly reminiscent of those recently reported by Heiles and coworkers for cold neutral medium sheets. In the 1D simulations, the inflows into the sheets produce line profiles with a central line of width $\sim 0.5 \kms$ and broad wings of width $\sim 1 \kms$. 3D numerical simulations show that the cold layer develops turbulent motions and increases its thickness, until it becomes a fully three-dimensional turbulent cloud. Fully developed turbulence arises on times ranging from $\sim 7.5$ Myr for inflow Mach number $\Mr = 2.4$ to $> 80$ Myr for $\Mr = 1.03$. These numbers should be considered upper limits. The highest-density turbulent gas (HDG, $n > 100 \pcc$) is always overpressured with respect to the mean WNM pressure by factors 1.5--4, even though we do not include self-gravity. The intermediate-density gas (IDG, $10 < n [{\rm cm}^ {-3}] < 100$) has a significant pressure scatter that increases with $\Mr$, so that at $\Mr = 2.4$, a significant fraction of the IDG is at a higher pressure than the HDG. Our results suggest that the turbulence and at least part of the excess pressure in molecular clouds can be generated by the compressive process that forms the clouds themselves, and that thin CNM sheets may be formed transiently by this mechanism, when the compressions are only weakly supersonic., Comment: Accepted for publication in ApJ. For correct display of the tables, download the postscript version. Animations can be downloaded from http://www.astrosmo.unam.mx/~e.vazquez/turbulence/movies.html

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<~ 0.5 (resp. 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

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., Comment: submitted to A&A

We review recent results on the nonlinear development of thermal instability in the context of the turbulent atomic interstellar medium (ISM). First, we pre- sent a brief summary of the linear theory, remarking that, in the atomic ISM, 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 $\eta$ of the cooling to the dynamical crossing times. Third, we consider the evolution of {\it velocity} perturbations. These correspond to the wave mode, and are stable at moderate amplitudes and small scales, as confirmed numerically. Fourth, we consider the behavior of magnetic pressure in turbulent regimes. We propose that recent findings of a poor B-rho correlation at low rho are due to the different B-rho scalings for the slow and fast modes of non- linear MHD waves. This implies that, in fully turbulent regimes, the magnetic field may not be a very efficient source of pressure, and that polytropic de- scriptions of magnetic pressure are probably not adequate. Finally, we discuss simulations of the ISM (and resolution issues) concerned with the possibility of significant amounts of gas being in the ``lukewarm'' temperature range be- tween the warm and cold stable phases. The mass fraction in this range in- creases, and the phase segregation decreases, as smaller scales are considered. We attribute this to the enhanced stability of moderate, adiabatic-like veloc- ity fluctuations with $\eta \gg 1$, to the recycling of gas from the dense to the diffuse phase by stellar energy injection, and to the magnetic field not being strongly turbulent there, possibly providing additional stability. Final- ly, we suggest that the lukewarm gas can be observationally distinguished through simultaneous determination of two of its thermodynamic variables., Comment: 39 pages, 15 figures. Invited talk, to appear in "Simulations of magnetohydrodynamic turbulence in astrophysics", eds. T. Passot & E. Falgarone, Springer Lecture Notes in Physics. Extensive modifications in response to referee's report, including a detailed discussion of resolution issues and new simulations. Conclusions unchanged

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., Comment: 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