Adriana Gazol

Molecular Cloud Evolution. I. Molecular Cloud and Thin Cold Neutral Medium Sheet Formation

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 one-dimensional simulations predict the thermodynamic conditions in the cold layer. After ~1 Myr of evolution, the layer has column density ~2.5 × 1019 cm-2, thickness ~0.03 pc, temperature ~25 K, and pressure ~6650 K cm-3. These conditions are strongly reminiscent of those recently reported by Heiles and coworkers for cold neutral medium sheets. In the one-dimensional simulations, the inflows into the sheets produce line profiles with a central line of width ~0.5 km s-1 and broad wings of width ~1 km s-1. Three-dimensional 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 ~7.5 Myr for inflow Mach number M1,r = 2.4 to >80 Myr for M1,r = 1.03. These numbers should be considered upper limits. The highest density turbulent gas (HDG, n > 100 cm-3) is always overpressured with respect to the mean WNM pressure by factors of 1.5-4, even though we do not include self-gravity. The intermediate-density gas (IDG, 10 < n/cm-3 < 100) has a significant pressure scatter that increases with M1,r, so that at M1,r = 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.

Gravity or turbulence? – II. Evolving column density probability distribution functions in molecular clouds

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.

Gravity or turbulence? II. Evolving column density PDFs in molecular clouds

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.

IS THERMAL INSTABILITY SIGNIFICANT IN TURBULENT GALACTIC GAS

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. We consider three sets of numerical simulations: (1) —ows in the presence of the instability only; (2) —ows in the presence of the instability and various types of turbulent energy injection (forcing), and (3) models of the ISM including the magnetic —eld, the Coriolis force, self-gravity and stellar energy injection. Simula- tions in the —rst group show that the condensation process that forms a dense phase (ii clouds ˇˇ) is highly dynamical and that the boundaries of the clouds are accretion shocks, rather than static density discon- tinuities. The density histograms (probability density functions (PDFs)) of these runs exhibit either bimodal shapes or a single peak at low densities plus a slope change at high densities. Final static situ- ations may be established, but the equilibrium is very fragile: small density —uctuations in the warm phase require large variations in that of the cold phase, probably inducing shocks in the clouds. Com- bined with the likely disruption of the clouds by Kelvin-Helmholtz instability, this result suggests that such con—gurations are highly unlikely. Simulations in the second group show that large-scale turbulent forcing is incapable of erasing the signature of TI in the density PDFs, but small-scale, stellar-like forcing causes the PDFs to transit from bimodal to a single-slope power law, erasing the signature of the instability. However, these simulations do not reach stationary regimes, with TI driving an ever- increasing star formation rate. Simulations in the third group show no signi—cant diUerence between the PDFs of stable and unstable cases and reach stationary regimes, suggesting that the combination of the stellar forcing and the extra eUective pressure provided by the magnetic —eld and the Coriolis force over- whelm TI as a density-structure generator in the ISM, with TI becoming a second-order eUect. We emphasize that a multimodal temperature PDF is not necessarily an indication of a multiphase medium, which must contain clearly distinct thermal equilibrium phases, and that this ii multiphase ˇˇ terminology is often inappropriately used. Subject headings: instabilitiesISM: structureturbulence

The nature of the velocity field in molecular clouds – I. The non-magnetic case

We present numerical simulations designed to test some of the hypotheses and predictions of recent models of star formation. We consider a set of three numerical simulations of randomly driven, isothermal, non-magnetic, self-gravitating turbulence with different rms Mach numbers Ms and physical sizes L, but with approximately the same value of the virial parameter, α ≈ 1.2. We obtain the following results: (i) we test the hypothesis that the collapsing centres originate from locally Jeans unstable (‘super-Jeans’), subsonic fragments; we find no such structures in our simulations, suggesting that collapsing centres can arise also from regions that have supersonic velocity dispersions but are nevertheless gravitationally unstable. (ii) We find that the fraction of small-scale super-Jeans structures is larger in the presence of self-gravity. (iii) There exists a trend towards more negative values of the velocity field’s mean divergence in regions with higher densities, implying the presence of organized inflow motions within the structures analysed. (iv) The density probability density function (PDF) deviates from a lognormal in the presence of self-gravity, developing an approximate power-law high-density tail, in agreement with previous results. (v) Turbulence alone in the large-scale simulation (L = 9 pc) does not produce regions with the same size and mean density as those of the small-scale simulation (L = 1 pc). Items (ii)–(v) 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 formation. We then measure the ‘star formation rate per free-fall time’, SFRff , 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, within the L = 9 pc simulation, subregions with similar density and size to those of the L = 1p c simulation differ qualitatively from the latter in that they exhibit a global convergence of the velocity field ∇·v ∼− 0.6 km s −1 pc −1 on average. This suggests that the assumption that turbulence in clouds and clumps is purely random is incomplete. We conclude that (i) part of the observed velocity dispersion in clumps must arise from clump-scale inwards motions, even in driven-turbulence situations, and (ii) 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.

The Mass Spectra of Cores in Turbulent Molecular Clouds and Implications for the Initial Mass Function

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 rms 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 can be described by a function that changes its shape continuously, probably similar to a lognormal function. The CMD in supersonic turbulent flows does not have a universal slope, which casts some doubt on attempts to directly relate the CMD to a universal initial mass function.

The Nonlinear Development of the Thermal Instability in the Atomic Interstellar Medium and Its Interaction with Random Fluctuations

We discuss the nonlinear development of the isobaric mode of thermal instability (TI) in the context of the atomic interstellar medium (ISM), in both isolation and in the presence of either density or velocity fluctuations, in order to assess the ability of TI to establish a well-segregated multiphase structure in the turbulent ISM. The key parameter is the ratio of the cooling time to the dynamical crossing time η. First, we discuss the degree to which the condensation process of large-scale perturbations generates large velocities and the times required for them to subside. Using high-resolution simulations in one dimension and fits to recently published cooling rates, we find that density perturbations of sizes 15 pc in media with mean density ~1 cm-3 develop inflow motions with Mach numbers larger than 0.5 and a shock that propagates outward from the condensation, bringing 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 3-75 pc. By the time the condensations have formed, a substantial fraction of the mass is still traversing the unstable range. Smaller (0.3-3 pc) perturbations may condense less dynamically and reach nearly static configurations in shorter times (e.g., ~3.5 Myr for perturbations of ~0.3 pc), but they may be stable if they have a turbulent origin (see below). We thus suggest that, even if TI were the sole cloud-forming agent in the ISM, clouds formed by it should be bounded by accreting gas traversing the unstable range, rather than by sharp transitions to the stable warm phase. Second, we discuss the competition between a spectrum of density perturbations of various sizes. We empirically find that, in order for small-scale perturbations not to significantly alter the global evolution, progressively larger values of η are necessary as the initial spectrum becomes shallower. Finally, we discuss the development of the instability in the presence of random velocity forcing, which we argue is the most realistic way to emulate density fluctuation production in the actual ISM. Such fluctuations are quasi-adiabatic rather than quasi-isobaric in the large-η limit and trigger the wave mode of TI, rather than the condensation mode, being stable to first order. Indeed, we find that the condensation process can be suppressed for arbitrarily long times if the forcing causes a moderate rms Mach number (0.3) and extends to small enough scales or occurs in low enough density environments that the turbulent crossing time becomes smaller than the cooling time at those scales. We suggest that this mechanism, and the long times required to evacuate the unstable phase, may be at the origin of the relatively large amounts of gas mass in the unstable regime found in both observations and simulations of the ISM. The gas with unstable temperatures is expected to be out of thermal equilibrium, suggesting that it can be observationally distinguished by simultaneously measuring two of its thermodynamic variables. We remark that in the (stable) warm diffuse medium, η is large enough that the response to velocity perturbations of scales up to several parsecs is close to adiabatic, implying that it is relatively weakly compressible and thus consistent with recent observations that suggest a nearly Kolmogorov power spectrum in this medium.

THE TEMPERATURE DISTRIBUTION IN TURBULENT INTERSTELLAR GAS

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, constituting a different process from that proposed in time-dependent models based on stochastic heating followed by cooling, although the latter mechanism may also be present. We also point out that a bimodal temperature probability distribution function is a simple consequence of the form of the interstellar cooling function and is not necessarily a signature of discontinuous phase transitions.

The Pressure Distribution in Thermally Bistable Turbulent Flows

We present a systematic numerical study of the effect of turbulent velocity fluctuations on the thermal pressure distribution in thermally bistable flows. The turbulent fluctuations are characterized by their rms Mach number M (with respect to the warm medium) and the energy injection (forcing) wavenumber kfor = 1/l, where l is the injection size scale in units of the box size L = 100 pc. The numerical simulations employ random turbulent driving generated in Fourier space rather than starlike heating, in order to allow for precise control of the parameters. Our range of parameters is 0.5 ≤ M ≤ 1.25 and 2 ≤ kfor ≤ 16. 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 γe of the simulations ranges between ~0.2 and ~1.1, and the mean pressure of the diffuse gas is generally reduced below the thermal equilibrium pressure Peq, while that of the dense gas is increased with respect to Peq. The fraction of high-density zones (n > 7.1 cm-3) with P > 104 cm-3 K increases from roughly 0.1% at kfor = 2 and M = 0.5 to roughly 70% for kfor = 16 and M = 1.25. A preliminary comparison with the recent pressure measurements of Jenkins in C I favors our case with M = 0.5 and kfor = 2. In all cases, the dynamic range of the pressure in any given density interval is larger than one order of magnitude, and the total dynamic range, 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 moreover develops near-power-law tails at high (low) pressures when γe 0.5 (γe 1), which occurs at kfor = 2 (kfor = 16) in our simulations. The opposite side of the pressure histogram decays rapidly, in an approximately lognormal form. This behavior resembles that of the corresponding density histograms, in spite of the large scatter of the pressure in any given density interval. 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 Mac Low et al.

On the Effects of Projection on Morphology

We study the eUects of projection of three-dimensional data onto the plane of the sky by means of numerical simulations of turbulence in the interstellar medium including the magnetic —eld, param- eterized cooling and diUuse 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 (ii channel maps ˇˇ), noting that the latter can be interpreted in two ways: either as maps of the column densitys spatial distribution (at a given line-of-sight (LOS) velocity) or as maps of the spatial distribu- tion 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 signi—cantly diUerent views. First, the mor- phology in the channel maps more closely resembles that of the spatial distribution of the LOS velocity component than that of the density —eld, as measured by pixel-to-pixel correlations between images. Second, the channel maps contain more small-scale structure than three-dimensional slices of the density and velocity —elds, a fact evident both in subjective appearance and in the power spectra of the images. This eUect may be due to a pseudorandom 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 signi—cantly from one position in the channel map to the next. Subject headings: ISM: generalISM: magnetic —eldsmethods: numericalturbulence