Search

Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, $s$, is well measured, but a theoretical understanding of the processes leading to this distribution remains elusive. We investigate these processes using Lagrangian tracer particles to track $s$ and $\frac{ds}{dt}$ in direct numerical simulations, and we show that their evolution can be modeled as a stochastic differential process with time-correlated noise. The temporal correlation functions of $s$ and $\frac{ds}{dt}$ decay exponentially, as predicted by the model, and the decay timescale is $\approx$ 1/6 the eddy turnover time. The behavior of the conditional averages of $\frac{ds}{dt}$ and $\frac{d^2s}{dt^2}$ is also well explained by the model, which shows that the density PDF arises from a balance between stochastic compressions/expansions, which tend to broaden the PDF, and the acceleration/deceleration of shocks by density gradients, which tends to narrow it., Comment: 40 pages, 10 figures, to appear in Science Advances

Protoplanetary disks are routinely described as finite mass reservoirs left over by the gravitational collapse of the protostar, an assumption that strongly constrains both disk evolution and planet formation models. We propose a different scenario where protoplanetary disks of pre-main sequence stars are assembled primarily by Bondi-Hoyle accretion from the parent gas cloud. We demonstrate that Bondi-Hoyle accretion can supply not only the mass, but also the angular momentum necessary to explain the observed size of protoplanetary disks, and we predict the dependence of the disk specific angular momentum on the stellar mass. Our results are based on an analytical derivation of the scaling of the angular momentum in a turbulent flow, which we also confirm with a numerical simulation of supersonic turbulence. This new scenario for disk formation and evolution may alleviate a number of observational problems as well as compel major revisions of disk and planet formation models., Comment: Submitted to Nature Astronomy

Stars form through the gravitational collapse of molecular cloud cores. Before collapsing, the cores are supported by thermal pressure and turbulent motions. A question of critical importance for the understanding of star formation is how to observationally discern whether a core has already initiated gravitational collapse or is still in hydrostatic balance. The canonical method to identify gravitational collapse is based on the observed density radial profile, which would change from a Bonnor-Ebert type toward power laws as the core collapses. In practice, due to the projection effect, the resolution limit, and other caveats, it has been difficult to directly reveal the dynamical status of cores, particularly in massive star-forming regions. We here propose a novel, straight-forward diagnostic, namely, the collapsing index (CI), which can be modeled and calculated based on the radial profile of the line width of dense gas. A meaningful measurement of CI requires spatially and spectrally resolved images of optically thin and chemically stable dense gas tracers. ALMA observations are making such data sets increasingly available for massive star-forming regions. Applying our method to one of the deepest dense-gas spectral images ever taken toward such a region, namely, the Orion molecular cloud, we detect the dynamical status of selected cores therein. We observationally distinguished a collapsing core in a massive star-forming region from a hydrostatical one. Our approach would help significantly improve our understanding of the interaction between gravity and turbulence within molecular cloud cores in the process of star formation., Comment: 15 pages, 9 figures, accepted by RAA

While the importance of supernova feedback in galaxies is well established, its role on the scale of molecular clouds is still debated. In this work, we focus on the impact of supernovae on individual clouds, using a high-resolution magneto-hydrodynamic simulation of a region of 250 pc where we resolve the formation of individual massive stars. The supernova feedback is implemented with real supernovae that are the natural evolution of the resolved massive stars, so their position and timing are self-consistent. We select a large sample of molecular clouds from the simulation to investigate the supernova energy injection and the resulting properties of molecular clouds. We find that molecular clouds have a lifetime of a few dynamical times, less then half of them contract to the point of becoming gravitationally bound, and the dispersal time of bound clouds, of order one dynamical time, is a factor of two shorter than that of unbound clouds. We stress the importance of internal supernovae, that is massive stars that explode inside their parent cloud, in setting the cloud dispersal time, and their huge overdensity compared to models where the supernovae are randomly distributed. We also quantify the energy injection efficiency of supernovae as a function of supernova distance to the clouds. We conclude that intermittent driving by supernovae can maintain molecular-cloud turbulence and may be the main process of cloud dispersal. The role of supernovae in the evolution of molecular clouds cannot be fully accounted for without a self-consistent implementation of their feedback., Comment: 33 pages, 23 figures, submitted to ApJ

We address the problem of the origin of massive stars, namely the origin, path and timescale of the mass flows that create them. Based on extensive numerical simulations, we propose a scenario where massive stars are assembled by large-scale, converging, inertial flows that naturally occur in supersonic turbulence. We refer to this scenario of massive-star formation as the "Inertial-Inflow Model". This model stems directly from the idea that the mass distribution of stars is primarily the result of turbulent fragmentation. Under this hypothesis, the statistical properties of the turbulence determine the formation timescale and mass of prestellar cores, posing definite constraints on the formation mechanism of massive stars. We quantify such constraints by the analysis of a simulation of supernova-driven turbulence in a 250-pc region of the interstellar medium, describing the formation of hundreds of massive stars over a time of approximately 30 Myr. Due to the large size of our statistical sample, we can say with full confidence that massive stars in general do not form from the collapse of massive cores, nor from competitive accretion, as both models are incompatible with the numerical results. We also compute synthetic continuum observables in Herschel and ALMA bands. We find that, depending on the distance of the observed regions, estimates of core mass based on commonly-used methods may exceed the actual core masses by up to two orders of magnitude, and that there is essentially no correlation between estimated and real core masses., Comment: 35 pages, 30 figures, ApJ in press

We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state, connecting it to the conditional statistics of the velocity divergence. Two sets of numerical simulations are carried out, using either a Riemann solver to evolve the Euler equations or a finite-difference method to evolve the Navier-Stokes (N-S) equations. After confirming the validity of our theoretical formulation with the N-S simulations, we examine the effects of dynamical processes on the PDF, showing that the nonlinear term in the divergence equation amplifies the right tail of the PDF and reduces the left one, the pressure term reduces both the right and left tails, and the viscosity term, counter-intuitively, broadens the right tail of the PDF. Despite the inaccuracy of the velocity divergence from the Riemann runs, as found in our previous work, we show that the density PDF from the Riemann runs is consistent with that from the N-S runs. Taking advantage of their much higher effective resolution, we then use the Riemann runs to study the dependence of the PDF on the Mach number, $\mathcal{M}$, up to $\mathcal{M}\sim30$. The PDF width, $\sigma_{s}$, follows the relation $\sigma_{s}^2 = \ln (1+b^2 {\mathcal M}^2)$, with $b\approx0.38$. However, the PDF exhibits a negative skewness that increases with increasing $\mathcal{M}$, so much of the growth of $\sigma_{s}$ is accounted for by the growth of the left PDF tail, while the growth of the right tail tends to saturate. Thus, the usual prescription that combines a lognormal shape with the standard variance-Mach number relation greatly overestimates the right PDF tail at large $\mathcal{M}$, which may have a significant impact on theoretical models of star formation., Comment: Submitted to ApJ

We examine the accuracy of spatial derivatives computed from numerical simulations of supersonic turbulence. Two sets of simulations, carried out using a finite-volume code that evolves the hydrodynamic equations with an approximate Riemann solver and a finite-difference code that solves the Navier-Stokes equations, are tested against a number of criteria based on the continuity equation, including exact results at statistically steady state. We find that the spatial derivatives in the Navier-Stokes runs are accurate and satisfy all the criteria. In particular, they satisfy our exact results that the conditional mean velocity divergence, $\langle \nabla \cdot {\bs u}|s\rangle$, where $s$ is the logarithm of density, and the conditional mean of the advection of $s$, $\langle {\bs u} \cdot \nabla s|s\rangle$, vanish at steady state for all density values, $s$. On the other hand, the Riemann solver simulations fail all the tests that require accurate evaluation of spatial derivatives, resulting in apparent violation of the continuity equation, even if the solver enforces mass conservation. In particular, analysis of the Riemann simulations may lead to the incorrect conclusion that the $\pdv$ work tends to preferentially convert kinetic energy into thermal energy, inconsistent with the exact result that the energy exchange by $\pdv$ work is symmetric in barotropic supersonic turbulence at steady state. The inaccuracy of spatial derivatives is a general problem in the post-processing of simulations of supersonic turbulence with Riemann solvers. Solutions from such simulations must be used with caution in post-processing studies concerning the spatial gradients., Comment: Submitted to ApJ

The probabilistic approach to turbulence is applied to investigate density fluctuations in supersonic turbulence. We derive kinetic equations for the probability distribution function (PDF) of the logarithm of the density field, $s$, in compressible turbulence in two forms: a first-order partial differential equation involving the average divergence conditioned on the flow density, $\langle \nabla \cdot {\bs u} | s\rangle$, and a Fokker-Planck equation with the drift and diffusion coefficients equal to $-\langle {\bs u} \cdot \nabla s | s\rangle$ and $\langle {\bs u} \cdot \nabla s | s\rangle$, respectively. Assuming statistical homogeneity only, the detailed balance at steady state leads to two exact results, $\langle \nabla \cdot {\bs u} | s \rangle =0$, and $\langle {\bs u} \cdot \nabla s | s\rangle=0$. The former indicates a balance of the flow divergence over all expanding and contracting regions at each given density. The exact results provide an objective criterion to judge the accuracy of numerical codes with respect to the density statistics in supersonic turbulence. We also present a method to estimate the effective numerical diffusion as a function of the flow density and discuss its effects on the shape of the density PDF., Comment: Accepted for publication in ApJL

We make use of new subgrid model of turbulent mixing to accurately follow the cosmological evolution of the first stars, the mixing of their supernova ejecta, and the impact on the chemical composition of the Galactic Halo. Using the cosmological adaptive mesh refinement code RAMSES, we implement a model for the pollution of pristine gas as described in Pan et al. Tracking the metallicity of Pop III stars with metallicities below a critical value allows us to account for the fraction of Z < Zcrit stars formed even in regions in which the gas' average metallicity is well above Zcrit. We demonstrate that such partially-mixed regions account for 0.5 to 0.7 of all Pop III stars formed up to z = 5. Additionally, we track the creation and transport of "primordial metals" (PM) generated by Pop III supernovae (SNe). These neutron-capture deficient metals are taken up by second-generation stars and likely lead to unique abundance signatures characteristic of carbon-enhanced, metal-poor (CEMP-no) stars. As an illustrative example, we associate primordial metals with abundance ratios used by Keller et al. to explain the source of metals in the star SMSS J031300.36-670839.3, finding good agreement with the observed [Fe/H], [C/H], [O/H], and [Mg/Ca] ratios in CEMP-no Milky Way halo stars. Similar future simulations will aid in further constraining the properties of Pop III stars using CEMP observations, as well as improve predictions of the spatial distribution of Pop III stars, as will be explored by the next generation of ground- and space-based telescopes., Comment: 19 pages, 13 figures, accepted by ApJ Oct 2016

We present a comparison of molecular clouds (MCs) from a simulation of supernova-driven interstellar medium (ISM) turbulence with real MCs from the Outer Galaxy Survey. The radiative transfer calculations to compute synthetic CO spectra are carried out assuming the CO relative abundance depends only on gas density, according to four different models. Synthetic MCs are selected above a threshold brightness temperature value, $T_{\rm B,min}=1.4$ K, of the $J=1-0$ $^{12}$CO line, generating 16 synthetic catalogs (four different spatial resolutions and four CO abundance models), each containing up to several thousands MCs. The comparison with the observations focuses on the mass and size distributions and on the velocity-size and mass-size Larson relations. The mass and size distributions are found to be consistent with the observations, with no significant variations with spatial resolution or chemical model, except in the case of the unrealistic model with constant CO abundance. The velocity-size relation is slightly too steep for some of the models, while the mass-size relation is a bit too shallow for all models only at a spatial resolution $dx\approx 1$ pc. The normalizations of the Larson relations show a clear dependence on spatial resolution, for both the synthetic and the real MCs. The comparison of the velocity-size normalization suggests that the SN rate in the Perseus arm is approximately 70\% or less of the rate adopted in the simulation. Overall, the realistic properties of the synthetic clouds confirm that supernova-driven turbulence can explain the origin and dynamics of MCs., Comment: accepted for publication in ApJ

The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of the compressive ratio, with a mean value $\approx 0.3$, lower than the equilibrium value of $\approx 0.5$ found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density PDF is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included., Comment: Accepted by ApJ

Turbulence is ubiquitous in molecular clouds (MCs), but its origin is still unclear because MCs are usually assumed to live longer than the turbulence dissipation time. Interstellar medium (ISM) turbulence is likely driven by SN explosions, but it has never been demonstrated that SN explosions can establish and maintain a turbulent cascade inside MCs consistent with the observations. In this work, we carry out a simulation of SN-driven turbulence in a volume of (250 pc)$^3$, specifically designed to test if SN driving alone can be responsible for the observed turbulence inside MCs. We find that SN driving establishes a velocity scaling consistent with the usual scaling laws of supersonic turbulence, suggesting that previous idealized simulations of MC turbulence, driven with a random, large-scale volume force, were correctly adopted as appropriate models for MC turbulence, despite the artificial driving. We also find that the same scaling laws extend to the interior of MCs, and that the velocity-size relation of the MCs selected from our simulation is consistent with that of MCs from the Outer-Galaxy Survey, the largest MC sample available. The mass-size relation and the mass and size probability distributions also compare successfully with those of the Outer Galaxy Survey. Finally, we show that MC turbulence is super-Alfv\'{e}nic with respect to both the mean and rms magnetic-field strength. We conclude that MC structure and dynamics are the natural result of SN-driven turbulence., Comment: ApJ, in press

Motivated by its importance for modeling dust particle growth in protoplanetary disks, we study turbulence-induced collision statistics of inertial particles as a function of the particle friction time, tau_p. We show that turbulent clustering significantly enhances the collision rate for particles of similar sizes with tau_p corresponding to the inertial range of the flow. If the friction time, tau_p,h, of the larger particle is in the inertial range, the collision kernel per unit cross section increases with increasing friction time, tau_p,l, of the smaller particle, and reaches the maximum at tau_p,l = tau_p,h, where the clustering effect peaks. This feature is not captured by the commonly-used kernel formula, which neglects the effect of clustering. We argue that turbulent clustering helps alleviate the bouncing barrier problem for planetesimal formation. We also investigate the collision velocity statistics using a collision-rate weighting factor to account for higher collision frequency for particle pairs with larger relative velocity. For tau_p,h in the inertial range, the rms relative velocity with collision-rate weighting is found to be invariant with tau_p,l and scales with tau_p,h roughly as ~ tau_p,h^(1/2). The weighting factor favors collisions with larger relative velocity, and including it leads to more destructive and less sticking collisions. We compare two collision kernel formulations based on spherical and cylindrical geometries. The two formulations give consistent results for the collision rate and the collision-rate weighted statistics, except that the spherical formulation predicts more head-on collisions than the cylindrical formulation., Comment: 20 pages, 9 figures, accepted to ApJ

Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau_p1 and tau_p2, of two particles of arbitrary sizes. The friction time of particles included in the simulation ranges from 0.1 tau_eta to 54T_L, with tau_eta and T_L the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau_p1, the PDF is the fattest for equal-size particles (tau_p2~tau_p1), and becomes thinner at both tau_p2tau_p1. Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in 1/2>T_L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanerary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem., Comment: 25 pages, 19 figures, accepted by ApJ

We conduct simulations of turbulent mixing in the presence of a magnetic field, grown by the small-scale dynamo. We show that the scalar gradient field, $\nabla C$, which must be large for diffusion to operate, is strongly biased perpendicular to the magnetic field, ${\mathbf B}$. This is true both early-on, when the magnetic field is negligible, and at late times, when the field is strong enough to back react on the flow. This occurs because $\nabla C$ increases within the plane of a compressive motion, but ${\mathbf B}$ increases perpendicular to it. At late times the magnetic field resists compression, making it harder for scalar gradients to grow and likely slowing mixing., Comment: ApJ Letters (in press)

We extend our earlier work on turbulence-induced relative velocity between equal-size particles (Pan and Padoan, Paper I) to particles of arbitrarily different sizes. The Pan and Padoan (PP10) model shows that the relative velocity between different particles has two contributions, named the generalized shear and acceleration terms, respectively. The generalized shear term represents the particles' memory of the spatial flow velocity difference across the particle distance in the past, while the acceleration term is associated with the temporal flow velocity difference on individual particle trajectories. Using the simulation of Paper I, we compute the root-mean-square relative velocity, ^1/2, as a function of the friction times, tau_p1 and tau_p2, of the two particles, and show that the PP10 prediction is in satisfactory agreement with the data, confirming its physical picture. For a given tau_p1 below the Lagrangian correlation time of the flow, T_L, ^1/2 as a function of tau_p2 shows a dip at tau_p2~tau_p1, indicating tighter velocity correlation between similar particles. Defining a ratio f=tau_pl/tau_ph, with tau_pl and tau_ph the friction times of the smaller and larger particles, we find that ^1/2 increases with decreasing f due to the generalized acceleration contribution, which dominates at f<1/4. At a fixed f, our model predicts that ^1/2 scales as tau_ph^1/2 for tau_p,h in the inertial range of the flow, stays roughly constant for T_L >T_L/f. The acceleration term is independent of the particle distance, r, and thus reduces the r-dependence of ^1/2 in the bidisperse case., Comment: 23 pages, 12 figures, Accepted to ApJ

Turbulent motions are essential to the mixing of entrained fluids and are also capable of amplifying weak initial magnetic fields by small-scale dynamo action. Here we perform a systematic study of turbulent mixing in magnetized media, using three-dimensional magnetohydrodynamic simulations that include a scalar concentration field. We focus on how mixing depends on the magnetic Prandtl number, Pm, from 1 to 4 and the Mach number, M}, from 0.3 to 2.4. For all subsonic flows, we find that the velocity power spectrum has a k^-5/3 slope in the early, kinematic phase, but steepens due to magnetic back reactions as the field saturates. The scalar power spectrum, on the other hand, flattens compared to k^-5/3 at late times, consistent with the Obukohov-Corrsin picture of mixing as a cascade process. At higher Mach numbers, the velocity power spectrum also steepens due to the presence of shocks, and the scalar power spectrum again flattens accordingly. Scalar structures are more intermittent than velocity structures in subsonic turbulence while for supersonic turbulence, velocity structures appear more intermittent than the scalars only in the kinematic phase. Independent of the Mach number of the flow, scalar structures are arranged in sheets in both the kinematic and saturated phases of the magnetic field evolution. For subsonic turbulence, scalar dissipation is hindered in the strong magnetic field regions, probably due to Lorentz forces suppressing the buildup of scalar gradients, while for supersonic turbulence, scalar dissipation increases monotonically with increasing magnetic field strength. At all Mach numbers, mixing is significantly slowed by the presence of dynamically-important small-scale magnetic fields, implying that mixing in the interstellar medium and in galaxy clusters is less efficient than modeled in hydrodynamic simulations., Comment: 16 pages, 8 figures, ApJ, in press

We conduct a comprehensive theoretical and numerical investigation of the pollution of pristine gas in turbulent flows, designed to provide new tools for modeling the evolution of the first generation of stars. The properties of such Population III (Pop III) stars are thought to be very different than later generations, because cooling is dramatically different in gas with a metallicity below a critical value Z_c, which lies between ~10^-6 and 10^-3 solar value. Z_c is much smaller than the typical average metallicity, , and thus the mixing efficiency of the pristine gas in the interstellar medium plays a crucial role in the transition from Pop III to normal star formation. The small critical value, Z_c, corresponds to the far left tail of the probability distribution function (PDF) of the metallicity. Based on closure models for the PDF formulation of turbulent mixing, we derive equations for the fraction of gas, P, lying below Z_c, in compressible turbulence. Our simulation data shows that the evolution of the fraction P can be well approximated by a generalized self-convolution model, which predicts dP/dt = -n/tau_con P (1-P^(1/n)), where n is a measure of the locality of the PDF convolution and the timescale tau_con is determined by the rate at which turbulence stretches the pollutants. Using a suite of simulations with Mach numbers ranging from M = 0.9 to 6.2, we provide accurate fits to n and tau_con as a function of M, Z_c/, and the scale, L_p, at which pollutants are added to the flow. For P>0.9, mixing occurs only in the regions surrounding the pollutants, such that n=1. For smaller P, n is larger as mixing becomes more global. We show how the results can be used to construct one-zone models for the evolution of Pop III stars in a single high-redshift galaxy, as well as subgrid models for tracking the evolution of the first stars in large cosmological simulations., Comment: 37 pages, accepted by ApJ

We study the relative velocity of inertial particles suspended in turbulent flows and discuss implications for dust particle collisions in protoplanetary disks. We simulate a weakly compressible turbulent flow, evolving 14 particle species with friction timescale, tau_p, covering the entire range of scales in the flow. The particle Stokes numbers, St, measuring the ratio of tau_p to the Kolmogorov timescale, are in the range from ~0.1 to ~800. Using simulation results, we show that the model by Pan & Padoan (PP10) gives satisfactory predictions for the rms relative velocity between identical particles. The probability distribution function (PDF) of the relative velocity is found to be highly non-Gaussian. The PDF tails are well described by a 4/3 stretched exponential function for particles with tau_p ~ 1-2 T_L, where T_L is the Lagrangian correlation timescale, consistent with a prediction based on PP10. The PDF approaches Gaussian only for very large particles with tau_p >~ 54 T_L. We split particle pairs at given distances into two types with low and high relative speeds, referred to as continuous and caustic types, respectively, and compute their contributions to the collision kernel. Although amplified by the effect of clustering, the continuous contribution vanishes in the limit of infinitesimal particle distance, where the caustic contribution dominates. The caustic kernel per unit cross section rises rapidly as St increases toward ~1, reaches a maximum at tau_p ~ 2 T_L, and decreases as tau_p^{-1/2} for tau_p >> T_L., Comment: 41 pages, major revisions, accepted to ApJ

Several lines of evidence, from isotopic analyses of meteorites to studies of the Sun's elemental and isotopic composition, indicate that the solar system was contaminated early in its evolution by ejecta from a nearby supernova (SN). Previous models have invoked SN material being injected into an extant protoplanetary disk, or isotropically expanding ejecta sweeping over a distant (>10 pc) cloud core, simultaneously enriching it and triggering its collapse. Here we consider a new astrophysical setting: the injection of clumpy SN ejecta, as observed in the Cas A SN remnant, into the molecular gas at the periphery of an HII region created by the SN's progenitor star. To track these interactions we have conducted a suite of high-resolution (1500^3 effective) 3D simulations that follow the evolution of individual clumps as they move into molecular gas. Even at these high resolutions, our simulations do not quite achieve numerical convergence, due to the challenge of properly resolving the small-scale mixing of ejecta and molecular gas, although they do allow some robust conclusions to be drawn. Isotropically exploding ejecta do not penetrate into the molecular cloud, but, if cooling is properly accounted for, clumpy ejecta penetrate to distances ~10^18 cm and mix effectively with star-forming molecular gas. The ~2 M_\odot high-metallicity ejecta from a core-collapse SN is likely to mix with ~2 \times 10^4 M_\odot of molecular gas. Thus all stars forming late (~5 Myr) in the evolution of an HII region may be contaminated by SN ejecta at a level ~10^-4. This level of contamination is consistent with the abundances of short-lived radionuclides and possibly some stable isotopic shifts in the early solar system, and is potentially consistent with the observed variability in stellar elemental abundances. SN contamination of forming planetary systems may be a common, universal process., Comment: 21 pages, 10 figures, accepted by ApJ

The interstellar medium in star-forming galaxies is a multiphase gas in which turbulent support is at least as important as thermal pressure. Sustaining this configuration requires continuous radiative cooling, such that the overall average cooling rate matches the decay rate of turbulent energy into the medium. Here we carry out a set of numerical simulations of a stratified, turbulently stirred, radiatively cooled medium, which uncover a fundamental transition at a critical one-dimensional turbulent velocity of ~ 35 km/s. At turbulent velocities below ~35 km/s, corresponding to temperatures below 300,000 K, the medium is stable, as the time for gas to cool is roughly constant as a function of temperature. On the other hand, at turbulent velocities above the critical value, the gas is shocked into an unstable regime in which the cooling time increases strongly with temperature, meaning that a substantial fraction of the interstellar medium is unable to cool on a turbulent dissipation timescale. This naturally leads to runaway heating and ejection of gas from any stratified medium with a one-dimensional turbulent velocity above ~35 km/s, a result that has implications for galaxy evolution at all redshifts., Comment: 16 Pages, 11 figures, ApJ, in press

The first generation of stars had very different properties than later stellar generations, as they formed from a "pristine" gas that was free of heavy elements. Normal star formation took place only after the first stars polluted the surrounding turbulent interstellar gas, increasing its local heavy element concentration, Z, beyond a critical value, Z_c (10^-8 < Z_c <10^-5). Motivated by this astrophysical problem, we investigate the fundamental physics of the pollution of pristine fluid elements in isotropic compressible turbulence. Turbulence stretches the pollutants, produces concentration structures at small scales, and brings the pollutants and the unpolluted flow in closer contact. Our theoretical approach employs the probability distribution function (PDF) method for turbulent mixing. We adopt three PDF closure models and derive evolution equations for the pristine fraction from the models. To test and constrain the theoretical models, we conduct numerical simulations for decaying passive scalars in isothermal turbulent flows with Mach numbers of 0.9 and 6.2, and compute the mass fraction, P(Z_c, t), of the flow with Z < Z_c. In the Mach 0.9 flow, the evolution of P(Z_c, t)$ is well described by a continuous convolution model and dP(Z_c, t)/dt = P(Z_c, t) ln[P(Z_c, t)]/tau_con, if the mass fraction of the polluted flow is larger than ~ 0.1. If the initial pollutant fraction is smaller than ~ 0.1, an early phase exists during which the pristine fraction follows an equation from a nonlinear integral model: dP(Z_c, t)/dt = P(Z_c, t) [P(Z_c, t)-1]/tau_int. The timescales tau_con and tau_int are measured from our simulations. When normalized to the flow dynamical time, the decay of P(Z_ c, t) in the Mach 6.2 flow is slower than at Mach 0.9, and we show that P(Z_c, t) in the Mach 6.2 flow can be well fit using a formula from a generalized version of the self-convolution model., Comment: 30 pages, 8 figure. Accepted by Journal of Fluid Mechanics

We study clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, $St$, defined as the ratio of the particle friction timescale, $\tau_{\rm p} $, to the Kolmogorov timescale in the flow. In the dissipation range, the clustering intensity strongly peaks at $St \simeq 1$, and the RDF for $St \sim 1$ shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these scales, the strongest clustering is from particles with $\tau_{\rm p}$ in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is $\sim\tau_{\rm p}$. Particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in recent models for planetesimal formation. We point out that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution., Comment: 24 pages, 13 figures, accepted by ApJ

We conduct a systematic numerical study of passive scalar structures in supersonic turbulent flows. We find that the degree of intermittency in the scalar structures increases only slightly as the flow changes from transonic to highly supersonic, while the velocity structures become significantly more intermittent. This difference is due to the absence of shock-like discontinuities in the scalar field. The structure functions of the scalar field are well described by the intermittency model of She and L\'{e}v\^{e}que [Phys. Rev. Lett. 72, 336 (1994)], and the most intense scalar structures are found to be sheet-like at all Mach numbers., Comment: 4 pages, 3 figures, to appear in PRE

In many astrophysical environments, mixing of heavy elements occurs in the presence of a supersonic turbulent velocity field. Here we carry out the first systematic numerical study of such passive scalar mixing in isothermal supersonic turbulence. Our simulations show that the ratio of the scalar mixing timescale, $\tau_{\rm c}$, to the flow dynamical time, $\tau_{\rm dyn}$ (defined as the flow driving scale divided by the rms velocity), increases with the Mach number, $M$, for $M \lsim3$, and becomes essentially constant for $M \gsim3.$ This trend suggests that compressible modes are less efficient in enhancing mixing than solenoidal modes. However, since the majority of kinetic energy is contained in solenoidal modes at all Mach numbers, the overall change in $\tau_{\rm c}/\tau_{\rm dyn}$ is less than 20\% over the range $1 \lsim M \lsim 6$. At all Mach numbers, if pollutants are injected at around the flow driving scale, $\tau_{\rm c}$ is close to $\tau_{\rm dyn}.$ This suggests that scalar mixing is driven by a cascade process similar to that of the velocity field. The dependence of $\tau_{\rm c}$ on the length scale at which pollutants are injected into flow is also consistent with this cascade picture. Similar behavior is found for the variance decay timescales for scalars without continuing sources. Extension of the scalar cascade picture to the supersonic regime predicts a relation between the scaling exponents of the velocity and the scalar structure functions, with the scalar structure function becoming flatter as the velocity scaling steepens with Mach number. Our measurements of the volume-weighted velocity and scalar structure functions confirm this relation for $M\lsim 2,$ but show discrepancies at $M \gsim 3$., Comment: Accepted by ApJ

We present a model for the relative velocity of inertial particles in turbulent flows. Our general formulation shows that the relative velocity has contributions from two terms, referred to as the generalized acceleration and generalized shear terms, because they reduce to the well known acceleration and shear terms in the Saffman-Turner limit. The generalized shear term represents particles' memory of the flow velocity difference along their trajectories and depends on the inertial particle pair dispersion backward in time. The importance of this backward dispersion in determining the particle relative velocity is emphasized. We find that our model with a two-phase separation behavior, an early ballistic phase and a later tracer-like phase, as found by recent simulations for the forward (in time) dispersion of inertial particle pairs, gives good fits to the measured relative speeds from simulations at low Reynolds numbers. In the monodisperse case with identical particles, the generalized acceleration term vanishes and the relative velocity is determined by the generalized shear term. At large Reynolds numbers, our model gives a $St^{1/2}$ dependence of the relative velocity on the Stokes number $St$ in the inertial range for both the ballistic behavior and the Richardson separation law. This leads to the same inertial-range scaling for the two-phase separation that well fits the simulation results. Our calculations for the bidisperse case show that, with the friction timescale of one particle fixed, the relative speed as a function of the other particle's friction time has a dip when the two timescales are similar. We find that the primary contribution at the dip is from the generalized shear term, while the generalized acceleration term is dominant for particles of very different sizes., Comment: Accepted by J. Fluid. Mech. 35 pages

We show that density-weighted moments of the dissipation rate, $\epsilon_l$, averaged over a scale $l$, in supersonic turbulence can be successfully explained by the She and L\'ev\^eque model [Phys. Rev. Lett. {\bf 72}, 336 (1994)]. A general method is developed to measure the two parameters of the model, $\gamma$ and $d$, based directly on their physical interpretations as the scaling exponent of the dissipation rate in the most intermittent structures ($\gamma$) and the dimension of the structures ($d$). We find that the best-fit parameters ($\gamma=0.71$ and $d=1.90$) derived from the $\epsilon_l$ scalings in a simulation of supersonic turbulence at Mach 6 agree with their direct measurements, confirming the validity of the model in supersonic turbulence., Comment: 4 pages, 3 figures, accepted by Phys. Rev. Lett

To evaluate the effect of turbulent heating in the thermal balance of interstellar clouds, we develop an extension of the log-Poisson intermittency model to supersonic turbulence. The model depends on a parameter, d, interpreted as the dimension of the most dissipative structures. By comparing the model with the probability distribution of the turbulent dissipation rate in a simulation of supersonic and super-Alfvenic turbulence, we find a best-fit value of d=1.64. We apply this intermittency model to the computation of the mass-weighted probability distribution of the gas temperature of molecular clouds, high-mass star-forming cores, and cold diffuse HI clouds. Our main results are: i) The mean gas temperature in molecular clouds can be explained as the effect of turbulent heating alone, while cosmic ray heating may dominate only in regions where the turbulent heating is low; ii) The mean gas temperature in high-mass star-forming cores with typical FWHM of ~6 km/s (corresponding to a 1D rms velocity of 2.5 km/s) may be completely controlled by turbulent heating, which predicts a mean value of approximately 36 K, two to three times larger than the mean gas temperature in the absence of turbulent heating; iii) The intermittency of the turbulent heating can generate enough hot regions in cold diffuse HI clouds to explain the observed CH+ abundance, if the rms velocity on a scale of 1 pc is at least 3 km/s, in agreement with previous results based on incompressible turbulence. Because of its importance in the thermal balance of molecular clouds and high-mass star-forming cores, the process of turbulent heating may be central in setting the characteristic stellar mass and in regulating molecular chemical reactions., Comment: Accepted by ApJ, 15 pages, 7 figures

We examine the effects of turbulent intermittency on the deflagration to detonation transition (DDT) in Type Ia supernovae. The Zel'dovich mechanism for DDT requires the formation of a nearly isothermal region of mixed ash and fuel that is larger than a critical size. We primarily consider the hypothesis by Khokhlov et al. and Niemeyer and Woosley that the nearly isothermal, mixed region is produced when the flame makes the transition to the distributed regime. We use two models for the distribution of the turbulent velocity fluctuations to estimate the probability as a function of the density in the exploding white dwarf that a given region of critical size is in the distributed regime due to strong local turbulent stretching of the flame structure. We also estimate lower limits on the number of such regions as a function of density. We find that the distributed regime, and hence perhaps DDT, occurs in a local region of critical size at a density at least a factor of 2-3 larger than predicted for mean conditions that neglect intermittency. This factor brings the transition density to be much larger than the empirical value from observations in most situations. We also consider the intermittency effect on the more stringent conditions for DDT by Lisewski et al. and Woosley. We find that a turbulent velocity of $10^8$ cm/s in a region of size $10^6$ cm, required by Lisewski et al., is rare. We expect that intermittency gives a weaker effect on the Woosley model with stronger criterion. The predicted transition density from this criterion remains below $10^7$ g/cm$^3$ after accounting for intermittency using our intermittency models., Comment: 31 pages, accepted for publication in ApJ

Motivated by an interpretation of $z \sim 3$ objects by Jimenez and Haiman (2006), we examine processes that control the fraction of primordial ($Z = 0$) gas, and so primordial stars, in high-SFR Lyman break galaxies. A primordial fraction different from 1 or 0 requires microscopic diffusion catalyzed by a velocity field with timescale comparable to the duration of star formation. The only process we found that satisfies this requirement for LBGs without fine-tuning is turbulence-enhanced mixing induced by exponential stretching and compressing of metal-rich ejecta. The time-dependence of the primordial fraction for this model is calculated. We show that conclusions for all the models discussed here are virtually independent of the IMF, including extremely top-heavy IMFs., Comment: 5 pages, 1 figure. Accepted for publication in ApJ Letters