Compressive isothermal turbulence is known to have a near lognormal density probability distribution function (PDF) with a width that scales with the sonic Mach number and nature of the turbulent driving (solenoidal vs compressive). However, the physical processes that mold the extreme high and low density structures in a turbulent medium can be different, with the densest structures being composed of strong shocks that evolve on shorter timescales than the low density fluid. The density PDF in a turbulent medium exhibits deviations from lognormal due to shocks, that increases with the sonic Mach number, which is often ignored in analytic models for turbulence and star formation. We develop a simple model for turbulence by treating it as a continuous Markov process, which explains both the density PDF and the transient timescales of structures as a function of density, using a framework developed in n Scannapieco & Safarzadeh (2018). Our analytic model depends on only a single parameter, the effective compressive sonic Mach number, and successfully describes the non-lognormal behavior seen in both 1D and 3D simulations of supersonic and subsonic compressive isothermal turbulence. The model quantifies the non-lognormal distribution of density structures in turbulent environments, and has application to star forming molecular clouds and star formation efficiencies.
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 S…
We propose a new, physically motivated fitting function for density PDFs in turbulent gas. Although it is known that when gas is isothermal, the PDF is approximately lognormal in the core, high-resolution simulations show large deviations from exact log-normality. The proposed function provides an extraordinarily accurate description of the density PDFs in simulations with Mach numbers ~0.1-15 and dispersion in log(rho) from ~0.01-4 dex. Compared to a lognormal or lognormal-skew-kurtosis model, the fits are improved by orders of magnitude in the wings of the distribution (with fewer free param…
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…
The probability distribution of density in isothermal, supersonic, turbulent gas is approximately lognormal. This behaviour can be traced back to the shock waves travelling through the medium, which randomly adjust the density by a random factor of the local sonic Mach number squared. Provided a certain parcel of gas experiences a large number of shocks, due to the central limit theorem, the resulting distribution for density is lognormal. We explore a model in which parcels of gas undergo finite number of shocks before relaxing to the ambient density, causing the distribution for density to d…
Recent observations of column densities in molecular clouds find lognormal distributions with power-law high-density tails. These results are often interpreted as indications that supersonic turbulence dominates the dynamics of the observed clouds. We calculate and present the column-density distributions of three clouds, modeled with very different techniques, none of which is dominated by supersonic turbulence. The first star-forming cloud is simulated using smoothed particle hydrodynamics (SPH); in this case gravity, opposed only by thermal-pressure forces, drives the evolution. The second …
We derive an analytic expression for the transitional column density value ($s_t$) between the lognormal and power-law form of the probability distribution function (PDF) in star-forming molecular clouds. Our expression for $s_t$ depends on the mean column density, the variance of the lognormal portion of the PDF, and the slope of the power-law portion of the PDF. We show that $s_t$ can be related to physical quantities such as the sonic Mach number of the flow and the power-law index for a self-gravitating isothermal sphere. This implies that the transition point between the lognormal and pow…
We performed a numerical experiment designed for core formation in a self-gravitating, magnetically supercritical, supersonically turbulent, isothermal cloud. A density probability distribution function (PDF) averaged over a converged turbulent state before turning self-gravity on is well-fitted with a lognormal distribution. However, after turning self-gravity on, the volume fractions of density PDFs at a high density tail, compared with the lognormal distribution, increase as time goes on. In order to see the effect of self-gravity on core formation rates, we compared the core formation rate…
A key parameter to the description of all star formation processes is the density structure of the gas. In this letter, we make use of probability distribution functions (PDFs) of Herschel column density maps of Orion B, Aquila, and Polaris, obtained with the Herschel Gould Belt survey (HGBS). We aim to understand which physical processes influence the PDF shape, and with which signatures. The PDFs of Orion B (Aquila) show a lognormal distribution for low column densities until Av 3 (6), and a power-law tail for high column densities, consistent with a rho r^-2 profile for the equivalent spher…
We present numerical simulations of decaying hydrodynamic turbulence initially driven by solenoidal (divergence-free) and compressive (curl-free) driving. Most previous numerical studies for decaying turbulence assume an isothermal equation of state (EOS). Here we use a polytropic EOS, $P$ $\propto$ $ρ^γ$, with polytropic $γ$ ranging from 0.7 to 5/3. We mainly aim at determining the effects of polytropic $γ$ and driving schemes on the decay law of turbulence energy, E $\propto$ $t^{-α}$. We additionally study probability density function (PDF) of gas density and skewness of the distribution in…
We use deep adaptive mesh refinement simulations of isothermal self-gravitating supersonic turbulence to study the imprints of gravity on the mass density distribution in molecular clouds. The simulations show that the density distribution in self-gravitating clouds develops an extended power-law tail at high densities on top of the usual lognormal. We associate the origin of the tail with self-similar collapse solutions and predict the power index values in the range from -7/4 to -3/2 that agree with both simulations and observations of star-forming molecular clouds.
Magnetic fields are a dynamically important agent for regulating structure formation in the interstellar medium. The study of the relative orientation between the local magnetic field and gas (column-) density gradient has become a powerful tool to analyse the magnetic field's impact on the dense gas formation in the Galaxy. In this study, we perform numerical simulations of a non-gravitating, isothermal gas, where the turbulence is driven either solenoidally or compressively. We find that only simulations with an initially strong magnetic field (plasma-$β<1$) show a change in the preferential…
We examine the relation between the density variance and the mean-square Mach number in supersonic, isothermal turbulence, assumed in several recent analytic models of the star formation process. From a series of calculations of supersonic, hydrodynamic turbulence driven using purely solenoidal Fourier modes, we find that the `standard' relationship between the variance in the log of density and the Mach number squared, i.e., sigma^2_(ln rho/rhobar)=ln (1+b^2 M^2), with b = 1/3 is a good fit to the numerical results in the supersonic regime up to at least Mach 20, similar to previous determina…
Recent observations suggest that dense gas clouds can survive even in hot galactic winds. Here we show that the inclusion of turbulent densities with different statistical properties has significant effects on the evolution of wind-swept clouds. We investigate how the initial standard deviation of the log-normal density field influences the dynamics of quasi-isothermal clouds embedded in supersonic winds. We compare uniform, fractal solenoidal, and fractal compressive cloud models in both 3D and 2D hydrodynamical simulations. We find that the processes of cloud disruption and dense gas entrain…
Molecular clouds are supersonically turbulent. This turbulence governs the initial mass function and the star formation rate. In order to understand the details of star formation, it is therefore essential to understand the properties of turbulence, in particular the probability distribution of density in turbulent clouds. We present formaldehyde volume density measurements of a non-star-forming cloud along the line of sight towards W49A. We use these measurements in conjunction with total mass estimates from 13CO to infer the shape of the density probability distribution function. This method…
We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high resolution (10243) numerical simulations, we confirm the theory that the spatial mean growth rate is proportional to the gas-density variance. This also results in broadening of the grain-size distribution (GSD) due to turbulence-induced variation of the grain-growth rate. We show, for the first time in a detailed numerical simulation of hydrodynamic turbulence, that the GSD evolves towards a shape which is a reflection of the gas-d…
The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths, and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temper…
Momentum deposition by radiation pressure from young, massive stars may help to destroy molecular clouds and unbind stellar clusters by driving large-scale outflows. We extend our previous numerical radiation hydrodynamic study of turbulent, star-forming clouds to analyze the detailed interaction between non-ionizing UV radiation and the cloud material. Our simulations trace the evolution of gas and star particles through self-gravitating collapse, star formation, and cloud destruction via radiation-driven outflows. These models are idealized in that we include only radiation feedback and adop…
Supersonic flows in the interstellar medium (ISM) are believed to be a key driver of the molecular cloud formation and evolution. Among molecular clouds' properties, the ratio between the solenoidal and compressive modes of turbulence plays important roles in determining the star formation efficiency. We use numerical simulations of supersonic converging flows of the warm neutral medium (WNM) resolving the thermal instability to calculate the early phase of molecular cloud formation, and investigate the turbulence structure and the density probability distribution function (density PDF) of the…
Molecular clouds exhibit lognormal probability density functions (PDF) of mass densities, which are thought to arise as a consequence of isothermal, supersonic turbulence. Star formation is then widely assumed to occur in perturbations in which gravitational collapse is faster than the rate of change due to turbulent motions. Here we use direct numerical simulations to measure this rate as a function of density for a range of turbulent Mach numbers, and show it is faster at high densities than at low densities. Furthermore, we show that both the density PDF and rate of change arise naturally i…
It has recently been shown that turbulence in the interstellar medium (ISM) can significantly accelerate the growth of dust grains by accretion of molecules, but the turbulent gas-density distribution also plays a crucial role in shaping the grain-size distribution. The growth velocity, i.e., the rate of change of the mean grain radius, is proportional to the local gas density if the growth species (molecules) are well-mixed in the gas. As a consequence, grain growth happens at vastly different rates in different locations, since the gas-density distribution of the ISM shows a considerable var…
Studying the driving modes of turbulence is important for characterizing the impact of turbulence in various astrophysical environments. The driving mode of turbulence is parameterized by $b$, which relates the width of the gas density PDF to the turbulent Mach number; $b\approx 1/3$, $1$, and $0.4$ correspond to driving that is solenoidal, compressive, and a natural mixture of the two, respectively. In this work, we use high-resolution (sub-pc) ALMA $^{12}$CO ($J$ = $2-1$), $^{13}$CO ($J$ = $2-1$), and C$^{18}$O ($J$ = $2-1$) observations of filamentary molecular clouds in the star-forming re…
This paper is a numerical study of the condensation of the warm neutral medium (WNM) into cold neutral medium (CNM) structures under the effect of turbulence and thermal instability. Using low resolution simulations we explored the impact of the WNM initial density and properties of the turbulence (stirring in Fourier with a varying mix of solenoidal and compressive modes) on the cold gas formation. Two sets of initial conditions which match the observations were selected to produce high resolution simulations (1024^3) allowing to study in details the properties of the produced dense structure…
Numerical simulations of shock-driven, supersonic interstellar turbulence in colliding three-temperature laboratory plasmas
Imperial College London（帝国理工学院）；Princeton University（普林斯顿大学）；University of Toronto（多伦多大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Massachusetts Institute of Technology（麻省理工学院）
The probability density function (PDF) of the logarithmic density contrast, $s=\ln (ρ/ρ_0)$, with gas density $ρ$ and mean density $ρ_0$, for hydrodynamical supersonic turbulence is well-known to have significant non-Gaussian (intermittent) features that monotonically increase with the turbulent Mach number, $\mathcal{M}$. By studying the mass- and volume-weighted $s$-PDF for an ensemble of 36 sub-to-trans-Alfvenic mean-field, supersonic, isothermal turbulence simulations with different modes of driving, relevant to molecular gas in the cool interstellar medium, we show that a more intricate p…
