The role of supersonic turbulence in structuring the interstellar medium (ISM) remains an unsettled question. Here, this problem is investigated using a newexact law of compressible isothermal hydrodynamic turbulence, which involves two-point correlations in physical space. The new law is shown to have a compact expression that contains a single flux term reminiscent of the incompressible case and a source term with a simple expression whose sign is given by the divergence of the velocity. The law is then used to investigate the properties of such a turbulence at integral Mach number $4$ produced by a massive numerical simulation with a grid resolution of $10,048^3$ points. The flux (resp. source) term was found to have positive (resp. negative) contribution to the total energy cascade rate, which is interpreted as a direct cascade amplified by compression, while their sum is constant in the inertial range. Using a local (in space) analysis it is shown that the source is mainly driven by filamentary structures in which the flux is negligible. Taking positive defined correlations reveals the existence of different turbulent regimes separated by the sonic scale, which determines the scale over which the non-negligible source modifies the scaling of the flux. Our study provides new insight into the dynamics and structures of supersonic interstellar turbulence.
The slope of the power spectrum of the density field in isothermal supersonic compressible turbulence
ENS de Lyon, CRAL UMR5574, Universite Claude Bernard Lyon 1, CNRS（里昂高等师范学校，CRAL UMR5574，克洛德·贝尔纳里昂大学，法国国家科学研究中心）；School of Physics, University of Exeter（埃克塞特大学物理学院）
Supersonic turbulence plays an important role in a number of extreme astrophysical and terrestrial environments, yet its understanding remains rudimentary. We use data from a three-dimensional simulation of supersonic isothermal turbulence to reconstruct an exact fourth-order relation derived analytically from the Navier-Stokes equations (Galtier and Banerjee, Phys. Rev. Lett., vol. 107, 2011, p. 134501). Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogues of the four-…
The turbulent dynamo may explain the origin of cosmic magnetism. While the exponential amplification of magnetic fields has been studied for incompressible gases, little is known about dynamo action in highly-compressible, supersonic plasmas, such as the interstellar medium of galaxies and the early Universe. Here we perform the first quantitative comparison of theoretical models of the dynamo growth rate and saturation level with three-dimensional magnetohydrodynamical simulations of supersonic turbulence with grid resolutions of up to 1024^3 cells. We obtain numerical convergence and find th…
Using data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier--Stokes equation by Falkovich, Fouxon and Oz [2010 New relations for correlation functions in Navier--Stokes turbulence. J. Fluid Mech. 644, 465]. That relation, for compressible barotropic fluids, was derived assuming turbulence generated by a large-scale force. However, compressible turbulence in simulations is usually initialized and maintained by a large-scale acceleration, as in gravity-driven astrophysic…
Based on ideas by Woodward et al., a subgrid scale model that is applicable to highly compressible turbulence is presented. Applying the subgrid scale model in large eddy simulations of forced supersonic turbulence, the bottleneck effect is largely reduced and, thereby, approximate scaling laws can be obtained at relatively low numerical resolution. In agreement with previous results from PPM simulations without explicit subgrid scale model, it is found that the energy spectrum function for the velocity field with fractional density-weighing, rho^(1/3)u, varies substantially with the forcing, …
We provide a procedure for identification of dominating compressible and Alfvenic MHD modes or isotropic turbulence in synchrotron emission polarization maps of Galactic objects. The results for the region of North Galactic Pole, Orion molecular cloud complex and the star-forming complex Cygnus X are presented.
The interstellar turbulence is magnetized and thus anisotropic. The anisotropy of turbulent magnetic fields and velocities is imprinted in the related observables, rotation measures (RMs), and velocity centroids (VCs). This anisotropy provides valuable information on both the direction and strength of the magnetic field. However, its measurement is difficult especially in highly supersonic turbulence in cold interstellar phases due to the distortions by isotropic density fluctuations. By using 3D simulations of supersonic and sub-Alfvénic magnetohydrodynamic(MHD) turbulence, we find that the p…
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressib…
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…
We introduce a new method for observationally estimating the fraction of momentum density ($ρ{\mathbf{v}}$) power contained in solenoidal modes (for which $\nabla \cdot ρ{\mathbf{v}} = 0$) in molecular clouds. The method is successfully tested with numerical simulations of supersonic turbulence that produce the full range of possible solenoidal/compressible fractions. At present the method assumes statistical isotropy, and does not account for anisotropies caused by (e.g.) magnetic fields. We also introduce a framework for statistically describing density--velocity correlations in turbulent cl…
Understanding the physics of turbulence is crucial for many applications, including weather, industry, and astrophysics. In the interstellar medium (ISM), supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars. Here we present a simulation of interstellar turbulence with a grid resolution of 10048^3 cells that allows us to determine the position and width of the sonic scale (l_s) - the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~ …
Owing to the complexity of turbulent magnetic fields, modeling the diffusion of cosmic rays is challenging. Based on the current understanding of anisotropic magnetohydrodynamic (MHD) turbulence, we use test particles to examine the cosmic rays' superdiffusion in the direction perpendicular to the mean magnetic field. By changing Alfven Mach number $M_A$ and sonic Mach number $M_S$ of compressible MHD simulations, our study covers a wide range of astrophysical conditions including subsonic warm gas phase and supersonic cold molecular gas. We show that freely streaming cosmic rays' perpendicula…
The emergence of large-scale magnetic fields observed in the diffuse interstellar medium is explained by a turbulent dynamo. The underlying transport coefficients have previously been extracted from numerical simulations. So far, this was restricted to the kinematic regime, but we aim to extend our analysis into the realm of dynamically important fields. This marks an important step on which derived mean-field models rely to explain observed equipartition strength fields. As in previous work, we diagnose turbulent transport coefficients by means of the test-field method. We derive quenching fu…
The rich structure that we observe in molecular clouds is due to the interplay between strong magnetic fields and supersonic (turbulent) velocity fluctuations. The velocity fluctuations interact with the magnetic field, causing it too to fluctuate. Using numerical simulations, we explore the nature of such magnetic field fluctuations, $\vec{δB}$, over a wide range of turbulent Mach numbers, $\mathcal{M} = 2 - 20$ (i.e., from weak to strong compressibility), and Alfvén Mach numbers, $\mathcal{M}_{\text{A}0} = 0.1 - 100$ (i.e., from strong to weak magnetic mean fields, $B_0$). We derive a compre…
A model, which is widely used for inertial rang statistics of supersonic turbulence in the context of molecular clouds and star formation, expresses (measurable) relative scaling exponents Z_p of two-point velocity statistics as a function of two parameters, beta and Delta. The model relates them to the dimension D of the most dissipative structures, D=3-Delta/(1-beta). While this description has proved most successful for incompressible turbulence (beta=Delta=2/3, and D=1), its applicability in the highly compressible regime remains debated. For this regime, theoretical arguments suggest D=2 …
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…
The interstellar medium of the Milky Way and nearby disk galaxies harbours large-scale coherent magnetic fields of Microgauss strength, that can be explained via the action of a mean-field dynamo. As in our previous work, we aim to quantify dynamo effects that are self-consistently emerging in realistic direct magnetohydrodynamic simulations, but we generalise our approach to the case of a non-local (non-instantaneous) closure relation, described by a convolution integral in space (time). To this end, we leverage our comprehensive simulation framework for the supernova-regulated turbulent mult…
Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new, higher order-accurate, low dissipation numerical method which requires no additional dissipation or local "fixes" for stable execution. We describe PPML, a local stencil variant of the popular PPM algorithm for solving the equations of compressible ideal magnetohydrodynamics. The principal difference between PPML and PPM is that cell interface states are evolv…
Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $σ^2_{ρ/ρ_0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parameterises the star formation (SF) rate of a cloud. However, models for $σ^2_{ρ/ρ_0}$ all share a common feature -- the variance is assumed to be isotropic. This assumption does not hold when …
This study is motivated by recent observations on the ubiquitous interstellar density filaments and guided by the modern theory of magnetohydrodynamic (MHD) turbulence. The interstellar turbulence shapes the observed density structure. The perpendicular turbulent mixing, as the fundamental dynamics of MHD turbulence, naturally entails parallel filaments presented in both the diffuse medium and molecular clouds (MCs). The minimum width is determined by the perpendicular neutral-ion decoupling scale in partially ionized media. Differently, dense perpendicular filaments arise in highly supersonic…
We investigate the clustering and dynamics of nano-sized particles (nano-dust) in high-resolution ($1024^3$) simulations of compressible isothermal hydrodynamic turbulence. It is well-established that large grains will decouple from a turbulent gas flow, while small grains will tend to trace the motion of the gas. We demonstrate that nano-sized grains may cluster in a turbulent flow (fractal small-scale clustering), which increases the local grain density by at least a factor of a few. In combination with the fact that nano-dust grains may be abundant in general, and the increased interaction …
Observations reveal a uniform Kolmogorov turbulence throughout the diffuse ionized interstellar medium (ISM) and supersonic turbulence preferentially located in the Galactic plane. Correspondingly, we consider the Galactic distribution of electron density fluctuations consisting of not only a Kolmogorov density spectrum but also a short-wave-dominated density spectrum with the density structure formed at small scales due to shocks. The resulting dependence of the scatter broadening time on the dispersion measure (DM) naturally interprets the existing observational data for both low and high-DM…
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 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 $\langle {\bs u} \cdot \nabla s | s\rangle$…
Coagulation driven by supersonic turbulence is primarily an astrophysical problem because coagulation processes on Earth are normally associated with incompressible fluid flows at low Mach numbers, while dust aggregation in the interstellar medium (ISM) for instance is an example of the opposite regime. We study coagulation of inertial particles in compressible turbulence using high-resolution direct and shock-capturing numerical simulations with a wide range of Mach numbers from nearly incompressible to moderately supersonic. The particle dynamics is simulated by representative particles and …
This study is motivated by recent observations on ubiquitous interstellar density filaments and guided by modern theories of compressible magnetohydrodynamic (MHD) turbulence. The interstellar turbulence shapes the observed density structures. As the fundamental dynamics of compressible MHD turbulence, perpendicular turbulent mixing of density fluctuations entails elongated density structures aligned with the local magnetic field, accounting for low-density parallel filaments seen in diffuse atomic and molecular gas. The elongation of low-density parallel filaments depends on the turbulence an…
We review the use of velocity centroids statistics to recover information of interstellar turbulence from observations. Velocity centroids have been used for a long time now to retrieve information about the scaling properties of the turbulent velocity field in the interstellar medium. We show that, while they are useful to study subsonic turbulence, they do not trace the statistics of velocity in supersonic turbulence, because they are highly influenced by fluctuations of density. We show also that for sub-Alfvénic turbulence (both supersonic and subsonic) two-point statistics (e.g. correlati…
Probing magnetic fields in the interstellar medium (ISM) is notoriously challenging. Motivated by the modern theories of magnetohydrodynamic (MHD) turbulence and turbulence anisotropy, we introduce the Structure-Function Analysis (SFA) as a new approach to measure the magnetic field orientation and estimate the magnetization. We analyze the statistics of turbulent velocities in three-dimensional compressible MHD simulations through the second-order structure functions in both local and global reference frames. In the sub-Alfvenic turbulence with the magnetic energy larger than the turbulent en…
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.
We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the densit…
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, $τ_{\rm c}$, to the flow dynamical time, $τ_{\rm dyn}$ (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…
The magnetic field strength in interstellar clouds can be estimated indirectly by using the spread of dust polarization angles ($δθ$). The method developed by Davis 1951 and by Chandrasekhar and Fermi 1953 (DCF) assumes that incompressible magnetohydrodynamic (MHD) fluctuations induce the observed dispersion of polarization angles, deriving $B\propto 1/δθ$ (or, $δθ\propto M_{A}$, in terms of the Alfvénic Mach number). However, observations show that the interstellar medium (ISM) is highly compressible. Recently, Skalidis & Tassis 2021 (ST) relaxed the incompressibility assumption and derived i…
Formation of interstellar clouds as a consequence of thermal instability is studied using two-dimensional two-fluid magnetohydrodynamic simulations. We consider the situation of converging, supersonic flows of warm neutral medium in the interstellar medium that generate a shocked slab of thermally unstable gas in which clouds form. We found, as speculated in paper I, that in the shocked slab magnetic pressure dominates thermal pressure and the thermal instability grows in the isochorically cooling, thermally unstable slab that leads formation of HI clouds whose number density is typically n < …
A continuous supersonic flow reactor has been used to measure rate constants for the C + NH3 reaction over the temperature range 50 to 296 K. C atoms were created by the pulsed laser photolysis of CBr4. The kinetics of the title reaction were followed directly by vacuum ultra-violet laser induced fluorescence (VUV LIF) of C loss and through H formation. The experiments show unambiguously that the reaction is rapid at 296 K, becoming faster at lower temperatures, reaching a value of 1.8 10-10 cm3 molecule-1 s-1 at 50 K. As this reaction is not currently included in astrochemical networks, its i…
Dust polarization is a powerful tool for studying the magnetic field properties in the interstellar medium (ISM). However, it does not provide a direct measurement of its strength. Different methods havebeen developed which employ both polarization and spectroscopic data in order to infer the field strength. The most widely applied methods have been developed by Davis (1951), Chandrasekhar & Fermi (1953) (DCF), Hildebrand et al. (2009) and Houde et al.(2009) (HH09). They rely on the assumption that isotropic turbulent motions initiate the propagation of Alvfén waves. Observations,however, indi…
The Galactic interstellar turbulence affects the density distribution and star formation. We introduce a new method of measuring interstellar turbulent density spectra by using the dispersion measures (DMs) of a large sample of pulsars. Without the need of invoking multiple tracers, we obtain nonuniversal density spectra in the multi-phase interstellar medium over different ranges of length scales. By comparing the analytical structure function of DMs with the observationally measured one in different areas of sky, we find a shallow density spectrum arising from the supersonic turbulence in co…
