We study energy dissipation and heating by supersonic MHD turbulence in molecular clouds using Athena, a new higher-order Godunov code. We analyze the dependence of the saturation amplitude, energy dissipation characteristics, power spectra, sonic scaling, and indicators of intermittency in the turbulence on factors such as the magnetic field strength, driving scale, energy injection rate, and numerical resolution. While convergence in the energies is reached at moderate resolutions, we find that the power spectra require much higher resolutions that are difficult to obtain. In a 1024^3 hydro run, we find a power law relationship between the velocity dispersion and the spatial scale on which it is measured, while for an MHD run at the same resolution we find no such power law. The time-variability and temperature intermittency in the turbulence both show a dependence on the driving scale, indicating that numerically driving turbulence by an arbitrary mechanism may not allow a realistic representation of these properties. We also note similar features in the power spectrum of the compressive component of velocity for supersonic MHD turbulence as in the velocity spectrum of an initially-spherical MHD blast wave, implying that the power law form does not rule out shocks, rather than a turbulent cascade, playing a significant role in the regulation of energy transfer between spatial scales.
The dynamics of molecular clouds is characterized by supersonic random motions in the presence of a magnetic field. We study this situation using numerical solutions of the three-dimensional compressible magneto-hydrodynamic (MHD) equations in a regime of highly supersonic random motions. The non-LTE radiative transfer calculations are performed through the complex density and velocity fields obtained as solutions of the MHD equations, and more than 5x10^5 synthetic molecular spectra are obtained. We use a numerical flow without gravity or external forcing. The flow is super-Alfvenic and corre…
We study the statistics of density for supersonic turbulence in a medium with magnetic pressure larger than the gaseous pressure. This study is motivated by molecular cloud research. Our simulations exhibit clumpy density structures, which contrast increases with the Mach number. At 10 Machs densities of some clumps are three orders of magnitude higher than the mean density. These clumps give rise to flat and approximately isotropic density spectrum corresponding to the random distribution of clumps in space. We claim that the clumps originate from our random, isotropic turbulence driving. Whe…
We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there are surprisingly similar relationships between the mean of the time-averaged PDF and the turbulent Mach number for driven hydrodynamic and strong-field MHD turbulence. There is, however, a large scatter about these relations, indicating a high level of temporal and spatial variability in the PDF. Thus, the PDF of the mass density is unlikely to be a good mea…
We discuss a new mechanism of dust acceleration that acts in a turbulent magnetized medium. The magnetohydrodynamic (MHD) turbulence includes both fluid motions and magnetic fluctuations. We show that while the fluid motions bring about grain motions through the drag, the electromagnetic fluctuations, can accelerate grains through resonant interactions. In this paper we calculate grain acceleration by gyroresonance in Cold Neutral Medium. We consider both incompressible and compressible MHD modes. We show that fast modes dominate grain acceleration. For the parameters chosen, fast modes render…
We compare the statistical properties of J=1-0 13CO spectra observed in the Perseus Molecular Cloud with synthetic J=1-0 13CO spectra from a 5 pc model cloud. The synthetic spectra are computed solving the non-LTE radiative transfer problem for a model cloud obtained as solutions of the 3-D magneto-hydrodynamic (MHD) equations in both the highly supersonic and super-Alfvenic regimes of random flows. We present several statistical results that demonstrate remarkable similarity between real data and the synthetic cloud. The three-dimensional structure and dynamics of molecular clouds like Perseu…
We present fully three-dimensional hydrodynamical and magnetohydrodynamical simulations of supersonic, radiative cooling jets propagating into homogeneous and stratified environments based on Smoothed Particle Hydrodynamics technique.
We consider MHD waves as a heating source of cool cores of galaxy clusters. In particular, we focus on transverse waves (Alfven waves), because they can propagate a longer distance than longitudinal waves (sound waves). Using MHD simulations, we found that the transverse waves can stably heat a cool core if the wave period is large enough (>~ 10^8 yr). Moreover, the longitudinal waves that are created as a by-product of the nonlinear evolution of the transverse waves could be observed as the 'ripples' found in cool cores.
We review how supersonic turbulence can both prevent and promote the collapse of molecular clouds into stars. First we show that decaying turbulence cannot significantly delay collapse under conditions typical of molecular clouds, regardless of magnetic field strength so long as the fields are not supporting the cloud magnetohydrostatically. Then we review possible drivers and examine simulations of driven supersonic and trans Alfvénic turbulence, finally including the effects of self-gravity. Our preliminary results show that, although turbulence can support regions against gravitational coll…
We report an extensive set of two-dimensional MHD simulations exploring the role and evolution of magnetic fields in the dynamics of supersonic plasma clumps. We examine the influence of both ambient field strength and orientation on the problem. Of those two characteristics, field orientation is far more important in the cases we have considered with $β_0 = p_g/p_b \ge 1$. That is due to the geometry-sensitivity of field stretching/amplification from large-scale shearing motions around the bullet. When the ambient magnetic field is transverse to the bullet motion, even a very modest field, we…
We calculate the relative grain-grain motions arising from interstellar magnetohydrodynamic (MHD) turbulence. The MHD turbulence includes both fluid motions and magnetic fluctuations. While the fluid motions accelerate grains through hydro-drag, the electromagnetic fluctuations accelerate grains through resonant interactions. We consider both incompressive (Alfvén) and compressive (fast and slow) MHD modes and use descriptions of MHD turbulence obtained in Cho & Lazarian (2002). Calculations of grain relative motion are made for realistic grain charging and interstellar turbulence that is cons…
Using Particle-In-Cell simulations i.e. in the kinetic plasma description the discovery of a new mechanism of parallel electric field generation was recently reported. Here we show that the electric field generation parallel to the uniform unperturbed magnetic field can be obtained in a much simpler framework using the ideal magnetohydrodynamics (MHD) description. In ideal MHD the electric field parallel to the uniform unperturbed magnetic field appears due to fast magnetosonic waves which are generated by the interaction of weakly non-linear Alfvén waves with the transverse density inhomogene…
Molecular clouds have broad linewidths suggesting turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. It has classically been thought that supersonic hydrodynamical turbulence would dissipate its energy quickly, but that the introduction of strong magnetic fields could maintain these motions. In a previous paper it has been shown, however, that isothermal, compressible, MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to mainta…
We present high resolution numerical simulations of compressible magnetohydrodynamic (MHD) turbulence. We concentrate on studies of spectra and anisotropy of velocity and density. We describe a technique of separating different magnetohydrodynamic (MHD) modes (slow, fast and Alfven) and apply it to our simulations. For the mildly supersonic case, velocity and density show anisotropy. However, for the highly supersonic case, we observe steepening of the slow mode velocity spectrum and isotropization of density. Our present studies show that the spectrum of density gets substantially {\it flatte…
We investigate coronal heating and acceleration of the high- and low-speed solar wind in the open field region by dissipation of fast and slow magnetohydrodynamical (MHD) waves through MHD shocks. Linearly polarized \Alfven (fast MHD) waves and acoustic (slow MHD) waves travelling upwardly along with a magnetic field line eventually form fast switch-on shock trains and hydrodynamical shock trains (N-waves) respectively to heat and accelerate the plasma. We determine one dimensional structure of the corona from the bottom of the transition region (TR) to 1AU under the steady-state condition by …
We report results of a three dimensional, high resolution (up to 512^3) numerical investigation of supersonic compressible magnetohydrodynamic turbulence. We consider both forced and decaying turbulence. The model parameters are appropriate to conditions found in Galactic molecular clouds. We find that the dissipation time of turbulence is of order the flow crossing time or smaller, even in the presence of strong magnetic fields. About half the dissipation occurs in shocks. Weak magnetic fields are amplified and tangled by the turbulence, while strong fields remain well ordered.
We show that the coronal heating and the acceleration of the fast solar wind in the coronal holes are natural consequence of the footpoint fluctuations of the magnetic fields at the photosphere by one-dimensional, time-dependent, and nonlinear magnetohydrodynamical simulation with radiative cooling and thermal conduction. We impose low-frequency (<0.05Hz) transverse photospheric motions, corresponding to the granulations, with velocity <dv> = 0.7$km/s. In spite of the attenuation in the chromosphere by the reflection, the sufficient energy of the generated outgoing Alfven waves transmit into t…
The photoelectric heating is believed to be the main heating mechanism in cool HI clouds. The heating rate can be estimated through observations of the [CII] line emission, since this is the main coolant in regions where the photoelectric effect dominates the heating. Comparison of the [CII] emission with the far-infrared (FIR) emission allows to constrain the efficiency of the photoelectric heating, using model calculations that take into account the strength of the radiation field. Recent [CII] observations carried out with the ISO satellite have made this study possible. In this work we stu…
We model the hydrodynamic evolution of the plasma confined in a coronal loop, 30000 km long, subject to the heating of nanoflares due to intermittent magnetic dissipative events in the MHD turbulence produced by loop footpoint motions. We use the time-dependent distribution of energy dissipation along the loop obtained from a hybrid shell model, occurring for a magnetic field of about 10 G in corona; the relevant heating per unit volume along the loop is used in the Palermo-Harvard loop plasma hydrodynamic model. We describe the results focussing on the effects produced by the most intense hea…
I review particle heating by MHD turbulence in collisionless plasmas appropriate to advection-dominated accretion flows. These considerations suggest that the preferential turbulent heating of protons assumed by theoretical models is only achieved for relatively subthermal magnetic fields.
A forward model is described in which we synthesize spectra from an ab-initio 3D MHD simulation of an outer stellar atmosphere, where the coronal heating is based on braiding of magnetic flux due to photospheric footpoint motions. We discuss the validity of assumptions such as ionization equilibrium and investigate the applicability of diagnostics like the differential emission measure inversion. We find that the general appearance of the synthesized corona is similar to the solar corona and that, on a statistical basis, integral quantities such as average Doppler shifts or differential emissi…
We discuss constraints on the rates of stirring and dissipation of MHD turbulence in molecular clouds. Recent MHD simulations suggest that turbulence in clouds decays rapidly, thus providing a significant source of energy input, particularly if driven at small scales by, for example, bipolar outflows. We quantify the heating rates by combining the linewidth-size relations, which describe global cloud properties, with numerically determined dissipation rates. We argue that, if cloud turbulence is driven on small internal scales, the $^{12}$CO flux (enhanced by emission from weakly supersonic sh…
Density is the turbulence statistics that is most readily available from observations. Different regimes of turbulence correspond to different density spectra. For instance, the viscosity-damped regime of MHD turbulence relevant, for instance, to partially ionized gas, can be characterized by shallow and very anisotropic spectrum of density. This spectrum can result in substantial variations of the column densities. Addressing MHD turbulence in the regime when viscosity is not important over the inertial range, we demonstrate with numerical simulations that it is possible to reproduce both the…
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for revisions in the picture of particle acceleration. We make use of the recently established scaling of slow and fast MHD modes in strong and weak MHD turbulence to provide a systematic study of particle acceleration in magnetic pressure (low-$β$) and gaseous pressure (high-$β$) dominated plasmas. We consider the acceleration by large scale compressions in both slow and fast particle diffusion limits. We compare the results with the acceleration rate that arises from resonance scattering and Transit-Time Damping (T…
We perform three-dimensional (3D) compressible MHD simulations over many dynamical times for an extended range of sonic and Alfven Mach numbers and analyze the statistics of 3D density and 2D column density, which include probability distribution functions, spectra, skewness, kurtosis, She-Leveque exponents, and genus. In order to establish the relation between the statistics of the observables, i.e. column densities, and the underlying 3D statistics of density, we analyze the effects of cloud boundaries. We define the parameter space for 3D measures to be recovered from column densities. In a…
We solve numerically ideal, 2.5D, MHD equations in Cartesian coordinates, with a plasma beta of 0.0001 starting from the equilibrium that mimics a footpoint of a large curvature radius solar coronal loop or a polar region plume. On top of such an equilibrium, a purely Alfvénic, linearly polarised, plane wave is launched. In the context of the coronal heating problem a new two stage mechanism of plasma heating is presented by putting emphasis, first, on the generation of parallel electric fields within an ideal MHD description directly, rather than focusing on the enhanced dissipation mechanism…
MHD turbulence plays a central role in the physics of star-forming molecular clouds and the interstellar medium. I here show that MHD turbulence in molecular clouds must be driven to account for the observed supersonic motions in the clouds, as even strongly magnetized turbulence decays quickly. I then show that driven MHD turbulence can globally support gravitationally unstable regions, but local collapse inevitably occurs. Differences in the strength of driving and the gas density may explain the very different rates of star formation observed in different galaxies. The driving mechanism for…
We investigate a possibility of heating of the loops and other closed magnetic structures in active regions of the solar corona by the flow of solar wind (plus other flows that may be present) across the magnetic field lines (that are perpendicular to the flow), in a similar manner as a conventional MHD generator works. A simple model is formulated which allows to calculate the typical currents generated by this mechanism. This enables to make a judgement whether the loops in solar active regions can be heated by the proposed mechanism through the associated Ohmic dissipation. It is shown that…
Long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary different regimes of turbulence develop: strong turbulence is found for …
An analytical MHD model of coronal loops with compressible flows and including heating is compared to observational data. The model is constructed via a systematic nonlinear separation of the variables method used to calculate several classes of exact MHD equilibria in Cartesian geometry and uniform gravity. By choosing a particularly versatile solution class with a large parameter space we are able to calculate models whose loop length, shape, plasma density, temperature and velocity profiles are fitted to loops observed with TRACE, SoHO/CDS and SoHO/SUMER. Synthetic emission profiles are als…
Modeling the structure of molecular clouds depends on good methods to statistically compare simulations with observations in order to constrain the models. Here we characterize a suite of hydrodynamical and magnetohydrodynamical (MHD) simulations of supersonic turbulence using an averaged wavelet transform, the Delta-variance, that has been successfully used to characterize observations. We find that, independent of numerical resolution and dissipation, the only models that produce scale-free, power-law Delta-variance spectra are those with hypersonic Mach numbers above M ~ 4, while slower sup…
Plasmas in an accretion flow are heated by MHD turbulence generated through the magneto-rotational instability. The viscous stress driving the accretion is intimately connected to the microscopic processes of turbulence dissipation. We show that, in a few well-observed black hole accretion systems, there is compelling observational evidence of efficient electron heating by turbulence or collective plasma effects in low accretion states, when Coulomb collisions are not efficient enough to establish a thermal equilibrium between electrons and ions at small radii. However, charged particles reach…
Recent work on Alfvenic turbulence by Goldreich & Sridhar (1995; GS) suggests that the energy cascades almost entirely perpendicular to the local magnetic field. As a result, the cyclotron resonance is unimportant in dissipating the turbulent energy. Motivated by the GS cascade, we calculate the linear collisionless dissipation of Alfven waves with frequencies much less than the proton cyclotron frequency, but with perpendicular wavelengths of order the Larmor radius of thermal protons. In plasmas appropriate to hot accretion flows (proton temperature much greater than electron temperature) th…
Particle heating in advection-dominated accretion flows (ADAFs) by nonlinear MHD (Alfvenic) turbulence is investigated. Such turbulence with highly-fluctuating magnetic fields, $\tilde B\sim B_0$, is believed to be naturally produced by the magnetic shearing instability near the nonlinear saturation. It is shown that the energy is dissipated in the parallel cascade, which occurs due to nonlinear compressibility of high-amplitude turbulence, and predominantly heats protons, but not electrons. The conservative limit on the electron--to--proton heating fraction is $δ\lesssim{\rm few}\times10^{-2}…
We aim to identify the physical processes which occur in the magnetic network of the chromosphere and which contribute to its dynamics and heating. Specifically, we study the propagation of transverse (kink) MHD waves which are impulsively excited in flux tubes through footpoint motions. When these waves travel upwards, they get partially converted to longitudinal waves through nonlinear effects (mode coupling). By solving the nonlinear, time-dependent MHD equations we find that significant longitudinal wave generation occurs in the photosphere typically for Mach numbers as low as 0.2 and that…
We present a direct numerical and analytical study of driven supersonic MHD turbulence that is believed to govern the dynamics of star-forming molecular clouds. We describe statistical properties of the turbulence by measuring the velocity difference structure functions up to the fifth order. In particular, the velocity power spectrum in the inertial range is found to be close to E(k) \~ k^{-1.74}, and the velocity difference scales as <|Δu|>~ L^{0.42}. The results agree well with the Kolmogorov--Burgers analytical model suggested for supersonic turbulence in [astro-ph/0108300]. We then genera…
Supersonic turbulent flows of magnetized gas are believed to play an important role in the dynamics of star-forming clouds in galaxies. Understanding statistical properties of such flows is crucial for developing a theory of star formation. In this letter we propose a unified approach for obtaining the velocity scaling in compressible and super--Alfvénic turbulence, valid for arbitrary sonic Mach number, \ms. We demonstrate with numerical simulations that the scaling can be described with the She--Lévêque formalism, where only one parameter, interpreted as the Hausdorff dimension of the most i…
