We present a physics-based statistical theory of a force-free magnetic field in the corona above a turbulent accretion disk. The field is represented by a statistical ensemble of loops tied to the disk. Each loop evolves under several physical processes: Keplerian shear, turbulent random walk of the disk footpoints, and reconnection with other loops. To build a statistical description, we introduce the distribution function of loops over their sizes and construct a kinetic equation that governs its evolution. This loop kinetic equation is formally analogous to Boltzmann's kinetic equation, with loop-loop reconnection described by a binary collision integral. A dimensionless parameter is introduced to scale the (unknown) overall rate of reconnection relative to Keplerian shear. After solving for the loop distribution function numerically, we calculate self-consistently the distribution of the mean magnetic pressure and dissipation rate with height, and the equilibrium shapes of loops of different sizes. We also compute the energy and torque associated with a given loop, as well as the total magnetic energy and torque in the corona. We explore the dependence of these quantities on the reconnection parameter and find that they can be greatly enhanced if reconnection between loops is suppressed.
We calculate the proton distribution function due to heating by subsonic (Alfvenic) turbulence in a weakly magnetized collisionless plasma. The distribution function is nonthermal. For non-relativistic energies, it is an exponential of the magnitude of the proton velocity. For ultra-relativistic energies, it can be characterized as a power law with a momentum-dependent slope.
We use three-dimensional magnetohydrodynamical (MHD) simulations to study the formation of a corona above an initially weakly magnetized, isothermal accretion disk. We also describe a modification to time-explicit numerical algorithms for MHD which enables us to evolve highly stratified disks for many orbital times. We find that MHD turbulence driven by the magnetorotational instability (MRI) produces strong amplification of weak fields within two scale heights of the disk midplane in a few orbital times. About 25 % of the magnetic energy generated by the MRI within two scale heights escapes d…
We present a detailed calculation of the mechanism by which the Accretion-Ejection Instability can extract accretion energy and angular momentum from a magnetized disk, and redirect them to its corona. In a disk threaded by a poloidal magnetic field of the order of equipartition with the gas pressure, the instability is composed of a spiral wave (analogous to galactic ones) and a Rossby vortex. The mechanism detailed here describes how the vortex, twisting the footpoints of field lines threading the disk, generates Alfven waves propagating to the corona. We find that this is a very efficient m…
X-ray binaries and AGN show observational evidence for magnetized hot plasmas. Despite years of data, very little is known on these {\it coronae} especially on the mechanisms responsible for their heating, and most models simply assume their existence. However, understanding its properties has now become a key issue of the AGN and microquasars modelling. Here we consider the effect of a strong vertical magnetic field on the corona AGN and X-ray binaries and show that its modeling (structure, heating) must be reconsidered. As a first step, we present one mechanism that could extract energy from…
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of this theory to protogalaxies is rather limited. The reason is that in protogalaxies …
Observations of protostellar disks indicate the presence of the magnetic field of thermal (or superthermal) strength. In such a strong magnetic field, many MHD instabilities responsible for turbulent transport of the angular momentum are suppressed. We consider the shear-driven instability that can occur in protostellar disks even if the field is superthermal. This instability is caused by the combined influence of shear and compressibility in a magnetized gas and can be an efficient mechanism to generate turbulence in disks. The typical growth time is of the order of several rotation periods.
The heating of magnetized plasma by propagation of Alfven waves is calculated as a function of the magnetic field spectral density. The results can be applied to evaluate the heating power of the solar corona at known data from satellites' magnetometers. This heating rate can be incorporated in global models for heating of the solar corona and creation of the solar wind. The final formula for the heating power is illustrated with a model spectral density of the magnetic field obtained by analysis of the Voyager 1 mission results. The influence of high frequency dissipative modes is also taken …
Using numerical methods, we systematically study in the framework of ideal MHD the effect of magnetic fields on heat transfer within a turbulent gas. We measure the rates of passive scalar diffusion within magnetized fluids and make the comparisons a) between MHD and hydro simulations, b) between different MHD runs with different values of the external magnetic field (up to the energy equipartition value), c) between thermal conductivities parallel and perpendicular to magnetic field. We do not find apparent suppression of diffusion rates by the presence of magnetic fields, which implies that …
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no the back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of the kinematic dynamo theory to protogalaxies is rather limited. The reason is th…
Context : We present a self-consistent model of solar coronal heating, originally developed by Heyvaert & Priest (1992), in which we include the dynamical effect of the background magnetic field along a coronal structure by using exact results from wave MHD turbulence (Galtier et al. 2000). Aims : We evaluate the heating rate and the microturbulent velocity for comparison with observations in the quiet corona, active regions and also coronal holes. Methods :The coronal structures are assumed to be in a turbulent state maintained by the slow erratic motions of the magnetic footpoints. A descrip…
We present the results of three-dimensional global magnetohydrodynamic (MHD) simulations of the Parker-shearing instability in a differentially rotating torus initially threaded by toroidal magnetic fields. An equilibrium model of magnetized torus is adopted as an initial condition. When $β_0 = P_{\rm gas}/P_{\rm mag} \sim 1$ at the initial state, magnetic flux buoyantly escapes from the disk and creates loop-like structures similar to those in the solar corona. Inside the torus, growth of non-axisymmetric magneto-rotational (or Balbus & Hawley) instability generates magnetic turbulence. Magne…
We use ZEUS-MP to perform high resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent fragmentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic wave…
We present an analytic description of turbulent, MHD disk accretion around black holes that specifically addresses the relationship between radial and vertical, transport, thereby complementing and extending numerical simulations. The azimuthal-vertical component of the magnetic stress is fundamental to an understanding of disk--corona--outflow coupling: when it is important for driving the angular momentum transport and mass accretion in the disk, it also has an important influence on the disk--corona--outflow energy budget. The Poynting flux derived from the product of this term with the Kep…
A new theory is presented for the development of circular polarization as radio waves propagate through the turbulent, birefringent interstellar medium. The fourth order moments of the wavefield are calculated and it is shown that unpolarized incident radiation develops a nonzero variance in circular polarization. A magnetized turbulent medium causes the Stokes parameters to scintillate in a non-identical manner. A specific model for this effect is developed for the case of density fluctuations in a uniform magnetic field.
We perform direct numerical simulations of an externally driven two-dimensional magnetohydrodynamic system over extended periods of time to simulate the dynamics of a transverse section of a solar coronal loop. A stationary and large-scale magnetic forcing was imposed, to model the photospheric motions at the magnetic loop footpoints. A turbulent stationary regime is reached, which corresponds to energy dissipation rates consistent with the heating requirements of coronal loops. The temporal behavior of quantities such as the energy dissipation rate show clear indications of intermittency, whi…
(Abridged) We present the results of three dimensional calculations for the MHD evolution of an adiabatic supernova remnant in both a uniform and turbulent interstellar medium using the RIEMANN framework of Balsara. In the uniform case, which contains an initially uniform magnetic field, the density structure of the shell remains largely spherical, while the magnetic pressure and synchrotron emissivity are enhanced along the plane perpendicular to the field direction. This produces a bilateral or barrel-type morphology in synchrotron emission for certain viewing angles. We then consider a case…
Context: The location of coronal heating in magnetic loops has been the subject of a long-lasting controversy: does it occur mostly at the loop footpoints, at the top, is it random, or is the average profile uniform? Aims: We try to address this question in model loops with MHD turbulence and a profile of density and/or magnetic field along the loop. Methods: We use the ShellAtm MHD turbulent heating model described in Buchlin & Velli (2006), with a static mass density stratification obtained by the HydRad model (Bradshaw & Mason 2003). This assumes the absence of any flow or heat conduction s…
We develop a model of thin turbulent accretion discs supported by magnetic pressure of turbulent magnetic fields. This applies when the turbulent kinetic and magnetic energy densities are greater than the thermal energy density in the disc. Whether such discs survive in nature or not remains to be determined, but here we simply demonstrate that self-consistent solutions exist when the alpha-prescription for the viscous stress, similar to that of the original Shakura-Sunyaev model, is used. We show that α\sim 1 for the strongly magnetized case and we calculate the radial structure and emission …
The molecular component of the Galaxy is comprised of turbulent, magnetized clouds, many of which are self-gravitating and form stars. To understand how these clouds' evolution may depend on their level of turbulence, mean magnetization, and degree of self-gravity, we perform a survey of direct numerical MHD simulations in 2.5 dimensions. Two of our independent survey parameters allow us to model clouds which either meet or fail conditions for magneto-Jeans stability and magnetic criticality. Our third survey parameter allows us to initiate turbulence of either sub- or super-Alfvénic amplitude…
The set of equations for magnetohydrodynamic (MHD) waves in a shear flow is consecutively derived. The proposed scenario involves the presence of a self-sustained turbulence and magnetic field. In the framework of Langevin--Burgers approach the influence of the turbulence is described by an additional external random force in the MHD system. Kinetic equation for the spectral density of the slow magnetosonic (Alfvenic) mode is derived in the short wavelength (WKB) approximation. The results show a pressing need for conduction of numerical Monte Carlo (MC) simulations with a random driver to tak…
We investigate the behavior of the magnetic pressure, $b^2$, in fully turbulent MHD flows in ``1+2/3'' dimensions by means of its effect on the probability density function (PDF) of the density field. We start by reviewing our previous results for general polytropic flows, according to which the value of the polytropic exponent $γ$ determines the functional shape of the PDF. A lognormal density PDF appears in the isothermal ($γ=1$) case, but a power-law tail at either large or small densities appears for large Mach numbers when $γ>1$ and $γ< 1$, respectively. In the isothermal magnetic case, t…
This paper studies the turbulent cascade of magnetic energy in weakly collisional magnetized plasmas. A cascade model is presented, based on the assumptions of local nonlinear energy transfer in wavenumber space, critical balance between linear propagation and nonlinear interaction times, and the applicability of linear dissipation rates for the nonlinearly turbulent plasma. The model follows the nonlinear cascade of energy from the driving scale in the MHD regime, through the transition at the ion Larmor radius into the kinetic Alfven wave regime, in which the turbulence is dissipated by kine…
We use global magnetohydrodynamic simulations, in a pseudo-Newtonian potential, to investigate the temporal variability of accretion discs around Schwarzschild black holes. We use the vertically-averaged magnetic stress in the simulated disc as a proxy for the rest-frame dissipation, and compute the observed emission by folding this through the transfer function describing the relativistic beaming, light bending and time delays near a non-rotating black hole. The temporal power spectrum of the predicted emission from individual annuli in the disc is described by a broken power law, with indice…
3D numerical simulations of a horizontal magnetic flux tube emergence with different twist are carried out in a computational domain spanning the upper layers of the convection zone to the lower corona. We use the Oslo Staggered Code to solve the full MHD equations with non-grey and non-LTE radiative transfer and thermal conduction along the magnetic field lines. The emergence of the magnetic flux tube input at the bottom boundary into a weakly magnetized atmosphere is presented. The photospheric and chromospheric response is described with magnetograms, synthetic images and velocity field dis…
We present a self-similar, steady-state model describing both a magnetized accretion disc and a magnetohydrodynamic jet. We focus on the role of a hot corona in such a structure. This corona enables the disc to launch various types of jets. By considering the energy conservation, we also present a diagnostic of the luminosity of the magnetized disc, which could explain some observational signatures of galactic objects.
We describe the results of a sequence of simulations of gravitational collapse in a turbulent magnetized region. The parameters are chosen to be representative of molecular cloud material. We find that several protostellar cores and filamentary structures of higher than average density form. The filaments inter-connect the high density cores. Furthermore, the magnetic field strengths are found to correlate positively with the density, in agreement with recent observations. We make synthetic channel maps of the simulations and show that material accreting onto the cores is channelled along the …
Heating of magnetized turbulent plasma is calculated in the framework of Burgers turbulence [A.M. Polyakov, Phys. Rev. E. 52, 6183 (1995)]. Explicit formula for the energy flux of Alfven waves along the magnetic field is presented. The Alfven waves are considered as intermediary between the turbulent energy and the heat. The derived results are related to a wave channel of heating of the solar corona. If we incorporate amplification of Alfven waves by shear flow the suggested model of heating can be applied to analysis of the missing viscosity of accretion discs and to reveal why the quasars a…
Aims: We investigate the formation of flux ropes in a flux emergence region and their rise into the outer atmosphere of the Sun. Methods: We perform 3D numerical experiments solving the time-dependent and resistive MHD equations. Results: A sub-photospheric twisted flux tube rises from the solar interior and expands into the corona. A flux rope is formed within the expanding field, due to shearing and reconnection of field lines at low atmospheric heights. If the tube emerges into a non-magnetized atmosphere, the flux rope rises, but remains confined inside the expanding magnetized volume. On …
Qualitative arguments are presented to demonstrate that the energy density of magnetic fields in matter accreting onto a black hole inside the marginally stable orbit is automatically comparable to the rest-mass energy density of the accretion flow. Several consequences follow: magnetic effects must be dynamically significant, but cannot be so strong as to dominate; outward energy transport in Alfven waves may alter the effective efficiency of energy liberation; and vertical magnetic stresses in this region may contribute to "coronal" activity.
We present steady-state calculations of self-similar magnetized accretion discs driving cold, adiabatic, non-relativistic jets. For the first time, both the magnetic torque due to the jets and a turbulent "viscous" torque are taken into account. This latter torque allows a dissipation of the accretion power as radiation at the disc surfaces, while the former predominantly provides jets with power. The parameter space of these structures has been explored. It is characterized by four free parameters, namely the disc aspect ratio and three MHD turbulence parameters, related to the anomalous magn…
A great deal of study has been carried out over the last twenty years on the origin of the magnetic activity in the Galactic center. One of the most popular hypotheses assumes milli-Gauss magnetic field with poloidal geometry, pervading the inner few hundred parsecs of the Galactic-center region. However, there is a growing observational evidence for the large-scale distribution of a much weaker field of B \lesssim 10 micro G in this region. Here, we propose that the Galactic-center magnetic field originates from turbulent activity that is known to be extreme in the central hundred parsecs. In…
By performing MHD simulations, we investigate the mass loss of intermediate- and low-mass stars from main sequence (MS) to red giant branch (RGB) phases. Alfven waves, which are excited by the surface convections travel outwardly and dissipate by nonlinear processes to accelerate and heat the stellar winds. We dynamically treat these processes in open magnetic field regions from the photospheres to 25 stellar radii. When the stars evolve to slightly blueward positions of the dividing line (Linsky & Haisch), the steady hot corona with temperature, ~ 1MK, suddenly disappears. Instead, many hot (…
We analyze 3D numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic field. We sum over nonlinear interactions within Fourier wavebands and find that the time scale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions we show that the turbulent motions in the plane perpendicular to the local mean magnetic field are similar to ordinary hydrodynamic turbulence while motions parallel to the field are consist…
We investigate the rotational equilibrium state of a disk accreting magnetized stars using axisymmetric magnetohydrodynamic (MHD) simulations. In this ``locked'' state, the spin-up torque balances the spin-down torque so that the net average torque on the star is zero. We investigated two types of initial conditions, one with a relatively weak stellar magnetic field and a high coronal density, and the other with a stronger stellar field and a lower coronal density. We observed that for both initial conditions the rotation of the star is locked to the rotation of the disk. In the second case, t…
In this paper and a companion work, we report on the first global numerical simulations of self-gravitating magnetized tori, subject in particular to the influence of the magnetorotational instability (MRI). In this work, paper I, we restrict our calculations to the study of the axisymmetric evolution of such tori. Our goals are twofold: (1) to investigate how self-gravity influences the global structure and evolution of the disks; and (2) to determine whether turbulent density inhomogeneities can be enhanced by self-gravity in this regime. As in non self-gravitating models, the linear growth …
We present a theoretical framework for plasma turbulence in astrophysical plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks). The key assumptions are that the turbulence is anisotropic with respect to the mean magnetic field and frequencies are low compared to the ion cyclotron frequency. The energy injected at the outer scale scale has to be converted into heat, which ultimately cannot be done without collisions. A KINETIC CASCADE develops that brings the energy to collisional scales both in space and velocity. Its nature depends on the physics of plasma fluctuations.…
We present two-dimensional MHD numerical simulations for the interaction of high-velocity clouds with both magnetic and non-magnetic Galactic thick gaseous disks. For the magnetic models, the initial magnetic field is oriented parallel to the disk, and we consider two different field topologies (with and without tension effects): parallel and perpendicular to the plane of motion of the clouds. The impinging clouds move in oblique trajectories and fall toward the central disk with different initial velocities. The $B$-field lines are distorted and compressed during the collision, increasing the…
Numerical simulations of turbulent, magnetized, differentially rotating flows driven by the magnetorotational instability are often used to calculate the effective values of alpha viscosity that is invoked in analytical models of accretion discs. In this paper we use various dynamical models of turbulent magnetohydrodynamic stresses, as well as numerical simulations of shearing boxes, to show that angular momentum transport in MRI-driven accretion discs cannot be described by the standard model for shear viscosity. In particular, we demonstrate that turbulent magnetorotational stresses are not…
We report the first attempt to mode decomposition of the velocity field using wavelet transforms in the application to the magnetized turbulence analysis. We compare results of the separation with respect to the global and local mean magnetic field for models with a strong and weak external magnetic field. We show, that for models with a strong external magnetic field our results are relatively consistent for both methods. However, for superAlfvénic turbulence with spatially variable direction of the local mean magnetic field the differences are substantial.
We present the first global simulations of self-gravitating magnetized tori. The simulations are performed with Zeus-2D and GLOBAL. We find the magnetorotational instability (MRI) to behave similarly in a self-gravitating environment as in previous simulations of non self-gravitating systems: enhancement of turbulent angular momentum transport follows the linear phase. The torus quickly develops a two component structure composed of an inner thick disk in Keplerian rotation and an outer massive disk. We compare this result with zero mass global simulations in 2D, and also present preliminary r…
We present the results of a 2-D, two fluid (ions and neutrals) simulation of the ambipolar filamentation process, in which a magnetized, weakly ionized plasma is stirred by turbulence in the ambipolar frequency range. The higher turbulent velocity of the neutrals in the most ionized regions gives rise to a non-linear force driving them out of these regions, so that the initial ionization inhomogeneities are strongly amplified. This effect, the ambipolar filamentation, causes the ions and the magnetic flux to condense and separate from the neutrals, resulting in a filamentary structure.
