In this paper, extending the investigation developed in an earlier paper (Cremaschini et al., 2008), we pose the problem of the kinetic description of gravitational Hall-MHD equilibria which may arise in accretion disks (AD) plasmas close to compact objects. When intense EM and gravitational fields, generated by the central object, are present, a convenient approach can be achieved in the context of the Vlasov-Maxwell description. In this paper the investigation is focused primarily on the following two aspects:
1) the formulation of the kinetic treatment of G-Hall-MHD equilibria. Based on the identification of the relevant first integrals of motion, we show that an explicit representation can be given for the equilibrium kinetic distribution function. For each species this is represented as a superposition of suitable generalized Maxwellian distributions;
2) the determination of the constraints to be placed on the fluid fields for the existence of the kinetic equilibria. In particular, this permits a unique determination of the functional form of the species number densities and of the fluid partial pressures, in terms of suitably prescribed flux functions.
In previous work stable approximately axisymmetric equilibrium configurations for magnetic stars were found by numerical simulation. Here I investigate the conditions under which more complex, non-axisymmetric configurations can form. I present numerical simulations of the formation of stable equilibria from turbulent initial conditions and demonstrate the existence of non-axisymmetric equilibria consisting of twisted flux tubes lying horizontally below the surface of the star, meandering around the star in random patterns. Whether such a non-axisymmetric equilibrium or a simple axisymmetric e…
The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fundamental importance for understanding the phenomenology of accretion disks (AD) around compact objects (black holes, neutron stars, etc.). The very existence of these equilibria is actually suggested by observations, which show evidence of quiescent, and essentially non-relativistic, AD plasmas close to compact stars, thus indicating that accretion disks may be characterized by slowly varying EM and fluid fields. These (EM) fields, in particular the electric field, may locally be extremely intense…
All axisymmetric self-similar equilibria of self-gravitating, rotating, isothermal systems are identified by solving the nonlinear Poisson equation analytically. There are two families of equilibria: (1) Cylindrically symmetric solutions in which the density varies with cylindrical radius as R^(-alpha), with 0 <= alpha <= 2. (2) Axially symmetric solutions in which the density varies as f(theta)/r^2, where `r' is the spherical radius and `theta' is the co-latitude. The singular isothermal sphere is a special case of the latter class with f(theta)=constant. The axially symmetric equilibrium con…
AIMS: We develop an optimization principle for computing stationary MHD equilibria. METHODS: Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma uses non-force-free MHD equilibria. Previous versions of the code have been used to compute non-linear force-free coronal magnetic fields from photospheric measurements. The program uses photospheric vector magnetograms and coronal EUV images as input. We tested our reconstruction code with the help of a semi-analytic MHD-equilibrium. The quality of the reconstruction was judged by comparing the exact and…
We present results from axisymmetric, time-dependent magnetohydrodynamic (MHD) simulations of the collapsar model for gamma-ray bursts. We begin the simulations after the 1.7 MSUN iron core of a 25 MSUN presupernova star has collapsed and study the ensuing accretion of the 7 MSUN helium envelope onto the central black hole formed by the collapsed iron core. We consider a spherically symmetric progenitor model, but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum and a weak radial magnetic field. Our MHD simulations include a realistic equation …
Numerical simulations of MHD accretion flows in the vicinity of a supermasssive black hole provide important insights to the problem of why and how systems -- such as the Galactic Center -- are underluminous and variable. To access applicability of such flows to real objects, we examine the dynamical MHD studies with computations of the time dependent radiation spectra predicted by the simulations. We apply Monte Carlo methods to calculate spectra predicted by the time-dependent model of an axisymmetic MHD flow accreting onto a black hole presented by Proga and Begelman. Our calculations show …
Magnetohydrodynamic (MHD) and two-fluid quasi-neutral equilibria with azimuthal symmetry, gravity and arbitrary ratios of (nonrelativistic) flow speed to acoustic and Alfven speeds are investigated. In the two-fluid case, the mass ratio of the two species is arbitrary, and the analysis is therefore applicable to electron-positron plasmas. The methods of derivation can be extended in an obvious manner to several charged species. Generalized Grad-Shafranov equations, describing the equilibrium magnetic field, are derived. Flux function equations and Bernoulli relations for each species, together…
The MHD instabilities can generate complex field topologies even if the initial field configuration is a very simple one. We consider the stability properties of magnetic configurations containing a toroidal and an axial field. In this paper, we concentrate mainly on the behavior of non-axisymmetric perturbations in axisymmetric magnetic configurations. The stability is treated by a linear analysis of ideal MHD equations.In the presence of an axial field, it is shown that the instability can occur for a wide range of the azimuthal wavenumber $m$, and its growth rate increases with increasing $…
We present the results of a series of axisymmetric time-dependent magnetohydrodynamic (MHD) simulations of the propagation of cooling, overdense jets, motivated by the properties of outflows associated with young stellar objects. A variety of initial field strengths and configurations are explored for both steady and time-variable (pulsed) jets. Even apparently weak magnetic fields with strengths B < 60 micro-G in the pre-shocked jet beam can have a significant effect on the dynamics, for example by altering the density, width, and fragmentation of thin shells formed by cooling gas. A linear a…
The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad-Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as $\Ma = 6\times 10^{-4}\Msun$, by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to $\Ma < 10^{-4}…
Using the fluid-magnetofluid formalism, we obtain axisymmetric stability criteria for a composite disc system consisting of stellar and gaseous magnetized singular isothermal discs (MSIDs). Lou & Zou recently constructed exact global stationary configurations for both axisymmetric and nonaxisymmetric coplanar MHD perturbations in such a composite MSID system and proposed the MHD $D_s-$criteria for axisymmetric stability by the hydrodynamic analogy. In a different perspective, we derive and analyze here the time-dependent WKBJ dispersion relation in the low-frequency and tight-winding regime to…
We present a systematic method for constructing two-dimensional magnetohydrodynamic equilibria with compressible flow in Cartesian geometry. This systematic method has already been developed in spherical geometry and applied in modelling solar and stellar winds and outflows (Vlahakis & Tsinganos,1998) but is derived here in Cartesian geometry in the context of the solar atmosphere for the first time. Using the method we find several new classes of solutions, some of which generalise known solutions, including the Kippenhahn & Schlüter (1957) and Hood & Anzer (1990) solar prominence models and …
In Paper I (Fiege & Pudritz, 1999), we constructed models of filamentary molecular clouds that are truncated by a realistic external pressure and contain a rather general helical magnetic field. We address the stability of our models to gravitational fragmentation and axisymmetric MHD-driven instabilities. By calculating the dominant modes of axisymmetric instability, we determine the dominant length scales and growth rates for fragmentation. We find that the role of pressure truncation is to decrease the growth rate of gravitational instabilities by decreasing the self-gravitating mass per un…
We report the results of 3-dimensional magnetohydrodynamic (MHD) simulations of a jet formation by the interaction between an accretion disk and a large scale magnetic field. The disk is not treated as a boundary condition but is solved self-consistently. To investigate the stability of MHD jet, the accretion disk is perturbed with a non-axisymmetric sinusoidal or random fluctuation of the rotational velocity. The dependences of the jet velocity $(v_z)$, mass outflow rate $(\dot{M}_w)$, and mass accretion rate $(\dot{M}_a)$ on the initial magnetic field strength in both non-axisymmetric cases …
We carried out global three-dimensional resistive magnetohydrodynamic simulations of galactic gaseous disks to investigate how the galactic magnetic fields are amplified and maintained. We adopt a steady axisymmetric gravitational potential given by \cite*{Miy80}. As the initial condition, we assume a warm ($T\sim10^{5} \mathrm{K}$) rotating gas torus centered at $\varpi=10 \mathrm{kpc}$ threaded by weak azimuthal magnetic fields. Numerical results indicate that in differentially rotating galactic gaseous disks, magnetic fields are amplified due to magneto-rotational instability and magnetic t…
My lecture is devoted to the analytical results available for a large class of axisymmetric stationary flows in the vicinity of compact astrophysical objects. First, the most general case is formulated corresponding to the axisymmetric stationary MHD flow in the Kerr metric. Then, I discuss the hydrodynamical version of the Grad-Shafranov equation. Although not so well-known as the full MHD one, it allows us to clarify the nontrivial structure of the Grad-Shafranov approach as well as to discuss the simplest version of the 3+1-split language -- the most convenient one for the description of id…
Current-carrying flows, in the laboratory and in astrophysical jets, can form remarkably stable magnetic structures. Decades of experience shows that such flows often build equilibria that reverse field directions, evolving to an MHD Taylor state, which has remarkable stability properties. We model jets and the magnetic bubbles they build as reversed field pinch equilibria by assuming the driver current to be stiff in the MHD sense. Taking the jet current as rigid and a fixed function of position, we prove a theorem: that the same, simple MHD stability conditions guarantee stability, even afte…
I show that the self-consistent solution of the problem of MHD plasma flow in magnetosphere of an oblique rotator with an initially split-monopole magnetic field is reduced to the solution of the similar problem for the axisymmetric rotator. All properties of the MHD cold plasma flows from the axisymmetric rotators with the initially split-monopole magnetic field are valid for the oblique rotators as well. Rotational losses of the oblique rotator do not depend on the inclination angle and there is no temporal evolution of this angle. Self-consistent analytical and numerical solutions for the a…
We present, for the first time, the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, ${\bf E\cdot B}=0$, everywhere. The unique distribution of electric current along the open magnetic field lines which is required for the solution to be continuous and smooth is obtained numerically. With the geometry of the field lines thus determined we compute the dynamics of the associated MHD wind. The main result is that …
Global stationary configurations of both aligned and logarithmic spiral MHD perturbations are constructed analytically within an axisymmetric background ofrazor-thin scale-free gas disc, which is embedded in an axisymmetric gravitational potential of a dark matter halo and involves an isopedic magnetic field almost vertically threaded through the disc plane. The scale-free index $β$ of the disc rotation speed $v_θ\propto R^{-β}$ falls in the rangeof $(-1/2 , 1/2)$ where $R$ is the cylindrical radius. With the holding-back of a deep background dark matter halo potential, the isopedic magnetic f…
We find exact and explicit solutions of the axisymmetric MHD equations of a self-gravitating polytropic gas. These solutions are able to describe a flat (uniform density) subsonic internal core, contracting homologously, of a collapsing cloud with aspherical pressure, aspherical gravitationnal potential, magnetic field and rotation. Two of the solutions describing the collapse of a rotating and magnetized cloud present outflow at the pole or at the equator.
The dynamical effects of magnetic fields in models of radiative, Herbig-Haro (HH) jets have been studied in a number of papers. For example, magnetized, radiative jets from variable sources have been studied with axisymmetric and 3D numerical simulations. In this paper, we present an analytic model describing the effect of a toroidal magnetic field on the internal working surfaces that result from a variability in the ejection velocity. We find that for parameters appropriate for HH jets the forces associated with the magnetic field dominate over the gas pressure force within the working surfa…
This is the first paper about the fragmentation and mass outflow in the molecular cloud by using three-dimensional MHD nested-grid simulations. The binary star formation process is studied paying particular attention to the fragmentation of a rotating magnetized molecular cloud. We assume an isothermal rotating and magnetized cylindrical cloud in hydrostatic balance. Non-axisymmetric as well as axisymmetric perturbations are added to the initial state and the subsequent evolutions are studied. The evolution is characterized by three parameters: the amplitude of the non-axisymmetric perturbatio…
This paper presents an application of the recent relativistic HLLC approximate Riemann solver by Mignone & Bodo to magnetized flows with vanishing normal component of the magnetic field. The numerical scheme is validated in two dimensions by investigating the propagation of axisymmetric jets with toroidal magnetic fields. The selected jet models show that the HLLC solver yields sharper resolution of contact and shear waves and better convergence properties over the traditional HLL approach.
We present results from axisymmetric, time-dependent magnetohydrodynamic (MHD) simulations of the collapsar model for gamma-ray bursts. Our main conclusion is that, within the collapsar model, MHD effects alone are able to launch, accelerate and sustain a strong polar outflow. We also find that the outflow is Poynting flux-dominated, and note that this provides favorable initial conditions for the subsequent production of a baryon-poor fireball.
Some basic structures in planetary nebulae are modeled as self-organized magnetohydrodynamic (MHD) plasma configurations with radial flow. These configurations are described by time self-similar dynamics, where space and time dependences of each physical variable are in separable form. Axisymmetric toroidal MHD plasma configuration is solved under the gravitational field of a central star of mass $M$. With an azimuthal magnetic field, this self-similar MHD model provides an equatorial structure in the form of an axisymmetric torus with nested and closed toroidal magnetic field lines. In the ab…
Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall-MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toro…
The linear stability of MHD Taylor-Couette flow of infinite vertical extension is considered for various magnetic Prandtl numbers Pm. The calculations are performed for a wide gap container with \hatη=0.5 with an axial uniform magnetic field excluding counterrotating cylinders. For both hydrodynamically stable and unstable flows the magnetorotational instability produces characteristic minima of the Reynolds number for certain (low) magnetic field amplitudes and Pm> 0.01. For Pm <~ 1 there is a characteristic magnetic field amplitude beyond which the instability sets in in form of nonaxisymmet…
We investigate a theoretical MHD disc problem involving a composite disc system of gravitationally coupled stellar and gaseous discs with a coplanar magnetic field in the presence of an axisymmetric dark matter halo. The two discs are expediently approximated as razor-thin, a ring-like magnetic field, and a power-law rotation curve in radius . By imposing the scale-free condition, we construct analytically stationary global MHD perturbation configurations for both aligned and logarithmic spiral patterns. MHD perturbation configurations in a composite system of partial discs in the presence of …
