R. V. E. Lovelace

ROSSBY WAVE INSTABILITY OF THIN ACCRETION DISKS - II. DETAILED LINEAR THEORY

In an earlier work we identi—ed a global, nonaxisymmetric instability associated with the presence of an extreme in the radial pro—le of the key function L(r) 4 (&)/i2)S2@! in a thin, inviscid, nonmagnetized accretion disk. Here &(r) is the surface mass density of the disk, )(r) is the angular rotation rate, S(r )i s the speci—c entropy, ! is the adiabatic index, and i(r) is the radial epicyclic frequency. The dispersion relation of the instability was shown to be similar to that of Rossby waves in planetary atmospheres. In this paper, we present the detailed linear theory of this Rossby wave instability and show that it exists for a wider range of conditions, speci—cally, for the case where there is a ii jump ˇˇ over some range of r in &(r) or in the pressure P(r). We elucidate the physical mechanism of this instability and its dependence on various parameters, including the magnitude of the ii bump ˇˇ or ii jump,ˇˇ the azimuthal mode number, and the sound speed in the disk. We —nd a large parameter range where the disk is stable to axisym- metric perturbations but unstable to the nonaxisymmetric Rossby waves. We —nd that growth rates of the Rossby wave instability can be high, for relative small jumps or bumps. We discuss possible D0.2) K conditions which can lead to this instability and the consequences of the instability. Subject headings: accretion, accretion diskshydrodynamicsinstabilitieswaves

Magnetohydrodynamic Simulations of Disk-Magnetized Star Interactions in the Quiescent Regime: Funnel Flows and Angular Momentum Transport

Magnetohydrodynamic (MHD) simulations have been used to study disk accretion to a rotating magnetized star with an aligned dipole moment. Quiescent initial conditions were developed in order to avoid the fast initial evolution seen in earlier studies. A set of simulations was performed for different stellar magnetic moments and rotation rates. Simulations have shown that the disk structure is significantly changed inside a radius rbr where magnetic braking is significant. In this region the disk is strongly inhomogeneous. Radial accretion of matter slows as it approaches the area of strong magnetic field, and a dense ring and funnel flow (FF) form at the magnetospheric radius rm, where the magnetic pressure is equal to the total, kinetic plus thermal, pressure of the matter. FFs, where the disk matter moves away from the disk plane and flows along the stellar magnetic field, are found to be stable features during many rotations of the disk. The dominant force driving matter into the FF is the pressure gradient force, while gravitational force accelerates it as it approaches the star. The magnetic force is much smaller than the other forces. The FF is found to be strongly sub-Alfvenic everywhere. The FF is subsonic close to the disk, but it becomes supersonic well above the disk. Matter reaches the star with a velocity close to that of free fall. Angular momentum is transported to the star dominantly by the magnetic field. In the disk the transport of angular momentum is mainly by the matter, but closer to the star the matter transfers its angular momentum to the magnetic field, and the magnetic field is dominant in transporting angular momentum to the surface of the star. For slowly rotating stars we observed that magnetic braking leads to the deceleration of the inner regions of the disk, and the star spins up. For a rapidly rotating star, the inner regions of the disk rotate with a super-Keplerian velocity, and the star spins down. The average torque is found to be zero when the corotation radius rcor ≈ 1.5rm. The evolution of the magnetic field in the corona of the disk depends on the ratio of magnetic to matter energies in the corona and in the disk. Most of the simulations were performed in the regime of a relatively dense corona where the matter energy-density was larger than the magnetic energy-density. In this case the coronal magnetic field gradually opens, but the velocity and density of outflowing matter are small. In a test case where a significant part of the corona was in the field-dominated regime, more dramatic opening of the magnetic field was observed with the formation of magnetocentrifugally driven outflows. Numerical applications of our simulation results are made to T Tauri stars. We conclude that our quasi-stationary simulations correspond to the classical T Tauri stage of evolution. Our results are also relevant to cataclysmic variables and magnetized neutron stars in X-ray binaries.

Magnetocentrifugally Driven Winds: Comparison of MHD Simulations with Theory

Stationary MHD outflows from a rotating accretion disk are investigated numerically by time-dependent axisymmetric simulations. The initial magnetic field is taken to be a split-monopole poloidal field configuration frozen into the disk. The disk is treated as a perfectly conducting, time-independent density boundary [?(r)] in Keplerian rotation. The outflow velocity from this surface is not specified but rather is determined self-consistently from the MHD equations. The temperature of the matter outflowing from the disk is small in the region where the magnetic field is inclined away from the symmetry axis (cv) but relatively high (c v) at very small radii in the disk, where the magnetic field is not inclined away from the axis. We have found a large class of stationary MHD winds. Within the simulation region, the outflow accelerates from thermal velocity ( ~cs) to a much larger asymptotic poloidal flow velocity of the order of ?, where M is the mass of the central object and ri is the inner radius of the disk. This asymptotic velocity is much larger than the local escape speed and is larger than fast magnetosonic speed by a factor of ~1.75. The acceleration distance for the outflow, over which the flow accelerates from ~0% to, say, 90% of the asymptotic speed, occurs at a flow distance of about 80ri. The outflows are approximately spherical, with only small collimation within the simulation region. The collimation distance over which the flow becomes collimated (with divergence less than, say, 100) is much larger than the size of our simulation region. Close to the disk the outflow is driven by the centrifugal force, while at all larger distances the flow is driven by the magnetic force, which is proportional to -(rB)2, where B is the toroidal field. Our stationary numerical solutions allow us to (1) compare the results with MHD theory of stationary flows, (2) investigate the influence of different outer boundary conditions on the flows, and (3) investigate the influence of the shape of the simulation region on the flows. Different comparisons were made with the theory. The ideal MHD integrals of motion (constants on flux surfaces) were calculated along magnetic field lines and were shown to be constants with an accuracy of 5%-15%. Other characteristics of the numerical solutions were compared with the theory, including conditions at the Alfv?n surface. Different outer boundary conditions on the toroidal component of the magnetic field were investigated. We conclude that the commonly used free boundary condition on the toroidal field leads to artificial magnetic forces on the outer boundaries, which can significantly influence to the calculated flows. New outer boundary conditions are proposed and investigated that do not give artificial forces. We show that simulated flows may depend on the shape of the simulation region. Namely, if the simulation region is elongated in the z-direction, then Mach cones on the outer cylindrical boundary may be partially directed inside the simulation region. Because of this, the boundary can have an artificial influence on the calculated flow. This effect is reduced if the computational region is approximately square or if it is spherical. Simulations of MHD outflows with an elongated computational region can lead to artificial collimation of the flow.

Theory of magnetic insulation

An investigation is made of the behavior of a high voltage diode for the situation where the cathode‐anode gap is initially filled with a transverse magnetic field. An exact relativistic self‐consistent equilibrium is found for the electron sheath which is expected to form under the condition where the applied magnetic field is sufficiently strong to prevent electrons from flowing between the electrodes. The condition on the magnetic field for “insulation” is found to be (eBy0d/mc2)2 > 2|eV0/mc2| + (eV0/mc2)2, where By0 is the applied magnetic field, V0 is the voltage across the diode, d is the cathode‐anode separation in the x direction, and —e and m are the electron charge and rest mass, respectively.

Self-collimated electromagnetic jets from magnetized accretion disks

The global electrodynamics of a viscous resistive accretion disk around a Schwarzschild black hole with a force-free plasma outside of the disk is worked out. The magnetic field in the disk is assumed to include a well-ordered component. The magnetic field and fluid dynamics of the disk are tested, simplifying the induction equation and solving for the flux function and the toroidal magnetic field. A Greens function method is used to obtain far-field solutions of the basic electromagnetic field equation for the plasma outside of the disk. The solutions are found to include self-collimated electromagnetic jets. The overall energy conservation for the disk-jet system is considered, and a global condition is derived which imposes an upper bound on the reaction of the accretion luminosity which can be carried away by the jets. 36 references.

Propeller regime of disk accretion to rapidly rotating stars

We present results of axisymmetric magnetohydrodynamic simulations of the interaction of a rapidly rotating, magnetized star with an accretion disk. The disk is considered to have a finite viscosity and magnetic diffusivity. The main parameters of the system are the star’s angular velocity and magnetic moment, and the disk’s viscosity and diffusivity. We focus on the “propeller” regime where the inner radius of the disk is larger than the corotation radius. Two types of magnetohydrodynamic flows have been found as a result of simulations: “weak” and “strong” propellers. The strong propellers are characterized by a powerful disk wind and a collimated magnetically dominated outflow or jet from the star. The weak propellers have only weak outflows. We investigated the time-averaged characteristics of the interaction between the main elements of the system, the star, the disk, the wind from the disk, and the jet. Rates of exchange of mass and angular momentum between the elements of the system are derived as a function of the main parameters. The propeller mechanism may be responsible for the fast spinningdown of the classical T Tauri stars in the initial stages of their evolution, and for the spinning-down of accreting millisecond pulsars.

Dynamics of Magnetic Loops in the Coronae of Accretion Disks

Axisymmetric magnetohydrodynamic (MHD) simulations are used to study the evolution of general magnetic field configurations where a magnetic field B threads different radii of a differentially rotating accretion disk. The differential rotation of the footpoints of B field loops at different radii on the disk surface causes a twisting of the coronal magnetic field, an increase in the coronal magnetic energy, and an opening of the loops in the region where the magnetic pressure is larger than the matter pressure (β 1). In the region where β 1, the loops may be only partially opened. Current layers form in the narrow regions that separate oppositely directed magnetic field lines. Reconnection occurs in these layers as a result of the small numerical magnetic diffusivity of the code. In contrast with the case of the solar coronal magnetic field, the combination of magnetic and centrifugal forces leads to significant matter outflow from the disk. The faster rotation of the inner part of the disk gives a stronger outflow from this part of the disk. The outflow accelerates with increasing distance from the disk up to velocities in excess of the escape speed. The outflows show some collimation within the computational region and have a large power output mainly in the form of a Poynting flux. Thus these outflows are pertinent to the origin of astrophysical jets. We present results of a survey of simulation runs for the behavior of magnetic loops and outflows for a wide range of field strengths B and mass outflow rates j. The model and processes observed are relevant to the coronae of accretion disks around stellar-mass objects, including pre-main-sequence stars, compact stars, and black holes, as well as the coronae of disks around massive black holes in active galactic nuclei. Opening of magnetic field loops may lead to transient and/or steady outflows, while reconnection events may be responsible for X-ray flares in such objects.

Magnetohydrodynamic simulations of outflows from accretion disks

Magnetohydrodynamic simulations have been made of the formation of outflows from a Keplerian disk threaded by a magnetic field. The disk is treated as a boundary condition, where matter is ejected with Keplerian azimuthal speed and poloidal speed less than the slow magnetosonic velocity, and where boundary conditions on the magnetic field correspond to a highly conducting disk. Initially, the space above the disk, the corona, is filled with high specific entropy plasma in thermal equilibrium in the gravitational potential of the central object. The initial magnetic field is poloidal and is represented by a superposition of monopoles located below the plane of the disk. The rotation of the disk twists the initial poloidal magnetic field, and this twist propagates into the corona pushing and collimating matter into jetlike outflow in a cylindrical region. Matter outflowing from the disk flows and accelerates in the z-direction owing to both the magnetic and pressure gradient forces. The flow accelerates through the slow magnetosonic and Alfven surfaces and at larger distances through the fast magnetosonic surface. The flow velocity of the jet is approximately parallel to the z-axis, and the collimation results from the pinching force of the toroidal magnetic field. For a nonrotating disk no collimation is observed.

Magnetically driven jets and winds

Four equations for the origin and propagation of nonrelativistic jets and winds are derived from the basic conservation laws of ideal MHD. The axial current density is negative in the vicinity of the axis and positive at larger radii; there is no net current because this is energetically favored. The magnetic field is essential for the jet solutions in that the zz-component of the magnetic stress acts, in opposition to gravity, to drive matter through the slow magnetosonic critical point. For a representative self-consistent disk/jet solution relevant to a protostellar system, the reaction of the accreted mass expelled in the jets is 0.1, the ratio of the power carried by the jets to the disk luminosity is 0.66, and the ratio of the boundary layer to disk luminosities is less than about 0.13. The stars rotation rate decreases with time even for rotation rates much less than the breakup rate.

Advection of Magnetic Fields in Accretion Disks: Not So Difficult After All

We show that a large-scale, weak magnetic field threading a turbulent accretion disk tends to be advected inward, contrary to previous suggestions that it will be stopped by outward diffusion. The efficient inward transport is a consequence of the diffuse, magnetically dominated surface layers of the disk, where the turbulence is suppressed and the conductivity is very high. This structure arises naturally in three-dimensional simulations of magnetorotationally unstable disks, and we demonstrate here that it can easily support inward advection and compression of a weak field. The advected field is anchored in the surface layer but penetrates the main body of the disk, where it can generate strong turbulence and produce values of α (i.e., the turbulent stress) that are large enough to match observational constraints; typical values of the vertical magnetic field merely need to reach a few percent of equipartition for this to occur. Overall, these results have important implications for models of jet formation that require strong, large-scale magnetic fields to exist over a region of the inner accretion disk.