M. M. Romanova

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.

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.

Accretion to magnetized stars through the Rayleigh–Taylor instability: global 3D simulations

We present results of 3D simulations of magnetohydrodynamics (MHD) instabilities at the accretion disc‐magnetosphere boundary. The instability is Rayleigh‐Taylor, and develops for a fairly broad range of accretion rates and stellar rotation rates and magnetic fields. It manifests itself in the form of tall, thin tongues of plasma that penetrate the magnetosphere in the equatorial plane. The shape and number of the tongues changes with time on the inner disc dynamical time-scale. In contrast with funnel flows, which deposit matter mainly in the polar region, the tongues deposit matter much closer to the stellar equator. The instability appears for relatively small misalignment angles, � � 30 ◦ , between the star’s rotation and magnetic axes, and is associated with higher accretion rates. The hotspots and light curves during accretion through instability are generally much more chaotic than during stable accretion. The unstable state of accretion has possible implications for quasi-periodic oscillations and intermittent pulsations from accreting systems, as well as planet migration.

Unstable Disk Accretion onto Magnetized Stars: First Global Three-dimensional Magnetohydrodynamic Simulations

We report on the first global three-dimensional (3D) MHD simulations of disk accretion onto a rotating magnetized star through the Rayleigh-Taylor instability. The star has a dipole field misaligned relative to the rotation axis by a small angle Θ. Simulations show that, depending on the accretion rate, a star may be in the stable or unstable regime of accretion. In the unstable regime, matter penetrates deep into the magnetosphere through several elongated tongues which deposit matter at random places on the surface of the star, leading to stochastic light curves. In the stable regime, matter accretes in ordered funnel streams and the light curves are almost periodic. A star may switch between these two regimes depending on the accretion rate and may thus show alternate episodes of ordered pulsations and stochastic light curves. In the intermediate regime, both stochastic and ordered pulsations are observed. For -->Θ > 30°, the instability is suppressed and stable accretion through funnel streams dominates.We report on the first global three-dimensional (3D) MHD simulations of disk accretion onto a rotating magnetized star through the Rayleigh-Taylor instability. The star has a dipole field misaligned relative to the rotation axis by a small angle Θ. Simulations show that, depending on the accretion rate, a star may be in the stable or unstable regime of accretion. In the unstable regime, matter penetrates deep into the magnetosphere through several elongated “tongues” which deposit matter at random places on the surface of the star, leading to stochastic light-curves. In the stable regime, matter accretes in ordered funnel streams and the light-curves are almost periodic. A star may switch between these two regimes depending on the accretion rate and may thus show alternate episodes of ordered pulsations and stochastic light-curves. In the intermediate regime, both stochastic and ordered pulsations are observed. For Θ > 30, the instability is suppressed and stable accretion through funnel streams dominates.

Lepton Acceleration by Relativistic Collisionless Magnetic Reconnection

We have calculated self-consistent equilibria of a collisionless relativistic electron-positron gas in the vicinity of a magnetic X-point. For the considered conditions, pertinent to extragalactic jets, we find that leptons are accelerated up to Lorentz factors Γ0 = κeB0L2/mc2 1, where B0 is the typical magnetic field strength, ≡ E0/B0, with E0 the reconnection electric field, L is the length scale of the magnetic field, and κ ≈ 12. The acceleration is due to the dominance of the electric field over the magnetic field in a region around the X-point. The distribution function of the accelerated leptons is found to be approximately dn/dγ ∝ γ-1 for γ Γ0. The apparent distribution function may be steeper than γ-1 due to the distribution of Γ0 values and/or the radiative losses. Self-consistent equilibria are found only for plasma inflow rates to the X-point less than a critical value.

Implosive accretion and outbursts of active galactic nuclei

A model and simulation code have been developed for time-dependent axisymmetric disk accretion onto a compact object including for the first time the influence of an ordered magnetic field. The accretion rate and radiative luminosity of the disk are naturally coupled to the rate of outflow of energy and angular momentum in magnetically driven (+/- z) winds. The magnetic field of the wind is treated in a phenomenological way suggested by self-consistent wind solutions. The radial accretion speed u(r, t) of the disk matter is shown to be the sum of the usual viscous contribution and a magnetic contribution proportional to r(exp 3/2)(B(sub p exp 2))/sigma, where B(sub p)(r,t) is the poloidal field threading the disk and sigma(r,t) is the disks surface mass density. An enhancement or variation in B(sub p) at a large radial distance leads to the formation of a soliton-like structure in the disk density, temperature, and B-field which propagates implosively inward. The implosion gives a burst in the power output in winds or jets and a simultaneous burst in the disk radiation. The model is pertinent to the formation of discrete fast-moving components in jets observed by very long baseline interferometry. These components appear to originate at times of optical outbursts of the active galactic nucleus.

The Propeller Regime of Disk Accretion to a Rapidly Rotating Magnetized Star

The propeller regime of disk accretion to a rapidly rotating magnetized star is investigated here for the first time by axisymmetric 2.5-dimensional magnetohydrodynamic simulations. An expanded, closed magnetosphere forms in which the magnetic field is predominantly toroidal. A smaller fraction of the stars poloidal magnetic flux inflates vertically, forming a magnetically dominated tower. Matter accumulates in the equatorial region outside magnetosphere and accretes to the star quasi-periodically through elongated funnel streams that cause the magnetic field to reconnect. The star spins down owing to the interaction of the closed magnetosphere with the disk. For the considered conditions, the spin-down torque varies with the angular velocity of the star (ω*) as ~-ω for a fixed mass accretion rate. The propeller stage may be important in the evolution of X-ray pulsars, cataclysmic variables, and young stars. In particular, it may explain the present slow rotation of the classical T Tauri stars.