MHD simulations of disk-star interaction

We discuss a number of topics relevant to disk-magnetosphere interaction and how numerical simulations illuminate them. The topics include: (1) disk-magnetosphere interaction and the problem of disk-locking; (2) the wind problem; (3) structure of the magnetospheric flow, hot spots at the star's surface, and the inner disk region; (4) modeling of spectra from 3D funnel streams; (5) accretion to a star with a complex magnetic field; (6) accretion through 3D instabilities; (7) magnetospheric gap and survival of protoplanets. Results of both 2D and 3D simulations are discussed.Comment: 12 pages, 10 figures, Star-Disk Interaction in Young Stars, Proceedings of the International Astronomical Union, IAU Symposium, Volume 243. See animations at http://astro.cornell.edu/~romanova/projects.htm and at http://astro.cornell.edu/us-rus

Launching of Conical Winds and Axial Jets from the Disk-Magnetosphere Boundary: Axisymmetric and 3D Simulations

We investigate the launching of outflows from the disk-magnetosphere boundary of slowly and rapidly rotating magnetized stars using axisymmetric and exploratory 3D magnetohydrodynamic (MHD) simulations. We find long-lasting outflows in both cases. (1) In the case of slowly rotating stars, a new type of outflow, a conical wind, is found and studied in simulations. The conical winds appear in cases where the magnetic flux of the star is bunched up by the disk into an X-type configuration. The winds have the shape of a thin conical shell with a half-opening angle 30-40 degrees. The conical winds may be responsible for episodic as well as long-lasting outflows in different types of stars. (2) In the case of rapidly rotating stars (the "propeller regime"), a two-component outflow is observed. One component is similar to the conical winds. A significant fraction of the disk matter may be ejected into the winds. A second component is a high-velocity, low-density magnetically dominated axial jet where matter flows along the opened polar field lines of the star. The jet has a mass flux about 10% that of the conical wind, but its energy flux (dominantly magnetic) can be larger than the energy flux of the conical wind. The jet's angular momentum flux (also dominantly magnetic) causes the star to spin-down rapidly. Propeller-driven outflows may be responsible for the jets in protostars and for their rapid spin-down. The jet is collimated by the magnetic force while the conical winds are only weakly collimated in the simulation region.Comment: 29 pages and 29 figures. This version has a major expansion after comments by a referee. The 1-st version is correct but mainly describes the conical wind. This version describes in greater detail both the conical winds and the propeller regime. Accepted to the MNRA

Relativistically expanding cylindrical electromagnetic fields

We study relativistically expanding electromagnetic fields of cylindrical geometry. The fields emerge from the side surface of a cylinder and are invariant under translations parallel to the axis of the cylinder. The expansion velocity is in the radial direction and is parametrized by $v=R/(ct)$. We consider force-free magnetic fields by setting the total force the electromagnetic field exerts on the charges and the currents equal to zero. Analytical and semi-analytical separable solutions are found for the relativistic problem. In the non-relativistic limit the mathematical form of the equations is similar to equations that have already been studied in static systems of the same geometry.Comment: 7 pages, 4 figures, accepted by MNRA

Tidal coupling of a Schwarzschild black hole and circularly orbiting moon

We describe the possibility of using LISA's gravitational-wave observations to study, with high precision, the response of a massive central body to the tidal gravitational pull of an orbiting, compact, small-mass object. Motivated by this application, we use first-order perturbation theory to study tidal coupling for an idealized case: a massive Schwarzschild black hole, tidally perturbed by a much less massive moon in a distant, circular orbit. We investigate the details of how the tidal deformation of the hole gives rise to an induced quadrupole moment in the hole's external gravitational field at large radii. In the limit that the moon is static, we find, in Schwarzschild coordinates and Regge-Wheeler gauge, the surprising result that there is no induced quadrupole moment. We show that this conclusion is gauge dependent and that the static, induced quadrupole moment for a black hole is inherently ambiguous. For the orbiting moon and the central Schwarzschild hole, we find (in agreement with a recent result of Poisson) a time-varying induced quadrupole moment that is proportional to the time derivative of the moon's tidal field. As a partial analog of a result derived long ago by Hartle for a spinning hole and a stationary distant companion, we show that the orbiting moon's tidal field induces a tidal bulge on the hole's horizon, and that the rate of change of the horizon shape leads the perturbing tidal field at the horizon by a small angle.Comment: 14 pages, 0 figures, submitted to Phys. Rev.

Gamma-ray Flares and VLBI Outbursts of Blazars

A model is developed for the time dependent electromagnetic - radio to gamma-ray - emission of active galactic nuclei, specifically, the blazars, based on the acceleration and creation of leptons at a propagating discontinuity or {\it front} of a Poynting flux jet. The front corresponds to a discrete relativistic jet component as observed with very-long-baseline-interferometry (VLBI). Equations are derived for the number, momentum, and energy of particles in the front taking into account synchrotron, synchrotron-self-Compton (SSC), and inverse-Compton processes as well as photon-photon pair production. The apparent synchrotron, SSC, and inverse-Compton luminosities as functions of time are determined. Predictions of the model are compared with observations in the gamma, optical and radio bands. The delay between the high-energy gamma-ray flare and the onset of the radio is explained by self-absorption and/or free-free absorption by external plasma. Two types of gamma-ray flares are predicted depending on pair creation in the front.Comment: 11 pages, submitted to ApJ. 10 figures can be obtained from R. Lovelace by sending postal address to [email protected]

General Relativistic Simulations of Jet Formation in a Rapidly Rotating Black Hole Magnetosphere

To investigate the formation mechanism of relativistic jets in active galactic nuclei and micro-quasars, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the first numerical simulation of jet formation in a rapidly-rotating (a=0.95) Kerr black hole magnetosphere. We study cases in which the Keplerian accretion disk is both co-rotating and counter-rotating with respect to the black hole rotation. In the co-rotating disk case, our results are almost the same as those in Schwarzschild black hole cases: a gas pressure-driven jet is formed by a shock in the disk, and a weaker magnetically-driven jet is also generated outside the gas pressure-driven jet. On the other hand, in the counter-rotating disk case, a new powerful magnetically-driven jet is formed inside the gas pressure-driven jet. The newly found magnetically-driven jet in the latter case is accelerated by a strong magnetic field created by frame dragging in the ergosphere. Through this process, the magnetic field extracts the energy of the black hole rotation.Comment: Co-rotating and counter-rotating disks; 8 pages; submitted to ApJ letter

Two-Stream Instability of Counter-Rotating Galaxies

The present study of the two-stream instability in stellar disks with counter-rotating components of stars and/or gas is stimulated by recently discovered counter-rotating spiral and S0 galaxies. Strong linear two-stream instability of tightly-wrapped spiral waves is found for one and two-armed waves with the pattern angular speed of the unstable waves always intermediate between the angular speed of the co-rotating matter ($+\Omega$) and that of the counter-rotating matter ($-\Omega$). The instability arises from the interaction of positive and negative energy modes in the co- and counter-rotating components. The unstable waves are in general convective - they move in radius and radial wavenumber space - with the result that amplification of the advected wave is more important than the local growth rate. For a galaxy of co-rotating stars and counter-rotating stars of mass-fraction $\xi_* < {1\over 2}$, or of counter-rotating gas of mass-fraction $\xi_g < {1\over 2}$, the largest amplification is usually for the one-armed leading waves (with respect to the co-rotating stars). For the case of both counter-rotating stars and gas, the largest amplifications are for $\xi_*+\xi_g \approx {1\over 2}$, also for one-armed leading waves. The two-armed trailing waves usually have smaller amplifications. The growth rates and amplifications all decrease as the velocity spreads of the stars and/or gas increase. It is suggested that the spiral waves can provide an effective viscosity for the gas causing its accretion.Comment: 14 pages, submitted to ApJ. One table and 17 figures can be obtained by sending address to R. Lovelace at [email protected]

Magneto-centrifugally driven winds: comparison of MHD simulations with theory

Stationary magnetohydrodynamic (MHD) outflows from a rotating, conducting Keplerian accretion disk threaded by B-field are investigated numerically by time-dependent, axisymmetric (2.5D) simulations using a Godunov-type code. A large class of stationary magneto-centrifugally driven winds are found where matter is accelerated from a thermal speed at the disk to much larger velocity, greater than the fast magnetosonic speed and larger than the escape speed. The flows are approximately spherical outflows with only small collimation within the simulation region. Numerical results are shown to coincide with the theoretical predictions of ideal, axisymmetric MHD to high accuracy. Investigation of the influence of outer boundary conditions, particularly that on the toroidal component of magnetic field shows that the commonly used ``free'' boundary condition leads to artificial magnetic forces which can act to give spurious collimation. New boundary conditions are proposed which do not generate artificial forces. Artificial results may also arise for cases where the Mach cones on the outer boundaries are partially directed into the simulation region.Comment: 19 pages, 18 figures, emulapj.sty is use

Three-dimensional Simulations of Accretion to Stars with Complex Magnetic Fields

Disk accretion to rotating stars with complex magnetic fields is investigated using full three-dimensional magnetohydrodynamic (MHD) simulations. The studied magnetic configurations include superpositions of misaligned dipole and quadrupole fields and off-centre dipoles. The simulations show that when the quadrupole component is comparable to the dipole component, the magnetic field has a complex structure with three major magnetic poles on the surface of the star and three sets of loops of field lines connecting them. A significant amount of matter flows to the quadrupole "belt", forming a ring-like hot spot on the star. If the maximum strength of the magnetic field on the star is fixed, then we observe that the mass accretion rate, the torque on the star, and the area covered by hot spots are several times smaller in the quadrupole-dominant cases than in the pure dipole cases. The influence of the quadrupole component on the shape of the hot spots becomes noticeable when the ratio of the quadrupole and dipole field strengths $B_q/B_d\gtrsim0.5$, and becomes dominant when $B_q/B_d\gtrsim1$. In the case of an off-centre dipole field, most of the matter flows through a one-armed accretion stream, forming a large hot spot on the surface, with a second much smaller secondary spot. The light curves may have simple, sinusoidal shapes, thus mimicking stars with pure dipole fields. Or, they may be complex and unusual. In some cases the light curves may be indicators of a complex field, in particular if the inclination angle is known independently. We also note that in the case of complex fields, magnetospheric gaps are often not empty, and this may be important for the survival of close-in exosolar planets.Comment: 13 pages, 21 figures, accepted for publication in MNRA