Three Disk Oscillation Modes of Rotating Magnetized Neutron Stars

We discuss three specific modes of accretion disks around rotating magnetized neutron stars which may explain the separations of the kilo Hertz quasi periodic oscillations (QPO) seen in low mass X-ray binaries. The existence of these modes requires that there be a maximum in the angular velocity of the accreting material, and that the fluid is in stable, nearly circular motion near this maximum rather than moving rapidly towards the star or out of the disk plane into funnel flows. It is presently not known if these conditions occur, but we are exploring this with 3D magnetohydrodynamic simulations and will report the results elsewhere. The first mode is a corotation mode which is radially trapped in the vicinity of the maximum of the disk rotation rate and is unstable. The second mode, relevant to relatively slowly rotating stars, is a magnetically driven eccentric ($m=1$) oscillation of the disk excited at a Lindblad radius in the vicinity of the maximum of the disk rotation. The third mode, relevant to rapidly rotating stars, is a magnetically coupled eccentric ($m=1$) and an axisymmetric ($m=0$) radial disk perturbation which has an inner Lindblad radius also in the vicinity of the maximum of the disk rotation. We suggest that the first mode is associated with the upper QPO frequency, $\nu_u$, the second with the lower QPO frequency, $\nu_\ell =\nu_u-\nu_*$, and the third with the lower QPO frequency, $\nu_\ell=\nu_u-\nu_*/2$, where $\nu_*$ is the star's rotation rate.Comment: 6 pages, 2 figure

Locking of the Rotation of Disk-Accreting Magnetized Stars

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, the radial field lines carry significant angular momentum out of the star. However, this did not appreciably change the condition for locking of the rotation of the star. We find that in the equilibrium state the corotation radius $r_{co}$ is related to the magnetospheric radius $r_A$ as $r_{co}/r_A\approx 1.2-1.3$ for case (1) and $r_{co}/r_A\approx 1.4-1.5$ for case (2). We estimated periods of rotation in the equilibrium state for classical T Tauri stars, dwarf novae and X-ray millisecond pulsars.Comment: 10 pages, 9 figures. Accepted by ApJ, will appear in vol. 634, 2005 December

Time Gauge Fixing and Hilbert Space in Quantum String Cosmology

Recently the low-energy effective string theory has been used by Gasperini and Veneziano to elaborate a very interesting scenario for the early history of the universe (``birth of the universe as quantum scattering''). Here we investigate the gauge fixing and the problem of the definition of a global time parameter for this model, and we obtain the positive norm Hilbert space of states.Comment: 13 pages, Plain TEX, no figure

"Propeller" Regime of Disk Accretion to Rapidly Rotating Stars

We present results of axisymmetic 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, 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 propeller is characterized by a powerful disk wind and a collimated magnetically dominated outflow or jet from the star. The weak propeller 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 spinning-down of the classical T Tauri stars in the initial stages of their evolution, and for the spinning-down of accreting millisecond pulsars.Comment: 18 pages, 16 figures, ApJ (accepted), added references, corrected typos; see animation at http://astrosun2.astro.cornell.edu/us-rus/disk_prop.ht

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.

Vortex migration in protoplanetary disks

We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulting spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a time scale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios.Comment: 13 pages, 13 figures, accepted for publication in Ap

Initial data transients in binary black hole evolutions

We describe a method for initializing characteristic evolutions of the Einstein equations using a linearized solution corresponding to purely outgoing radiation. This allows for a more consistent application of the characteristic (null cone) techniques for invariantly determining the gravitational radiation content of numerical simulations. In addition, we are able to identify the {\em ingoing} radiation contained in the characteristic initial data, as well as in the initial data of the 3+1 simulation. We find that each component leads to a small but long lasting (several hundred mass scales) transient in the measured outgoing gravitational waves.Comment: 18 pages, 4 figure

Influence of the Magnetic Coupling Process on the Advection Dominated Accretion Flows around Black Holes

A large-scale closed magnetic field can transfer angular momentum and energy between a black hole (BH) and its surrounding accretion flow. We investigate the effects of this magnetic coupling (MC) process on the dynamics of a hot accretion flow (e.g., an advection dominated accretion flow, hereafter ADAF). The energy and angular momentum fluxes transported by the magnetic field are derived by an equivalent circuit approach. For a rapidly rotating BH, it is found that the radial velocity and the electron temperature of the accretion flow decrease, whereas the ion temperature and the surface density increase. The significance of the MC effects depends on the value of the viscous parameter \alpha. The effects are obvious for \alpha=0.3 but nearly ignorable for \alpha=0.1. For a BH with specific angular momentum, a_*=0.9, and \alpha=0.3, we find that for reasonable parameters the radiative efficiency of a hot accretion flow can be increased by about 30%.Comment: 21 pages, 7 figures. Changed after the referee's suggestions. Accepted for publication in the Astrophysical Journa

Type I planet migration in nearly laminar disks - long term behavior

We carry out 2-D high resolution numerical simulations of type I planet migration with different disk viscosities. We find that the planet migration is strongly dependent on disk viscosities. Two kinds of density wave damping mechanisms are discussed. Accordingly, the angular momentum transport can be either viscosity dominated or shock dominated, depending on the disk viscosities. The long term migration behavior is different as well. Influences of the Rossby vortex instability on planet migration are also discussed. In addition, we investigate very weak shock generation in inviscid disks by small mass planets and compare the results with prior analytic results.Comment: Accepted for publication in Ap