Outward Angular Momentum Flux Research Articles

Magnetohydrodynamics in a cylindrical shearing box

ABSTRACT We develop a framework for magnetohydrodynamical (MHD) simulations in a local cylindrical shearing box by extending the formulation of the Cartesian shearing box. We construct shearing-periodic conditions at the radial boundaries of a simulation box from the conservation relations of the basic MHD equations, taking into account the explicit radial dependence of physical quantities. We demonstrate quasi-steady mass accretion, which cannot be handled by the standard Cartesian shearing box model, with an ideal MHD simulation in a vertically unstratified cylindrical shearing box for up to 200 rotations. In this demonstrative run we set up (i) net vertical magnetic flux, (ii) a locally isothermal equation of state, and (iii) a sub-Keplerian equilibrium rotation, whereas the sound velocity and the initial Alfvén velocity have the same radial dependence as that of the Keplerian velocity. Inward mass accretion is induced to balance the outward angular momentum flux of the MHD turbulence triggered by the magnetorotational instability in a self-consistent manner. We discuss detailed physical properties of the saturated magnetic field, in comparison to the results of a Cartesian shearing box simulation.

The life cycles of Be viscous decretion discs: The case of ω CMa

We analyzed V-band photometry of the Be star {\omega} CMa, obtained during the last four decades, during which the star went through four complete cycles of disc formation and dissipation. The data were simulated by hydrodynamic models based on a time-dependent implementation of the viscous decretion disc (VDD) paradigm, in which a disc around a fast-spinning Be star is formed by material ejected by the star and driven to progressively larger orbits by means of viscous torques. Our simulations offer a good description of the photometric variability during phases of disc formation and dissipation, which suggests that the VDD model adequately describes the structural evolution of the disc. Furthermore, our analysis allowed us to determine the viscosity parameter {\alpha}, as well as the net mass and angular momentum (AM) loss rates. We find that {\alpha} is variable, ranging from 0.1 to 1.0, not only from cycle to cycle but also within a given cycle. Additionally, build-up phases usually have larger values of {\alpha} than the dissipation phases. Furthermore, during dissipation the outward AM flux is not necessarily zero, meaning that {\omega} CMa does not experience a true quiescence but, instead, switches between a high to a low AM loss rate during which the disc quickly assumes an overall lower density but never zero. We confront the average AM loss rate with predictions from stellar evolution models for fast-rotating stars, and find that our measurements are smaller by more than one order of magnitude.

Auroral radio emission from ultracool dwarfs: a Jovian model

A number of fast-rotating ultra cool dwarfs (UCDs) emit pulsed coherent radiation, attributed to the electron cyclotron maser instability, a phenomenon that occurs in the solar system at planets with strong auroral emission. In this paper we examine magnetosphere-ionosphere coupling currents in UCDs, adopting processes used in models of Jovian emission. We consider the angular velocity gradient arising from a steady outward flux of angular momentum from an internal plasma source, as analogous to the jovian main oval current system, as well as the interaction of a rotating magnetosphere with the external medium. Both of these mechanisms are seen in the solar system to be responsible for the production of radio emission. We present the results of an investigation over a range of relevant plasma and magnetosphere-ionosphere coupling parameters to determine regimes consistent with observed UCD radio luminosities. Both processes are able to explain observed UCD luminosities with ionospheric Pedersen conductances of ~1-2 mho, either for a closed magnetosphere with a plasma mass outflow rate of ~10$^5$ kg/s, i.e. a factor of ~100 larger than that observed at Jupiter's moon Io, or for a dwarf with an open magnetosphere moving through the interstellar medium at ~50 km/s and a plasma mass outflow rate of ~1000 kg/s. The radio luminosity resulting from these mechanisms have opposing dependencies on the magnetic field strength, a point which may be used to discriminate between the two models as more data become available.

The excitation of spiral density waves through turbulent fluctuations in accretion discs - I. WKBJ theory

We study and elucidate the mechanism of spiral density wave excitation in a differentially rotating turbulent flow. We formulate a set of wave equations with sources that are only non-zero in the presence of turbulent fluctuations. We solve these in a shearing box domain using a WKBJ method. It is found that, for a particular azimuthal wave length, the wave excitation occurs through a sequence of regularly spaced swings during which the wave changes from leading to trailing form. This is a generic process that is expected to occur in shearing discs with turbulence. Trailing waves of equal amplitude propagating in opposite directions are produced, both of which produce an outward angular momentum flux that we give expressions for as functions of the disc parameters and azimuthal wave length. By solving the wave amplitude equations numerically we justify the WKBJ approach for a Keplerian rotation law for all parameter regimes of interest. In order to quantify the wave excitation completely the important wave source terms need to be specified. Assuming conditions of weak nonlinearity, these can be identified and are associated with a quantity related to the potential vorticity, being the only survivors in the linear regime. Under the additional assumption that the source has a flat power spectrum at long azimuthal wave lengths, the optimal azimuthal wave length produced is found to be determined solely by the WKBJ response and is estimated to be 2 pi H, with H being the nominal disc scale height.

The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs

The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we present the first formal analytical proof showing that, during the exponential growth of the instability, the mean (averaged over the disc scale-height) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds stresses during the late times of the exponential growth of the instability is determined only by the local shear and does not depend on the initial spectrum of perturbations or the strength of the seed magnetic. Even though we derived these properties of the stress tensors for the exponential growth of the instability in incompressible flows, numerical simulations of shearing boxes show that this characteristic is qualitatively preserved under more general conditions, even during the saturated turbulent state generated by the instability.

Magnetically Driven Accretion Flows in the Kerr Metric. IV. Dynamical Properties of the Inner Disk

This paper continues the analysis of a set of general relativistic 3D MHD simulations of accreting tori in the Kerr metric with different black hole spins. We focus on bound matter inside the initial pressure maximum, where the time-averaged motion of gas is inward and an accretion disk forms. We use the flows of mass, angular momentum, and energy in order to understand dynamics in this region. The sharp reduction in accretion rate with increasing black hole spin reported in Paper I of this series is explained by a strongly spin-dependent outward flux of angular momentum conveyed electromagnetically; when a/M > 0.9, this flux can be comparable to the inward angular momentum flux carried by the matter. In all cases, there is outward electromagnetic angular momentum flux throughout the flow; in other words, contrary to the assertions of traditional accretion disk theory, there is in general no edge, no surface within which the stress is zero. The retardation of accretion in the inner disk by electromagnetic torques also alters the radial distribution of surface density, an effect that may have consequences for observable properties such as Compton reflection. The net accreted angular momentum is sufficiently depressed by electromagnetic effects that in the most rapidly-spinning black holes mass growth can lead to spindown. Spinning black holes also lose energy by Poynting flux; this rate is also a strongly increasing function of black hole spin, rising to 10% or more of the rest-mass accretion rate at very high spin. As the black hole spins faster, the path of the Poynting flux changes from being predominantly within the accretion disk to predominantly within the funnel outflow.

The Evolution of Protoplanetary Disk Edges

We investigate gap formation in gaseous protostellar disks by a planet in a circular orbit in the limit of low disk viscosity. This regime may be appropriate to an aging disk after the epoch of planet formation. We find that the distance of the planet to the gap outer boundary can be between the location of the m = 2 and 1 outer Lindblad resonances. This distance is weakly dependent on both the planet's mass and disk viscosity. We find that the evolution of the disk edge takes place on two timescales. The first timescale is set by the spiral density waves driven by the planet. The second timescale depends on the viscosity of the disk. The disk approaches a state in which the outward angular momentum flux caused by the disk viscosity is balanced by the dissipation of spiral density waves that are driven at the Lindblad resonances. This occurs inefficiently, however, because of the extremely low gas density near the planet. We find that the distance between the planet and the peak density at the disk outer edge is only weakly dependent on the viscosity and planet mass; however, the ratio of the gas density near the planet to that in the disk (or the slope of density along the disk edge) is strongly dependent on both quantities. We find that the disk density profile along the edge scales approximately with the disk viscosity divided by the square of the planet mass. We account for this behavior with a simple scenario in which the dissipation of angular momentum from the spiral density waves is balanced against the diffusion in the steep edge of the disk.

A Measurement of the Electromagnetic Luminosity of a Kerr Black Hole

Some active galactic nuclei, microquasars, and gamma-ray bursts may be powered by the electromagnetic braking of a rapidly rotating black hole. We investigate this possibility via axisymmetric numerical simulations of a black hole surrounded by a magnetized plasma. The plasma is described by the equations of general relativistic magnetohydrodynamics, and the effects of radiation are neglected. The evolution is followed for 2000GM/c3, and the computational domain extends from inside the event horizon to typically 40GM/c2. We compare our results to two analytic steady state models, including the force-free magnetosphere of Blandford & Znajek. Along the way we present a self-contained rederivation of the Blandford-Znajek model in Kerr-Schild (horizon penetrating) coordinates. We find that (1) low-density polar regions of the numerical models agree well with the Blandford-Znajek model, (2) many of our models have an outward Poynting flux on the horizon in the Kerr-Schild frame, (3) none of our models have a net outward energy flux on the horizon, and (4) one of our models, in which the initial disk has net magnetic flux, shows a net outward angular momentum flux on the horizon. We conclude with a discussion of the limitations of our model, astrophysical implications, and problems to be addressed by future numerical experiments.

The Formation and Role of Vortices in Protoplanetary Disks

We carry out a two-dimensional, compressible, simulation of a disk, including dust particles, to study the formation and role of vortices in protoplanetary disks. We find that anticyclonic vortices can form out of an initial random perturbation of the vorticity field. Vortices have a typical decay time of the order of 50 orbital periods (for a viscosity parameter alpha=0.0001 and a disk aspect ratio of H/r = 0.15). If vorticity is continuously generated at a constant rate in the flow (e.g. by convection), then a large vortex can form and be sustained (due to the merger of vortices). We find that dust concentrates in the cores of vortices within a few orbital periods, when the drag parameter is of the order of the orbital frequency. Also, the radial drift of the dust induces a significant increase in the surface density of dust particles in the inner region of the disk. Thus, vortices may represent the preferred location for planetesimal formation in protoplanetary disks. We show that it is very difficult for vortex mergers to sustain a relatively coherent outward flux of angular momentum.

On the Angular Momentum Transport Associated with Convective Eddies in Accretion Disks

Protostellar disks are intrinsically unstable against thermal convection in the direction normal to the plane of the disk. Because the origin of effective disk viscosity is unknown it is of great theoretical interest to investigate the effect of convection on the transport of angular momentum. To study this effect we present here results of direct two-dimensional simulations of compressible convection in axisymmetric accretion disks. In order to make the problem tractable an underlying viscosity (possibly due to shear instabilities and/or smaller scale convection) is used such that the calculations are performed for a Rayleigh number 10 times the critical value for marginal stability. Under these conditions the results show that the convection cells cross the equatorial plane and extend over the entire vertical height. They have, for the chosen underlying viscosity, a radial extension comparable to but somewhat less than the disk height. We show that the convection modifies both the heat and angular momentum transport. The modification is such that in order to transmit a given outward angular momentum flux coming from a stable region, the structure adjusts such that the mean viscous flux is increased, this being counterbalanced by a negative advected flux. This suggests that the nonlinear viscous dissipation and mixing associated with large-scale axisymmetric convective motions leads to an inward flux of angular momentum. However, we point out that this result may not apply to the convective motion when the underlying viscosity is much smaller or when nonaxisymmetric modes are considered.

Numerical Study of a Gravitating System of Colliding Particles; Formation and Dynamics of Discs

The study of gravitating systems of colliding particles has many potential astrophysical applications, for instance the dynamics of Saturn's ring, the formation of the solar system, the flattening of protogalaxies and the evolution of galactic nuclei. We consider numerically a three-dimensional system of particles moving in the gravitational field of a central mass point and interacting through inelastic collisions. After a very fast flattening, the system forms a disc of finite thickness: this disc spreads slowly, and collisions still occur. A central condensation is formed and there is an outward flux of angular momentum. The energy which is continually lost in the inelastic collisions is obtained at the expense of the bodies which fall inwards.