Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs

We consider the stability of warping modes in Keplerian discs. We find them to be parametrically unstable using two lines of attack, one based on three-mode couplings and the other on Floquet theory. We confirm the existence of the instability, and investigate its nonlinear development in three dimensions, via numerical experiment. The most rapidly growing non-axisymmetric disturbances are the most nearly axisymmetric (low m) ones. Finally, we offer a simple, somewhat speculative model for the interaction of the parametric instability with the warp. We apply this model to the masing disc in NGC 4258 and show that, provided the warp is not forced too strongly, parametric instability can fix the amplitude of the warp.Comment: 14 pages, 6 figures, revised version with appendix added, to be published in MNRA

The Stability of Magnetized Rotating Plasmas with Superthermal Fields

During the last decade it has become evident that the magnetorotational instability is at the heart of the enhanced angular momentum transport in weakly magnetized accretion disks around neutron stars and black holes. In this paper, we investigate the local linear stability of differentially rotating, magnetized flows and the evolution of the magnetorotational instability beyond the weak-field limit. We show that, when superthermal toroidal fields are considered, the effects of both compressibility and magnetic tension forces, which are related to the curvature of toroidal field lines, should be taken fully into account. We demonstrate that the presence of a strong toroidal component in the magnetic field plays a non-trivial role. When strong fields are considered, the strength of the toroidal magnetic field not only modifies the growth rates of the unstable modes but also determines which modes are subject to instabilities. We find that, for rotating configurations with Keplerian laws, the magnetorotational instability is stabilized at low wavenumbers for toroidal Alfven speeds exceeding the geometric mean of the sound speed and the rotational speed. We discuss the significance of our findings for the stability of cold, magnetically dominated, rotating fluids and argue that, for these systems, the curvature of toroidal field lines cannot be neglected even when short wavelength perturbations are considered. We also comment on the implications of our results for the validity of shearing box simulations in which superthermal toroidal fields are generated.Comment: 24 pages, 12 figures. Accepted for publication in ApJ. Sections 2 and 5 substantially expanded, added Appendix A and 3 figures with respect to previous version. Animations are available at http://www.physics.arizona.edu/~mpessah/research

Did Fomalhaut, HR 8799, and HL Tauri Form Planets via the Gravitational Instability? Placing Limits on the Required Disk Masses

Disk fragmentation resulting from the gravitational instability has been proposed as an efficient mechanism for forming giant planets. We use the planet Fomalhaut b, the triple-planetary system HR 8799, and the potential protoplanet associated with HL Tau to test the viability of this mechanism. We choose the above systems since they harbor planets with masses and orbital characteristics favored by the fragmentation mechanism. We do not claim that these planets must have formed as the result of fragmentation, rather the reverse: if planets can form from disk fragmentation, then these systems are consistent with what we should expect to see. We use the orbital characteristics of these recently discovered planets, along with a new technique to more accurately determine the disk cooling times, to place both lower and upper limits on the disk surface density--and thus mass--required to form these objects by disk fragmentation. Our cooling times are over an order of magnitude shorter than those of Rafikov (2005),which makes disk fragmentation more feasible for these objects. We find that the required mass interior to the planet's orbital radius is ~0.1 Msun for Fomalhaut b, the protoplanet orbiting HL Tau, and the outermost planet of HR 8799. The two inner planets of HR 8799 probably could not have formed in situ by disk fragmentation.Comment: 5 pages, 1 figure, accepted for publication in ApJ

Vortices in Thin, Compressible, Unmagnetized Disks

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, . This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.Comment: 8 pages, 10 figures (high resolution figures available in ApJ electronic edition

The thermal-viscous disk instability model in the AGN context

Accretion disks in AGN should be subject to the same type of instability as in cataclysmic variables (CVs) or in low-mass X-ray binaries (LMXBs), which leads to dwarf nova and soft X-ray transient outbursts. It has been suggested that this thermal/viscous instability can account for the long term variability of AGNs. We test this assertion by presenting a systematic study of the application of the disk instability model (DIM) to AGNs. We are using the adaptative grid numerical code we have developed in the context of CVs, enabling us to fully resolve the radial structure of the disk. We show that, because in AGN disks the Mach numbers are very large, the heating and cooling fronts are so narrow that they cannot be resolved by the numerical codes that have been used until now. In addition, these fronts propagate on time scales much shorter than the viscous time. As a result, a sequence of heating and cooling fronts propagate back and forth in the disk, leading only to small variations of the accretion rate onto the black hole, with short quiescent states occurring for very low mass transfer rates only. Truncation of the inner part of the disk by e.g. an ADAF does not alter this result, but enables longer quiescent states. Finally we discuss the effects of irradiation by the central X-ray source, and show that, even for extremely high irradiation efficiencies, outbursts are not a natural outcome of the model.Comment: Astronomy & Astrophysics - in pres

Pair Production in Low Luminosity Galactic Nuclei

Electron-positron pairs may be produced near accreting black holes by a variety of physical processes, and the resulting pair plasma may be accelerated and collimated into a relativistic jet. Here we use a self-consistent dynamical and radiative model to investigate pair production by \gamma\gamma collisions in weakly radiative accretion flows around a black hole of mass M and accretion rate \dot{M}. Our flow model is drawn from general relativistic magnetohydrodynamic simulations, and our radiation field is computed by a Monte Carlo transport scheme assuming the electron distribution function is thermal. We argue that the pair production rate scales as r^{-6} M^{-1} \dot{M}^{6}. We confirm this numerically and calibrate the scaling relation. This relation is self-consistent in a wedge in M, \dot{M} parameter space. If \dot{M} is too low the implied pair density over the poles of the black hole is below the Goldreich-Julian density and \gamma\gamma pair production is relatively unimportant; if \dot{M} is too high the models are radiatively efficient. We also argue that for a power-law spectrum the pair production rate should scale with the observables L_X \equiv X-ray luminosity and M as L_X^2 M^{-4}. We confirm this numerically and argue that this relation likely holds even for radiatively efficient flows. The pair production rates are sensitive to black hole spin and to the ion-electron temperature ratio which are fixed in this exploratory calculation. We finish with a brief discussion of the implications for Sgr A* and M87.Comment: 21 pages, 10 figures, 1 table. Accepted for publication in Ap

Imaging an Event Horizon: Mitigation of Source Variability of Sagittarius A*

The black hole in the center of the Galaxy, associated with the compact source Sagittarius A* (Sgr A*), is predicted to cast a shadow upon the emission of the surrounding plasma flow, which encodes the influence of general relativity in the strong-field regime. The Event Horizon Telescope (EHT) is a Very Long Baseline Interferometry (VLBI) network with a goal of imaging nearby supermassive black holes (in particular Sgr A* and M87) with angular resolution sufficient to observe strong gravity effects near the event horizon. General relativistic magnetohydrodynamic (GRMHD) simulations show that radio emission from Sgr A* exhibits vari- ability on timescales of minutes, much shorter than the duration of a typical VLBI imaging experiment, which usually takes several hours. A changing source structure during the observations, however, violates one of the basic assumptions needed for aperture synthesis in radio interferometry imaging to work. By simulating realistic EHT observations of a model movie of Sgr A*, we demonstrate that an image of the average quiescent emission, featuring the characteristic black hole shadow and photon ring predicted by general relativity, can nonetheless be obtained by observing over multiple days and subsequent processing of the visibilities (scaling, averaging, and smoothing) before imaging. Moreover, it is shown that this procedure can be combined with an existing method to mitigate the effects of interstellar scattering. Taken together, these techniques allow the black hole shadow in the Galactic center to be recovered on the reconstructed image.Comment: 10 pages, 12figures, accepted for publication in Ap