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

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.Comment: 38 pages, 18 figures, submitted to Ap

Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport

The magneto-rotational instability is presently the most promising source of turbulent transport in accretion disks. However, some important issues still need to be addressed to quantify the role of MRI in disks; in particular no systematic investigation of the role of the physical dimensionless parameters of the problem on the dimensionless transport has been undertaken yet. First, we complete existing investigations on the field strength dependence by showing that the transport in high magnetic pressure disks close to marginal stability is highly time-dependent and surprisingly efficient. Second, we bring to light a significant dependence of the global transport on the magnetic Prandtl number, with $\alpha\propto Pm^\delta$ for the explored range: $0.12<Pm<8$ and $200<Re<6400$ ($\delta$ being in the range 0.25 to 0.5). We show that the dimensionless transport is not correlated to the dimensionless linear growth rate, contrarily to a largely held expectation. More generally, these results stress the need to control dissipation processes in astrophysical simulations.Comment: 11 pages, 11 figures, accepted to MNRA

The Evolution of Protoplanetary Disks Around Millisecond Pulsars: The PSR 1257 +12 System

We model the evolution of protoplanetary disks surrounding millisecond pulsars, using PSR 1257+12 as a test case. Initial conditions were chosen to correspond to initial angular momenta expected for supernova-fallback disks and disks formed from the tidal disruption of a companion star. Models were run under two models for the viscous evolution of disks: fully viscous and layered accretion disk models. Supernova-fallback disks result in a distribution of solids confined to within 1-2 AU and produce the requisite material to form the three known planets surrounding PSR 1257+12. Tidal disruption disks tend to slightly underproduce solids interior to 1 AU, required for forming the pulsar planets, while overproducing the amount of solids where no body, lunar mass or greater, exists. Disks evolving under 'layered' accretion spread somewhat less and deposit a higher column density of solids into the disk. In all cases, circumpulsar gas dissipates on $\lesssim 10^{5}$ year timescales, making formation of gas giant planets highly unlikely.Comment: 16 pages, 17 figures, Accepted for publication in The Astrophysical Journal (September 20, 2007 issue

Linear coupling of modes in 2D radially stratified astrophysical discs

We investigate mode coupling in a two dimensional compressible disc with radial stratification and differential rotation. We employ the global radial scaling of linear perturbations and study the linear modes in the local shearing sheet approximation. We employ a three-mode formalism and study the vorticity (W), entropy (S) and compressional (P) modes and their coupling properties. The system exhibits asymmetric three-mode coupling: these include mutual coupling of S and P-modes, S and W-modes, and asymmetric coupling between the W and P-modes. P-mode perturbations are able to generate potential vorticity through indirect three-mode coupling. This process indicates that compressional perturbations can lead to the development of vortical structures and influence the dynamics of radially stratified hydrodynamic accretion and protoplanetary discs.Comment: 10 pages, 10 figures, MNRAS (accepted