On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos

Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin, and requires that the plasma $\beta \sim 1$. Until now most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at $\beta \gg 1$. This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of $\beta \gg 1$. We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as ${\mathcal R}_{\rm m}^{2/3}$. We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around 6 orders of magnitude less than the physical value found in dwarf nova discs of ${\mathcal R}_{\rm m} \sim 10^{10}$. We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.Comment: 20 pages, 6 figures, accepted for publication in the Journal of Plasma Physic

Radiation-Driven Warping: The Origin of Warps and Precession in Accretion Disks

A geometrically thin, optically thick, warped accretion disk with a central source of luminosity is subject to non-axisymmetric forces due to radiation pressure; the resulting torque acts to modify the warp. In a recent paper, \cite{pri96} used a local analysis to show that initially planar accretion disks are unstable to warping driven by radiation torque. Here we extend this work with a global analysis of the stable and unstable modes. We confirm Pringle's conclusion that thin centrally-illuminated accretion disks are generically unstable to warping via this mechanism; we discuss the time-evolution and likely steady-state of such systems and show specifically that this mechanism can explain the warping of the disk of water masers in NGC 4258 and the 164-day precession period of the accretion disk in SS 433. Radiation-driven warping and precession provides a robust mechanism for producing warped, precessing accretion disks in active galactic nuclei and X-ray binary systems.Comment: 16 pages, latex, 3 figure

An instability mechanism for particulate pipe flow

We present linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles two-way coupled to the fluid velocity field via Stokes drag (Saffman 1962). We extend previous analysis in a channel (Klinkenberg et al. 2011) to allow for the initial distribution of particles to be inhomogeneous and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability at experimentally realistic parameters. The results are compared to the experimental work of Matas et al. (2004a) and are shown to be consistent with the reported flow regimes.Comment: 15 pages, 11 figure

Highly-symmetric travelling waves in pipe flow

The recent theoretical discovery of finite-amplitude travelling waves in pipe flow has re-ignited interest in the transitional phenomena that Osborne Reynolds studied 125 years ago. Despite all being unstable, these waves are providing fresh insight into the flow dynamics. Here we describe two new classes of highly-symmetric travelling waves (possessing rotational, shift-&-reflect and mirror symmetries) and report a new family of mirror-symmetric waves which is the first found in pipe flow not to have shift-&-reflect symmetry. The highly-symmetric waves appear at lower Reynolds numbers than the originally-discovered non-mirror-symmetric waves found by Faisst & Eckhardt 2003 and Wedin & Kerswell 2004 and have much higher wall shear stresses. The first M-class comprises of the various discrete-rotationally-symmetric analogues of the mirror-symmetric wave found in Pringle & Kerswell (2007) and have a distinctive double layer structure of fast and slow streaks across the pipe radius. The second N-class has the more familiar separation of fast streaks to the exterior and slow streaks to the interior and looks the precursor to the class of non-mirror-symmetric waves already known.Comment: 16 pages, 8 figures, for Phil Trans theme issue on pipe flo

Self-Similar Magnetocentrifugal Disk Winds with Cylindrical Asymptotics

We construct a two-parameter family of models for self-collimated, radially self-similar magnetized outflows from accretion disks. A flow at zero initial poloidal speed leaves the surface of a rotating disk and is accelerated and redirected toward the pole by helical magnetic fields threading the disk. At large distances from the disk, the flow streamlines asymptote to wrap around the surfaces of nested cylinders. In constrast to previous disk wind modeling, we have explicitly implemented the cylindrical asymptotic boundary condition to examine the consequences for flow dynamics. The solutions are characterized by the logarithmic gradient of the magnetic field strength and the ratios between the footpoint radius R_0 and asymptotic radius R_1 of streamlines; the Alfven radius must be found as an eigenvalue. Cylindrical solutions require the magnetic field to drop less steeply than 1/R. We find that the asymptotic poloidal speed on any streamline is typically just a few tenths of the Kepler speed at the corresponding disk footpoint. The asymptotic toroidal Alfven speed is, however, a few times the footpoint Kepler speed. We discuss the implications of the models for interpretations of observed optical jets and molecular outflows from young stellar systems. We suggest that the difficulty of achieving strong collimation in vector velocity simultaneously with a final speed comparable to the disk rotation rate argues against isolated jets and in favor of models with broader winds.Comment: 39 pages, Latex (uses AAS Latex macros), 6 eps figures, postscript preprint with embedded figures available from http://www.astro.umd.edu/~ostriker/professional/publications.html , to appear in ApJ 9/1/9

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

Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos

We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At and above this threshold, the optimising search naturally seeks out disturbances that trigger turbulence by the end of the period, and convergence is then practically impossible. The first disturbance found to trigger turbulence as the amplitude is increased identifies the `minimal seed' for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. This seems at least approximately true for our choice of energy growth functional and the pipe flow geometry chosen here.Comment: 27 pages, 19 figures, submitted to JF

A trio of month long flares in the nova-like variable V704 And

We present the discovery of an unusual set of flares in the nova-like variable V704 And. Using data from AAVSO, ASAS-SN, and ZTF, of the nova-like variable V704 And, we have discovered a trio of brightening events that occurred during the high state. These events elevate the optical brightness of the source from $\sim13.5$ magnitude to $\sim12.5$ magnitude. The events last for roughly a month, and exhibit the unusual shape of a slow rise and faster decay. Just after the third event we obtained data from regular monitoring with Swift, although by this time the flares had ceased and the source returned to its pre-flare level of activity in the high-state. The Swift observations confirm that during the high-state the source is detectable in the X-rays, and provide simultaneous UV and optical fluxes. As the source is already in the high-state prior to the flares, and thus the disc is expected to already be in the high-viscosity state, we conclude that the driver of the variations must be changes in the mass transfer rate from the companion star and we discuss possible mechanisms for such short-timescale mass transfer variations to occur.Comment: 5 pages + appendix. Accepted for publication in A&A Letter