Application of the Cubed-Sphere Grid to Tilted Black-Hole Accretion Disks

In recent work we presented the first results of global general relativistic magnetohydrodynamic (GRMHD) simulations of tilted (or misaligned) accretion disks around rotating black holes. The simulated tilted disks showed dramatic differences from comparable untilted disks, such as asymmetrical accretion onto the hole through opposing "plunging streams" and global precession of the disk powered by a torque provided by the black hole. However, those simulations used a traditional spherical-polar grid that was purposefully underresolved along the pole, which prevented us from assessing the behavior of any jets that may have been associated with the tilted disks. To address this shortcoming we have added a block-structured "cubed-sphere" grid option to the Cosmos++ GRMHD code, which will allow us to simultaneously resolve the disk and polar regions. Here we present our implementation of this grid and the results of a small suite of validation tests intended to demonstrate that the new grid performs as expected. The most important test in this work is a comparison of identical tilted disks, one evolved using our spherical-polar grid and the other with the cubed-sphere grid. We also demonstrate an interesting dependence of the early-time evolution of our disks on their orientation with respect to the grid alignment. This dependence arises from the differing treatment of current sheets within the disks, especially whether they are aligned with symmetry planes of the grid or not.Comment: 15 pages, 11 figures, submitted to Ap

Oscillation modes of relativistic slender tori

Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary specific angular momentum distribution, orbiting in an arbitrary axisymmetric spacetime with reflection symmetry. We discuss the physical nature of the modes, present general analytic expressions and illustrations for those which are low order, and show that they can be excited in numerical simulations of relativistic tori. The mode oscillation spectrum simplifies dramatically for near Keplerian angular momentum distributions, which appear to be generic in global simulations of the magnetorotational instability. We discuss our results in light of observations of high frequency QPO's, and point out the existence of a new pair of modes which can be in an approximate 3:2 ratio for arbitrary black hole spins and angular momentum distributions, provided the torus is radiation pressure dominated. This mode pair consists of the axisymmetric vertical epicyclic mode and the lowest order axisymmetric breathing mode.Comment: submitted to MNRA

Radiative Models of Sagittarius A* and M87 from Relativistic MHD Simulations

Ongoing millimeter VLBI observations with the Event Horizon Telescope allow unprecedented study of the innermost portion of black hole accretion flows. Interpreting the observations requires relativistic, time-dependent physical modeling. We discuss the comparison of radiative transfer calculations from general relativistic MHD simulations of Sagittarius A* and M87 with current and future mm-VLBI observations. This comparison allows estimates of the viewing geometry and physical conditions of the Sgr A* accretion flow. The viewing geometry for M87 is already constrained from observations of its large-scale jet, but, unlike Sgr A*, there is no consensus for its millimeter emission geometry or electron population. Despite this uncertainty, as long as the emission region is compact, robust predictions for the size of its jet launching region can be made. For both sources, the black hole shadow may be detected with future observations including ALMA and/or the LMT, which would constitute the first direct evidence for a black hole event horizon.Comment: 8 pages, 2 figures, submitted to the proceedings of AHAR 2011: The Central Kiloparse

Observing Lense-Thirring Precession in Tidal Disruption Flares

When a star is tidally disrupted by a supermassive black hole (SMBH), the streams of liberated gas form an accretion disk after their return to pericenter. We demonstrate that Lense-Thirring precession in the spacetime around a rotating SMBH can produce significant time evolution of the disk angular momentum vector, due to both the periodic precession of the disk and the nonperiodic, differential precession of the bound debris streams. Jet precession and periodic modulation of disk luminosity are possible consequences. The persistence of the jetted X-ray emission in the Swift J164449.3+573451 flare suggests that the jet axis was aligned with the spin axis of the SMBH during this event.Comment: 4 pages, 4 figures. Accepted for publication in Physical Review Letters. Minor changes made to match proof

The Submillimeter Bump in Sgr A* from Relativistic MHD Simulations

Recent high resolution observations of the Galactic center black hole allow for direct comparison with accretion disk simulations. We compare two-temperature synchrotron emission models from three dimensional, general relativistic magnetohydrodynamic simulations to millimeter observations of Sgr A*. Fits to very long baseline interferometry and spectral index measurements disfavor the monochromatic face-on black hole shadow models from our previous work. Inclination angles \le 20 degrees are ruled out to 3 \sigma. We estimate the inclination and position angles of the black hole, as well as the electron temperature of the accretion flow and the accretion rate, to be i=50+35-15 degrees, \xi=-23+97-22 degrees, T_e=(5.4 +/- 3.0)x10^10 K and Mdot=(5+15-2)x10^-9 M_sun / yr respectively, with 90% confidence. The black hole shadow is unobscured in all best fit models, and may be detected by observations on baselines between Chile and California, Arizona or Mexico at 1.3mm or .87mm either through direct sampling of the visibility amplitude or using closure phase information. Millimeter flaring behavior consistent with the observations is present in all viable models, and is caused by magnetic turbulence in the inner radii of the accretion flow. The variability at optically thin frequencies is strongly correlated with that in the accretion rate. The simulations provide a universal picture of the 1.3mm emission region as a small region near the midplane in the inner radii of the accretion flow, which is roughly isothermal and has \nu/\nu_c ~ 1-20, where \nu_c is the critical frequency for thermal synchrotron emission.Comment: 14 pages, 17 figures, accepted by Ap

Numerical Modeling of the Radio Nebula from the 2004 December 27 Giant Flare of SGR 1806-20

We use the relativistic hydrodynamics code Cosmos++ to model the evolution of the radio nebula triggered by the Dec. 27, 2004 giant flare event of soft gamma repeater 1806-20. We primarily focus on the rebrightening and centroid motion occurring subsequent to day 20 following the flare event. We model this period as a mildly relativistic (gamma ~ 1.07 - 1.67) jetted outflow expanding into the interstellar medium (ISM). We demonstrate that a jet with total energy ~ 10^46 ergs confined to a half opening angle ~ 20 degrees fits the key observables of this event, e.g. the flux lightcurve, emission map centroid position, and aspect ratio. In particular, we find excellent agreement with observations if the rebrightening is due to the jet, moving at 0.5c and inclined ~ 0 - 40 degrees toward the observer, colliding with a density discontinuity in the ISM at a radius of several 10^16 cm. We also find that a jet with a higher velocity, >~ 0.7c, and larger inclination, >~ 70 degrees, moving into a uniform ISM can fit the observations in general, but tends to miss the details of rebrightening. The latter, uniform ISM model predicts an ISM density more than 100 times lower than that of the former model, and thus suggests an independent test which might discriminate between the two. One of the strongest constraints of both models is that the data seems to require a non-uniform jet in order to be well fit