Warner A. Miller

Line Emission from an Accretion Disk around a Rotating Black Hole: Toward a Measurement of Frame Dragging

Line emission from an accretion disk and a corotating hot spot about a rotating black hole are considered for possible signatures of the frame-dragging effect. We explicitly compare integrated line profiles from a geometrically thin disk about a Schwarzschild and an extreme Kerr black hole, and show that the line profile differences are small if the inner radius of the disk is near or above the Schwarzschild stable-orbit limit of radius 6GM/c2. However, if the inner disk radius extends below this limit, as is possible in the extreme Kerr spacetime, then differences can become significant, especially if the disk emissivity is stronger near the inner regions. We demonstrate that the first three moments of a line profile define a three-dimensional space in which the presence of material at small radii becomes quantitatively evident in broad classes of disk models. In the context of the simple, thin disk paradigm, this moment-mapping scheme suggests formally that the iron line detected by the Advanced Satellite for Cosmology and Astrophysics mission from MCG -6-30-15 (Tanaka et al.) is ~3 times more likely to originate from a disk about a rotating black hole than from a Schwarzschild system. A statistically significant detection of black hole rotation in this way may be achieved after only modest improvements in the quality of data. We also consider light curves and frequency shifts in line emission as a function of time for corotating hot spots in extreme Kerr and Schwarzschild geometries. The frequency-shift profile is a valuable measure of orbital parameters and might possibly be used to detect frame dragging even at radii approaching 6GM/c2 if the inclination angle of the orbital plane is large. The light curve from a hot spot shows differences as well, although these too are pronounced only at large inclination angles.

Tidal disruptions by supermassive black holes - Hydrodynamic evolution of stars on a Schwarzschild background

We present a three-dimensional numerical study of tidal disruption of a main-sequence star (M * =1 M ○. ) by a supermassive black hole (M h =106 M ○. ). The simulations include general relativistic erects which are important in this regime. We analyze stars in a marginally bound orbit around the black hole with pericentric separation of a few Schwarzschild radii. We show that during a close passage, as a result of relativistic effects analogous to the perihelion shift, the trajectories of the debris of the star fan out into a crescent-like shape centered on the black hole

Holographic generation of complex fields with spatial light modulators: application to quantum key distribution

There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2pi optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.

The inner edge of the accretion disk around a supermassive black hole

Massive black holes are generally thought to exist at the centres of galaxies, but an unambiguous identification of a black hole has been impeded by a lack of evidence for the strong-field relativistic effects expected in the vicinity of such an object. Several years ago, a very broad iron emission line was discovered in the active galaxy MCG-6-30-15, indicative of emission from an accretion disk near the event horizon of a black hole. But this interpretation, based on the line profile, was somewhat model dependent (refs 2–5). Here we present an analysis of the iron-line emission from MCG-6-30-15 that is insensitive to the details (for example, diskthickness and emissivity) of the disk model used. We find that the inner edge of the disk material giving rise to the line is within 2.6 ± 0.3 times the Schwarzschild radius—the event horizon of a non-rotating black hole—at the 95% confidence level. Changes to the disk parameters can only decrease the inner radius of the emitting region, and so we can be confident that we are observing emission from gravitationally bound material in the strong-field region of a supermassive black hole. Moreover, we find that the black hole is rotating at a rate which is [gsims]23 ± 17% of the theoretical maximum, although this conclusion is model dependent.

Parallelizable implicit evolution scheme for Regge calculus

The role of Regge calculus as a tool for numerical relativity is discussed, and a parallelizable implicit evolution scheme described. Because of the structure of the Regge equations, it is possible to advance the vertices of a triangulated spacelike hypersurface in isolation, solving at each vertex a purely local system of implicit equations for the new edge lengths involved. (In particular, equations of global “elliptic type” do not arise.) Consequently, there exists a parallel evolution scheme which divides the vertices into families of nonadjacent elements and advances all the vertices of a family simultaneously. The relation between the structure of the equations of motion and the Bianchi identities is also considered. The method is illustrated by a preliminary application to a 600-cell Friedmann cosmology. The parallelizable evolution algorithm described in this paper should enable Regge calculus to be a viable discretization technique in numerical relativity.

Smoothed particle hydrodynamics near a black hole

We derive the smoothed particle hydrodynamic equations for a relativistic fluid in a static curved spacetime geometry. We apply this technique to develop a three-dimensional numerical code for the study of fluid flows around black holes. We present here three one-dimensional benchmarks used in the calibration of our code: (1) relativistic shock tubes, (2) dust infall onto a black hole, and (3) Bondi collapse. Moreover, we describe briefly the use of this computational tool to analyze the tidal disruption of stars by supermassive black holes

A fully -dimensional Regge calculus model of the Kasner cosmology

We describe the first discrete-time 4-dimensional numerical application of Regge calculus. The spacetime is represented as a complex of 4-dimensional simplices, and the geometry interior to each 4-simplex is flat Minkowski spacetime. This simplicial spacetime is constructed so as to be foliated with a one parameter family of spacelike hypersurfaces built of tetrahedra. We implement a novel two-surface initial-data prescription for Regge calculus, and provide the first fully 4-dimensional application of an implicit decoupled evolution scheme (the “Sorkin evolution scheme”). We benchmark this code on the Kasner cosmology — a cosmology which embodies generic features of the collapse of many cosmological models. We (1) reproduce the continuum solution with a fractional error in the 3-volume of 10−5 after 10000 evolution steps, (2) demonstrate stable evolution, (3) preserve the standard deviation of spatial homogeneity to less than 10−10 and (4) explicitly display the existence of diffeomorphism freedom in Regge calculus. We also present the second-order convergence properties of the solution to the continuum. PACS numbers: 04.20.-q, 04.25.Dm, 04.60.Nc. 1. Regge calculus as an independent tool in general relativity In this paper we describe the first fully (3+1)-dimensional application of Regge calculus [1, 2] to general relativity. We develop an initial-value prescription based on the standard York formalism, and implement a 4-stage parallel evolution algorithm. We benchmark these on the Kasner cosmological model. We present three findings. First, that the Regge solution exhibits second-order convergence of the physical variables to the continuum Kasner solution. Secondly, ‡ Permanent address: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia. Email: adrian@newton.maths.monash.edu.au

Spin dynamics of the LAGEOS satellite in support of a measurement of the Earth's gravitomagnetism.

LAGEOS is an accurately tracked, dense spherical satellite covered with 426 retroreflectors. Ciufolini has suggested the launch of an additional satellite (LAGEOS-3) into an orbit supplementary to that of the 1976-launched LAGEOS-1. In addition to providing a more accurate real-time measurement of the Earths length of day and polar wobble, this paired-satellite experiment would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite, and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. Consequently, we undertake here a theoretical effort to model the spin dynamics of LAGEOS. In this paper we derive, and solve numerically, a set of Euler equations that evolve the angular momentum vector for a slightly oblate spheroid of brass orbiting an Earth-like mass, idealized as being a perfect sphere and having a perfect polar-oriented dipole magnetic field. We have identified three phases of the rotational dynamics---a fast spin phase, a spin-orbit resonance phase, and an asymptotic (tidally locked) phase. From our numerical runs we give analytic expressions for this tidally locked phase.

Off-Axis Neutrino Scattering in Gamma-Ray Burst Central Engines

The search for an understanding of an energy source great enough to explain the gamma-ray burst (GRB) phenomenon has attracted much attention from the astrophysical community since its discovery. In this paper we extend the work of Asano and Fukuyama, and Salmonson and Wilson and analyze the off-axis contributions to the energy-momentum deposition rate (MDR) from the ν- collisions above a rotating black hole/thin accretion disk system. Our calculations are performed by imaging the accretion disk at a specified observer using the full geodesic equations and calculating the cumulative MDR from the scattering of all pairs of neutrinos and antineutrinos arriving at the observer. Our results shed light on the beaming efficiency of GRB models of this kind. Although we confirm Asano and Fukuyamas conjecture as to the constancy of the beaming for small angles away from the axis, we find that the dominant contribution to the MDR comes from near the surface of the disk with a tilt of approximately π/4 in the direction of the disks rotation. We find that the MDR at large radii is directed outward in a conic section centered around the symmetry axis and is larger by a factor of 10-20 than the on-axis values. By including this off-axis disk source, we find a linear dependence of the MDR on the black hole angular momentum.

Estimation of Relativistic Accretion Disk Parameters From Iron Line Emission

The observed iron Kα fluorescence lines in Seyfert 1 galaxies provide strong evidence for an accretion disk near a supermassive black hole as a source of the emission. Here we present an analysis of the geometrical and kinematic properties of the disk based on the extreme frequency shifts of a line profile as determined by measurable flux in both the red and blue wings. The edges of the line are insensitive to the distribution of the X-ray flux over the disk and hence provide a robust alternative to profile fitting of disk parameters. Our approach yields new, strong bounds on the inclination angle of the disk and the location of the emitting region. We apply our method to interpret observational data from MCG -6-30-15 and find that the commonly assumed inclination 30° for the accretion disk in MCG -6-30-15 is inconsistent with the position of the blue edge of the line at a 3 σ level. A thick turbulent disk model or the presence of highly ionized iron may reconcile the bounds on inclination from the line edges with the full line profile fits based on simple, geometrically thin disk models. The bounds on the innermost radius of disk emission indicate that the black hole in MCG -6-30-15 is rotating faster than 30% of theoretical maximum. When applied to data from NGC 4151, our method gives bounds on the inclination angle of the X-ray-emitting inner disk of 50° ± 10°, consistent with the presence of an ionization cone grazing the disk as proposed by Pedlar. The frequency extrema analysis also provides limits to the innermost disk radius in another Seyfert 1 galaxy, NGC 3516, and is suggestive of a thick-disk model.