Scott C. Noble

Dependence of Inner Accretion Disk Stress on Parameters: The Schwarzschild Case

We explore the parameter dependence of inner disk stress in black hole accretion by contrasting the results of a number of simulations, all employing three-dimensional general relativistic MHD in a Schwarzschild spacetime. Five of these simulations were performed with the intrinsically conservative code HARM3D, which allows careful regulation of the disk aspect ratio, H/R; our simulations span a range in H/R from 0.06 to 0.17. We contrast these simulations with two previously reported simulations in a Schwarzschild spacetime in order to investigate possible dependence of the inner disk stress on magnetic topology. In all cases, much care was devoted to technical issues: ensuring adequate resolution and azimuthal extent, and averaging only over those time periods when the accretion flow is in approximate inflow equilibrium. We find that the time-averaged radial dependence of fluid-frame electromagnetic stress is almost completely independent of both disk thickness and poloidal magnetic topology. It rises smoothly inward at all radii (exhibiting no feature associated with the innermost stable circular orbit, ISCO) until just outside the event horizon, where the stress plummets to zero. Reynolds stress can also be significant near the ISCO and in the plunging region; the magnitude of this stress, however, depends on both disk thickness and magnetic topology. The two stresses combine to make the net angular momentum accreted per unit rest mass 7%-15% less than the angular momentum of the ISCO.

Direct calculation of the radiative efficiency of an accretion disk around a black hole

Numerical simulation of magnetohydrodynamic (MHD) turbulence makes it possible to study accretion dynamics in detail. However, special effort is required to connect inflow dynamics (dependent largely on angular momentum transport) to radiation (dependent largely on thermodynamics and photon diffusion). To this end, we extend the flux-conservative, general relativistic MHD (GRMHD) code HARM from axisymmetry to full three dimensions. The use of an energy conserving algorithm allows the energy dissipated in the course of relativistic accretion to be captured as heat. The inclusion of a simple optically thin cooling function permits explicit control of the simulated disks geometric thickness as well as a direct calculation of both the amplitude and location of the radiative cooling associated with the accretion stresses. Fully relativistic ray-tracing is used to compute the luminosity received by distant observers. For a disk with aspect ratio H/r 0.1 accreting onto a black hole with spin parameter a/M = 0.9, we find that there is significant dissipation beyond that predicted by the classical Novikov-Thorne model. However, much of it occurs deep in the potential, where photon capture and gravitational redshifting can strongly limit the net photon energy escaping to infinity. In addition, with these parameters and this radiation model, significant thermal and magnetic energy remains with the gas and is accreted by the black hole. In our model, the net luminosity reaching infinity is 6% greater than the Novikov-Thorne prediction. If the accreted thermal energy were wholly radiated, the total luminosity of the accretion flow would be 20% greater than the Novikov-Thorne value.

General Relativistic Hydrodynamic Simulation of Accretion Flow from a Stellar Tidal Disruption

We study how the matter dispersed when a supermassive black hole tidally disrupts a star joins an accretion flow. Combining a relativistic hydrodynamic simulation of the stellar disruption with a relativistic hydrodynamics simulation of the tidal debris motion, we track such a system until ~80% of the stellar mass bound to the black hole has settled into an accretion flow. Shocks near the stellar pericenter and also near the apocenter of the most tightly-bound debris dissipate orbital energy, but only enough to make the characteristic radius comparable to the semi-major axis of the most-bound material, not the tidal radius as previously thought. The outer shocks are caused by post-Newtonian effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is non-monotonic and slow, requiring ~3--10x the orbital period of the most tightly-bound tidal streams, while the inflow time for most of the mass may be comparable to or longer than the mass accumulation time. Deflection by shocks does, however, remove enough angular momentum and energy from some mass for it to move inward even before most of the mass is accumulated into the accretion flow. Although the accretion rate rises sharply and then decays roughly as a power-law, its maximum is ~0.1x the previous expectation, and the duration of the peak is ~5x longer than previously predicted. The geometric mean of the black hole mass and stellar mass inferred from a measured event timescale is therefore ~0.2x the value given by classical theory.

CIRCUMBINARY MAGNETOHYDRODYNAMIC ACCRETION INTO INSPIRALING BINARY BLACK HOLES

We have simulated the magnetohydrodynamic evolution of a circumbinary disk surrounding an equal-mass binary comprising two non-spinning black holes during the period in which the disk inflow time is comparable to the binary evolution time due to gravitational radiation. Both the changing spacetime and the binary orbital evolution are described by an innovative technique utilizing high-order post-Newtonian approximations. Prior to the beginning of the inspiral, the structure of the circumbinary disk is predicted well by extrapolation from Newtonian results: a gap of roughly two binary separation radii is cleared, and matter piles up at the outer edge of this gap as inflow is retarded by torques exerted by the binary; the accretion rate is roughly half its value at large radius. During inspiral, the inner edge of the disk initially moves inward in coordination with the shrinking binary, but—as the orbital evolution accelerates—the inward motion of the disk edge falls behind the rate of binary compression. In this stage, the binary torque falls substantially, but the accretion rate decreases by only 10%-20%. When the binary separation is tens of gravitational radii, the rest-mass efficiency of disk radiation is a few percent, suggesting that supermassive binary black holes could be very luminous at this stage of their evolution. Inner disk heating is modulated at a beat frequency comparable to the binary orbital frequency. However, a disk with sufficient surface density to be luminous may be optically thick, suppressing periodic modulation of the luminosity.

Simulating the emission and outflows from accretion discs

The radio source Sagittarius A* (Sgr A*) is believed to be a hot, inhomogeneous, magnetized plasma flowing near the event horizon of the 3.6 × 106 M⊙ black hole at the galactic centre. At a distance of 8 kpc ( 2.5 × 1022 cm) the black hole would be among the largest black holes as judged by angular size. Recent observations are consistent with the idea that the millimetre and sub-millimetre photons are dominated by optically thin, thermal synchrotron emission. Anticipating future Very Long Baseline Interferometry (VLBI) observations of Sgr A* at these wavelengths, we present here the first dynamically self-consistent models of millimetre and sub-millimetre emission from Sgr A* based on general relativistic numerical simulations of the accretion flow. Angle-dependent spectra are calculated assuming a thermal distribution of electrons at the baryonic temperature dictated by the simulation and the accretion rate, which acts as a free parameter in our model. The effects of varying model parameters (black hole spin and inclination of the spin to the line of sight) and source variability on the spectrum are shown. We find that the accretion rate value needed to match our calculated millimetre flux to the observed flux is consistent with constraints on the accretion rate inferred from detections of the rotation measure. We also describe the relativistic jet that is launched along the black hole spin axis by the accretion disc and evolves to scales of ~103GMc−2, where M is the mass of the black hole.

Near-infrared and X-Ray Quasi-periodic Oscillations in Numerical Models of Sgr?A*

We report transient quasi-periodic oscillations (QPOs) on minute timescales in relativistic, radiative models of the galactic center source Sgr A*. The QPOs result from nonaxisymmetric m = 1 structure in the accretion flow excited by MHD turbulence. Near-infrared (NIR) and X-ray power spectra show significant peaks at frequencies comparable to the orbital frequency at the innermost stable circular orbit (ISCO) f{sub o} . The excess power is associated with inward propagating magnetic filaments inside the ISCO. The amplitudes of the QPOs are sensitive to the electron distribution function. We argue that transient QPOs appear at a range of frequencies in the neighborhood of f{sub o} and that the power spectra, averaged over long times, likely show a broad bump near f{sub o} rather than distinct, narrow QPO features.

GLOBAL GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF BLACK HOLE ACCRETION FLOWS: A CONVERGENCE STUDY

Global, general relativistic magnetohydrodynamic (GRMHD) simulations of non-radiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of four in linear resolution, from 96 × 96 × 64 to 384 × 384 × 256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma β ;( 2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma β decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of two in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model (“shearing box”) calculations and with the recent non-relativistic global convergence studies of Hawley et al.Global, general relativistic magnetohydrodynamic (GRMHD) simulations of nonradiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of 4 in linear resolution, from 96× 96× 64 to 384×384×256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma β; (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma β decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of 2 in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model (“shearing box”) calculations and with the recent nonrelativistic global convergence studies of Hawley et al. (2011). Department of Astronomy, University of Illinois at Urbana-Champaign, 1002West Green Street, Urbana, IL 61801 Department of Astronomy, University of Illinois at Urbana-Champaign, 1002West Green Street, Urbana, IL 61801; Current address: Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623

GRMHD PREDICTION OF CORONAL VARIABILITY IN ACCRETING BLACK HOLES

On the basis of data from an energy-conserving three-dimensional general relativistic MHD simulation, we predict the statistical character of variability in the coronal luminosity from accreting black holes. When the inner boundary of the corona is defined to be the electron scattering photosphere, its location depends only on the mass accretion rate in Eddington units . Nearly independent of viewing angle and , the power spectrum over the range of frequencies from approximately the orbital frequency at the ISCO to ~100 times lower is well approximated by a power law with index –2, crudely consistent with the observed power spectra of hard X-ray fluctuations in active galactic nuclei and the hard states of Galactic black hole binaries. The underlying physical driver for variability in the light curve is variations in the accretion rate caused by the chaotic character of MHD turbulence, but the power spectrum of the coronal light output is significantly steeper. Part of this contrast is due to the fact that the mass accretion rate can be significantly modulated by radial epicyclic motions that do not result in dissipation, and therefore do not drive luminosity fluctuations. The other part of this contrast is due to the inward decrease of the characteristic inflow time, which leads to decreasing radial coherence length with increasing fluctuation frequency.

GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit

We present the new general-relativistic magnetohydrodynamics (GRMHD) capabilities of the Einstein toolkit, an open-source community-driven numerical relativity and computational relativistic astrophysics code. The GRMHD extension of the toolkit builds upon previous releases and implements the evolution of relativistic magnetized fluids in the ideal MHD limit in fully dynamical spacetimes using the same shock-capturing techniques previously applied to hydrodynamical evolution. In order to maintain the divergence-free character of the magnetic field, the code implements both constrained transport and hyperbolic divergence cleaning schemes. We present test results for a number of MHD tests in Minkowski and curved spacetimes. Minkowski tests include aligned and oblique planar shocks, cylindrical explosions, magnetic rotors, Alfv´ en waves and advected loops, as well as a set of tests designed to study the response of the divergence cleaning scheme to numerically generated monopoles. We study the code’s performance in curved spacetimes with spherical accretion onto a black hole on a fixed background spacetime

Numerical Calculation of Magnetobremsstrahlung Emission and Absorption Coefficients

Magnetobremsstrahlung (MBS) emission and absorption play a role in many astronomical systems. We describe a general numerical scheme for evaluating MBS emission and absorption coefficients for both polarized and unpolarized light in a plasma with a general distribution function. Along the way we provide an accurate scheme for evaluating Bessel functions of high order. We use our scheme to evaluate the accuracy of earlier fitting formulae and approximations. We also provide an accurate fitting formula for mildly relativistic (kT /(mec 2 ) 0.5) thermal electron emission (and therefore absorption). Our scheme is too slow, at present, for direct use in radiative transfer calculations but will be useful for anyone seeking to fit emission or absorption coefficients in a particular regime.