Shane W. Davis

SUSTAINED MAGNETOROTATIONAL TURBULENCE IN LOCAL SIMULATIONS OF STRATIFIED DISKS WITH ZERO NET MAGNETIC FLUX

We examine the effects of density stratification on magnetohydrodynamic turbulence driven by the magnetorotational instability in local simulations that adopt the shearing box approximation. Our primary result is that, even in the absence of explicit dissipation, the addition of vertical gravity leads to convergence in the turbulent energy densities and stresses as the resolution increases, contrary to results for zero net flux, unstratified boxes. The ratio of total stress to midplane pressure has a mean of ~0.01, although there can be significant fluctuations on long (50?orbits) timescales. We find that the time-averaged stresses are largely insensitive to both the radial and the vertical aspect ratios of our simulation domain. For simulations with explicit dissipation, we find that stratification extends the range of Reynolds and magnetic Prandtl numbers for which turbulence is sustained, but the behavior of such simulations on long timescales is highly variable. Confirming the results of previous studies, we find oscillations in the large-scale toroidal field with periods of ~10?orbits and describe the dynamo process that underlies these cycles. We discuss possible origins for the different convergence properties of the stratified and unstratified domains and identify open questions that remain to be answered.

Relativistic accretion disk models of high-state black hole X-ray binary spectra

We present calculations of non-LTE, relativistic accretion disk models applicable to the high/soft state of black hole X-ray binaries. We include the effects of thermal Comptonization and bound-free and free-free opacities of all abundant ion species. Taking into account the relativistic propagation of photons from the local disk surface to an observer at infinity, we present spectra calculated for a variety of accretion rates, black hole spin parameters, disk inclinations, and stress prescriptions. We also consider nonzero inner torques on the disk and explore different vertical dissipation profiles, including some that are motivated by recent radiation magnetohydrodynamic (MHD) simulations of magnetorotational turbulence. Bound-free metal opacity generally produces significantly less spectral hardening than previous models that only considered Compton scattering and free-free opacity. We find that the resulting effective photosphere usually lies at a small fraction of the total column depth, producing spectra that are remarkably independent of the stress prescription and vertical structure assumptions. We provide detailed comparisons between our models and the widely used multicolor disk model. Frequency-dependent discrepancies exist that may affect the parameters of other spectral components when this simpler disk model is used to fit modern X-ray data. For a given source, our models predict that the luminosity in the high/soft state should approximately scale with the fourth power of the empirically inferred maximum temperature, but with a slight hardening at high luminosities. This is in good agreement with observations.

The Radiative Efficiency of Accretion Flows in Individual Active Galactic Nuclei

The radiative efficiency of AGN is commonly estimated based on the total mass accreted and the total AGN light emitted per unit volume in the universe integrated over time (the Soltan argument). In individual AGN, thin accretion disk model spectral fits can be used to deduce the absolute accretion rate u M, if the black hole mass M is known. The radiative efficiencyη is then set by the ratio of the bolometric luminosity Lbol to u Mc 2 . We apply this method to determine η in a sample of 80 PG quasars with well determined Lbol, where u M is set by thin accretion disk model fits to the optical luminosity density, and the M determination based on the bulge stellar velocity dispersion (13 objects) or the broad line region (BLR). For the BLR-based masses, we derive a mean logη = −1.05 ± 0.52 consistent with the Soltan argument based estimates. We find a strong correlation of η with M, rising from η ∼ 0.03 at M = 10 7 M⊙ and L/LEdd ∼ 1 to η ∼ 0.4 at M = 10 9 M⊙ and L/LEdd ∼ 0.3. This trend is related to the overall uniformity of Lopt/Lbol in our sample, particularly the lack of the expected increase in Lopt/Lbol with increasing M (and decreasing L/LEdd), which is a generic property of thermal disk emission at fixed η. The significant uncertainty in the M determination is not large enough to remove the correlation. The rising η with M may imply a rise in the black hole spin with M, as proposed based on other indirect arguments. Subject headings: accretion, accretion disks — black hole physics — galaxies: active — galaxies: quasars: general

Estimating the spin of stellar-mass black holes by spectral fitting of the X-ray continuum

We fit X-ray spectral data in the thermal-dominant, or high-soft, state of two dynamically confirmed black holes, GRO J1655-40 and 4U 1543-47, and estimate the dimensionless spin parameters a* ≡ a/M of the two holes. For GRO J1655-40, using a spectral hardening factor computed for a non-LTE relativistic accretion disk, we estimate a* ~ 0.75 and a* ~ 0.65-0.75, respectively, from ASCA and RXTE data. For 4U 1543-47, we estimate a* ~ 0.75-0.85 from RXTE data. Thus, neither black hole has a spin approaching the theoretical maximum a* = 1.

The Eddington Limit in Cosmic Rays: An Explanation for the Observed Faintness of Starbursting Galaxies

We show that the luminosity of a star-forming galaxy is capped by the production and subsequent expulsion of cosmic rays from its interstellar medium. By defining an Eddington luminosity in cosmic rays, we show that the star formation rate of a given galaxy is limited by its mass content and the cosmic-ray mean free path. When the cosmic-ray luminosity and pressure reach a critical value as a result of vigorous star formation, hydrostatic balance is lost, a galactic-scale cosmic-ray-driven wind develops, and star formation is choked off. Cosmic-ray pressure driven winds are likely to produce wind velocities in proportion to and significantly in excess of the galactic escape velocity. It is possible that cosmic-ray feedback results in the Faber-Jackson relation for a plausible set of input parameters that describe cosmic-ray production and transport, which are calibrated by observations of the Milky Ways interstellar cosmic rays as well as other nearby galaxies.

A grid of relativistic, non-lte accretion disk models for spectral fitting of black hole binaries

Self-consistent vertical structure models together with non-LTE radiative transfer should produce spectra from accretion disks around black holes, which differ from multitemperature blackbodies at levels that may be observed. High-resolution, high signal-to-noise observations warrant spectral modeling that both accounts for relativistic effects and treats the physics of radiative transfer in detail. In Davis et al. we presented spectral models that accounted for non-LTE effects, Compton scattering, and the opacities due to ions of abundant metals. Using a modification of this method, we have tabulated spectra for black hole masses typical of Galactic binaries. We make them publicly available for spectral fitting as an XSPEC model. These models represent the most complete realization of standard accretion disk theory to date. Thus, they are well suited both for testing the theorys applicability to observed systems and for constraining properties of the black holes, including their spins.

On the Thermal Stability of Radiation-dominated Accretion Disks

We study the long-term thermal stability of radiation-dominated disks in which the vertical structure is determined self-consistently by the balance of heating due to the dissipation of MHD turbulence driven by magneto-rotational instability (MRI) and cooling due to radiation emitted at the photosphere. The calculations adopt the local shearing box approximation and utilize the recently developed radiation transfer module in the Athena MHD code based on a variable Eddington tensor rather than an assumed local closure. After saturation of the MRI, in many cases the disk maintains a steady vertical structure for many thermal times. However, in every case in which the box size in the horizontal directions are at least one pressure scale height, fluctuations associated with MRI turbulence and dynamo action in the disk eventually trigger a thermal runaway that causes the disk to either expand or contract until the calculation must be terminated. During runaway, the dependence of the heating and cooling rates on total pressure satisfy the simplest criterion for classical thermal instability. We identify several physical reasons why the thermal runaway observed in our simulations differ from the standard α disk model; for example, the advection of radiation contributes a non-negligible fraction to the vertical energy flux at the largest radiation pressure, most of the dissipation does not happen in the disk mid-plane, and the change of dissipation scale height with mid-plane pressure is slower than the change of density scale height. We discuss how and why our results differ from those published previously. Such thermal runaway behavior might have important implications for interpreting temporal variability in observed systems, but fully global simulations are required to study the saturated state before detailed predictions can be made.

Measuring black hole spin by the continuum-fitting method: effect of deviations from the Novikov–Thorne disc model

The X-ray spectra of accretion discs of eight stellar mass black holes have been analysed to date using the thermal continuum-fitting method, and the spectral fits have been used to estimate the spin parameters of the black holes. However, the underlying model used in this method of estimating spin is the general relativistic thin-disc model of Novikov & Thorne, which is only valid for razor-thin discs. We therefore expect errors in the measured values of spin due to inadequacies in the theoretical model. We investigate this issue by computing spectra of numerically calculated models of thin accretion discs around black holes, obtained via three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. We apply the continuum-fitting method to these computed spectra to estimate the black hole spins and check how closely the values match the actual spin used in the GRMHD simulations. We find that the error in the dimensionless spin parameter is up to about 0.2 for a non-spinning black hole, depending on the inclination. For black holes with spins of 0.7, 0.9 and 0.98, the errors are up to about 0.1, 0.03 and 0.01, respectively. These errors are comparable to or smaller than those arising from current levels of observational uncertainty. Furthermore, we estimate that the GRMHD simulated discs from which these error estimates are obtained correspond to effective disc luminosities of about 0.4–0.7 Eddington, and that the errors will be smaller for discs with luminosities of 0.3 Eddington or less, which are used in the continuum-fitting method. We thus conclude that use of the Novikov–Thorne thin-disc model does not presently limit the accuracy of the continuum-fitting method of measuring black hole spin.

The origin of the Fe K features in Markarian 205 and Markarian 509

We examine the 3-10 keV EPIC spectra of Mrk 205 and 509 to investigate their Fe K features. The most significant feature in the spectra of both objects is an emission line at 6.4 keV. The spectra can be adequately modelled with a power law and a relatively narrow (sigma < 0.2 keV) Fe Kalpha emission line. Better fits are obtained when an additional Gaussian emission line, relativistic accretion-disc line, or Compton reflection from cold material, is added to the spectral model. We obtain similar goodness of fit for any of these three models, but the model including Compton reflection from cold material offers the simplest, physically self-consistent solution, because it only requires one reprocessing region. Thus the Fe K spectral features in Mrk 205 and 509 do not present strong evidence for reprocessing in the inner, relativistic parts of accretion discs.

A Radiation Transfer Solver for Athena Using Short Characteristics

We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athenas MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.