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 3-d 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 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.Comment: Accepted for publication in ApJ, 52 pages, 38 figures, AASTEX. High-resolution versions can be found at the following links: http://ccrg.rit.edu/~scn/papers/schwarzstress.ps, http://ccrg.rit.edu/~scn/papers/schwarzstress.pd

Extending learning opportunities: a framework for self-evaluation in study support

The Extending Learning Opportunities (ELO) framework for selfevaluation in study support is a tool to use when quality assuring learning opportunities for children and young people outside of normal lesson time. This framework is a revised edition of the ELO (2009) DCSF publication. It provides a framework for all schools, and school consortiums including Complementary Supplementary Schools, Children’s Centres, Playing for Success (PfS) centres, Higher Education Institutions (HEIs) and organisations such as libraries, museums, galleries, theatres, including youth and community/volunteer projects that offer a structured learning programmes to young people, to extend and enhance their provision and so to improve their outcomes. It is based on self–evaluation and sets out criteria against which schools, HEIs and other organisations, can review their extended provision, the planning and practices which support it and the overall ethos which supports learning. The criteria, which take the form of Key Indicators, are at three levels: Emerged, Established and Advanced

Radiative efficiency and thermal spectrum of accretion onto Schwarzschild black holes

Recent general relativistic magneto-hydrodynamic (MHD) simulations of accretion onto black holes have shown that, contrary to the basic assumptions of the Novikov-Thorne model, there can be substantial magnetic stress throughout the plunging region. Additional dissipation and radiation can therefore be expected. We use data from a particularly well-resolved simulation of accretion onto a non-spinning black hole to compute both the radiative efficiency of such a flow and its spectrum if all emitted light is radiated with a thermal spectrum whose temperature matches the local effective temperature. This disk is geometrically thin enough (H/r ~= 0.06) that little heat is retained in the flow. In terms of light reaching infinity (i.e., after allowance for all relativistic effects and for photon capture by the black hole), we find that the radiative efficiency is at least ~=6-10% greater than predicted by the Novikov-Thorne model (complete radiation of all heat might yield another ~6%). We also find that the spectrum more closely resembles the Novikov-Thorne prediction for a/M ~= 0.2--0.3 than for the correct value, a/M=0. As a result, if the spin of a non-spinning black hole is inferred by model-fitting to a Novikov-Thorne model with known black hole mass, distance, and inclination, the inferred a/M is too large by ~= 0.2--0.3.Comment: Submitted to ApJ, 26 pages, 12 figures (some in color), AASTE

Pair Production in Low Luminosity Galactic Nuclei

Electron-positron pairs may be produced near accreting black holes by a variety of physical processes, and the resulting pair plasma may be accelerated and collimated into a relativistic jet. Here we use a self-consistent dynamical and radiative model to investigate pair production by \gamma\gamma collisions in weakly radiative accretion flows around a black hole of mass M and accretion rate \dot{M}. Our flow model is drawn from general relativistic magnetohydrodynamic simulations, and our radiation field is computed by a Monte Carlo transport scheme assuming the electron distribution function is thermal. We argue that the pair production rate scales as r^{-6} M^{-1} \dot{M}^{6}. We confirm this numerically and calibrate the scaling relation. This relation is self-consistent in a wedge in M, \dot{M} parameter space. If \dot{M} is too low the implied pair density over the poles of the black hole is below the Goldreich-Julian density and \gamma\gamma pair production is relatively unimportant; if \dot{M} is too high the models are radiatively efficient. We also argue that for a power-law spectrum the pair production rate should scale with the observables L_X \equiv X-ray luminosity and M as L_X^2 M^{-4}. We confirm this numerically and argue that this relation likely holds even for radiatively efficient flows. The pair production rates are sensitive to black hole spin and to the ion-electron temperature ratio which are fixed in this exploratory calculation. We finish with a brief discussion of the implications for Sgr A* and M87.Comment: 21 pages, 10 figures, 1 table. Accepted for publication in Ap

Numerical Models of Viscous Accretion Flows Near Black Holes

We report on a numerical study of viscous fluid accretion onto a black hole. The flow is axisymmetric and uses a pseudo-Newtonian potential to model relativistic effects near the event horizon. The numerical method is a variant of the ZEUS code. As a test of our numerical scheme, we are able to reproduce results from earlier, similar work by Igumenshchev and Abramowicz and Stone et al. We consider models in which mass is injected onto the grid as well as models in which an initial equilibrium torus is accreted. In each model we measure three ``eigenvalues'' of the flow: the accretion rate of mass, angular momentum, and energy. We find that the eigenvalues are sensitive to r_{in}, the location of the inner radial boundary. Only when the flow is always supersonic on the inner boundary are the eigenvalues insensitive to small changes in r_{in}. We also report on the sensitivity of the results to other numerical parameters.Comment: 14 pages, 4 figures, 2 tables, to appear in v573 n2 pt1 ApJ July 10, 200

Vortices in Thin, Compressible, Unmagnetized Disks

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, . This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.Comment: 8 pages, 10 figures (high resolution figures available in ApJ electronic edition

GRMHD prediction of coronal variability in accreting black holes

On the basis of data from an energy-conserving 3D 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 (\dot{M}). Nearly independent of viewing angle and \dot{M}, the power spectrum over the range of frequencies from approximately the orbital frequency at the innermost stable circular orbit (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 AGN and the hard states of Galactic binary black holes. 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.Comment: Accepted for publication in ApJ, 35 pages, 11 figures (8 color and 3 greyscale), AASTEX. High-resolution versions can be found at the following links: [PS] http://www.pha.jhu.edu/~scn/papers/grmhd_var.ps [PDF] http://www.pha.jhu.edu/~scn/papers/grmhd_var.pd

On the evolution of mean motion resonances through stochastic forcing: Fast and slow libration modes and the origin of HD128311

Aims. We clarify the response of extrasolar planetary systems in a 2:1 mean motion commensurability with masses ranging from the super Jovian range to the terrestrial range to stochastic forcing that could result from protoplanetary disk turbulence. The behaviour of the different libration modes for a wide range of system parameters and stochastic forcing magnitudes is investigated. The growth of libration amplitudes is parameterized as a function of the relevant physical parameters. The results are applied to provide an explanation of the configuration of the HD128311 system. Methods. We first develop an analytic model from first principles without making the assumption that both eccentricities are small. We also perform numerical N-body simulations with additional stochastic forcing terms to represent the effects of putative disk turbulence. Results. Systems are quickly destabilized by large magnitudes of stochastic forcing but some stability is imparted should systems undergo a net orbital migration. The slow mode, which mostly corresponds to motion of the angle between the apsidal lines of the two planets, is converted to circulation more readily than the fast mode which is associated with oscillations of the semi-major axes. This mode is also vulnerable to the attainment of small eccentricities which causes oscillations between periods of libration and circulation. Conclusions. Stochastic forcing due to disk turbulence may have played a role in shaping the configurations of observed systems in mean motion resonance. It naturally provides a mechanism for accounting for the HD128311 system.Comment: 15 pages, 8 figures, added discussion in h and k coordinates, recommended for publicatio

A longitudinal study of muscle rehabilitation in the lower leg after cast removal using Magnetic Resonance Imaging and strength assessment

Acknowledgements We thank the A&E nurses and plaster technicians for identifying suitable patients, the MRI radiographers for performing the scanning, Dr Scott Semple for invaluable help in some of the pilot studies and Mr E. C. Stevenson for constructing the footrest used in the scanner. We are very grateful to the dedicated patients themselves who gave considerable amounts of time to come in for scanning, exercise and assessment during the course of this study.Peer reviewedPublisher PD

Estimation of bladder contractility from intravesical pressure–volume measurements

© 2016 Wiley Periodicals, Inc. Aims: To describe parameters from urodynamic pressure recordings that describe urinary bladder contractility through the use of principles of muscle mechanics. Methods: Subtracted detrusor pressure and voided flow were recorded from patients undergoing filling cystometry. The isovolumetric increase of detrusor pressure, P, of a voluntary bladder contraction before voiding was used to generate a plot of (dP/dt)/P versus P. Extrapolation of the plot to the y-axis and the x-axis generated a contractility parameter, vCE (the maximum rate of pressure development) and the maximum isovolumetric pressure, P0, respectively. Similar curves were obtained in ex vivo pig bladders with different concentrations of the inotropic agent carbachol and shown in a supplement. Results: Values of vCE, but not P0, diminished with age in female subjects. vCE was most significantly associated with the 20–80% duration of isovolumetric contraction t20–80; and a weaker association with maximum flow rate and BCI in women. P0 was not associated with any urodynamic variable in women, but in men was with t20–80 and isovolumetric pressure indices. Conclusions: The rate of isovolumetric subtracted detrusor pressure (t20–80) increase shows a very significant association with indices of bladder contractility as derived from a derived force–velocity curve. We propose that t20–80 is a detrusor contractility parameter (DCP). Neurourol. Urodynam. 36:1009–1014, 2017. © 2016 Wiley Periodicals, Inc