Robert F. Penna

Simulations of magnetized discs around black holes: effects of black hole spin, disc thickness and magnetic field geometry

The standard general relativistic model of a razor-thin accretion disc around a black hole, developed by Novikov & Thorne (NT) in 1973, assumes the shear stress vanishes at the radius of the innermost stable circular orbit (ISCO) and that, outside the ISCO, the shear stress is produced by an effective turbulent viscosity. However, astrophysical accretion discs are not razor thin; it is uncertain whether the shear stress necessarily vanishes at the ISCO, and the magnetic field, which is thought to drive turbulence in discs, may contain large-scale structures that do not behave like a simple local scalar viscosity. We describe 3D general relativistic magnetohydrodynamic simulations of accretion discs around black holes with a range of spin parameters, and we use the simulations to assess the validity of the NT model. Our fiducial initial magnetic field consists of multiple (alternating polarity) poloidal field loops whose shape is roughly isotropic in the disc in order to match the isotropic turbulence expected in the poloidal plane. For a thin disc with an aspect ratio |h/r| ∼ 0.07 around a non-spinning black hole, we find a decrease in the accreted specific angular momentum of 2.9 per cent relative to the NT model and an excess luminosity from inside the ISCO of 3.5 per cent. The deviations in the case of spinning black holes are also of the same order. In addition, the deviations decrease with decreasing |h/r|. We therefore conclude that magnetized thin accretion discs in X-ray binaries in the thermal/high-soft spectral state ought to be well described by the NT model, especially at luminosities below 30 per cent of Eddington where we expect a very small disc thickness |h/r| ≲ 0.05. We use our results to determine the spin equilibrium of black hole accretion discs with a range of thicknesses and to determine how electromagnetic stresses within the ISCO depend upon black hole spin and disc thickness. We find that the electromagnetic stress and the luminosity inside the ISCO depend on the assumed initial magnetic field geometry. We consider a second geometry with field lines following density contours, which for thin discs leads to highly radially elongated magnetic field lines. This gives roughly twice larger deviations from NT for both the accreted specific angular momentum and the luminosity inside the ISCO. Lastly, we find that the discs corona (including any wind or jet) introduces deviations from NT in the specific angular momentum that are comparable to those contributed by the disc component, while the excess luminosity of bound gas from within the ISCO is dominated by only the disc component. Based on these indications, we suggest that differences in results between our work and other similar work are due to differences in the assumed initial magnetic field geometry as well as the inclusion of disc gas versus all the gas when comparing the specific angular momentum from the simulations with the NT model.

Measuring the spins of accreting black holes

A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the x-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit, whose radius depends only on the mass and spin of the black hole. In the Fe Kα method, which applies to both classes of black holes, one models the profile of the relativistically broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuum-fitting (CF) method, which has so far only been applied to stellar-mass black holes, one models the thermal x-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the CF method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.

GRMHD simulations of magnetized advection‐dominated accretion on a non‐spinning black hole: role of outflows

We present results from two long-duration general relativistic magneto-hydrodynamic (GRMHD) simulations of advection-dominated accretion around a non-spinning black hole. The first simulation was designed to avoid significant accumulation of magnetic flux around the black hole. This simulation was run for a time of 200 000 GM/c3 and achieved inflow equilibrium out to a radius ∼90 GM/c2. Even at this relatively large radius, the mass outflow rate is found to be only 60 per cent of the net mass inflow rate into the black hole. The second simulation was designed to achieve substantial magnetic flux accumulation around the black hole in a magnetically arrested disc. This simulation was run for a shorter time of 100 000 GM/c3. Nevertheless, because the mean radial velocity was several times larger than in the first simulation, it reached inflow equilibrium out to a radius ∼170 GM/c2. Here, becomes equal to at r ∼ 160 GM/c2. Since the mass outflow rates in the two simulations do not show robust convergence with time, it is likely that the true outflow rates are lower than our estimates. The effect of black hole spin on mass outflow remains to be explored. Neither simulation shows strong evidence for convection, though a complete analysis including the effect of magnetic fields is left for the future.

High-energy particle acceleration at the radio-lobe shock of Centaurus A

We present new results on the shock around the southwest radio lobe of Centaurus A using data from the Chandra Very Large Programme observations (740 ks total observing time). The X-ray spectrum of the emission around the outer southwestern edge of the lobe is well described by a single power-law model with Galactic absorption ‐ thermal models are strongly disfavoured, except in the region closest to the nucleus. We conclude that a significant fraction of the X-ray emission around the southwest part of the lobe is synchrotron, not thermal. We infer that in the region where the shock is strongest and the ambient gas density lowest, the inflation of the lobe is accelerating particles to X-ray sync hrotron emitting energies, similar to supernova remnants such as SN1006. This interpretation resolves a problem of our earlier, purely thermal, interpretation for this emission, namely t hat the density compression across the shock was required to be much larger than the theoretically expected factor of 4. We describe a self-consistent model for the lobe dynamics and shock properties using the shell of thermal emission to the north of the lobe to estimate the lobe pressure. Based on this model, we estimate that the lobe is expanding to the southwest with a velocity of �2600 km s 1 , roughly Mach 8 relative to the ambient medium. We discuss the spatial variation of spectral index across the shock region, concluding that our observations constrain γmax for the accelerated particles to be �10 8 at the strongest part of the shock, consistent with expectat ions from diffusive shock acceleration theory. Finally, we consider the implications of these results for the production of ultra-high energy cosmic rays (UHECRs) and TeV emission from Centaurus A, concluding that the shock front region is unlikely to be a significant source of UHECRs, but that TeV emission from this region is expected at levels comparable to current limits at TeV energies, for plausible assumed magnetic field strength s.

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.

Energy, momentum and mass outflows and feedback from thick accretion discs around rotating black holes

Using long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficient accretion discs, the energy, momentum and mass outflow rates from such systems are estimated. Outflows occur via two fairly distinct modes: a relativistic jet and a sub-relativistic wind. The jet power depends strongly on the black hole spin and on the magnetic flux at the horizon. Unless these are very small, the energy output in the jet dominates over that in the wind. For a rapidly spinning black hole accreting in the magnetically arrested limit, it is confirmed that jet power exceeds the total rate of accretion of rest mass energy. However, because of strong collimation, the jet probably does not have a significant feedback effect on its immediate surroundings. The power in the wind is more modest and shows a weaker dependence on black hole spin and magnetic flux. Nevertheless, because the wind subtends a large solid angle, it is expected to provide efficient feedback on a wide range of scales inside the host galaxy. Empirical formulae are obtained for the energy and momentum outflow rates in the jet and the wind.

The eye of the storm: light from the inner plunging region of black hole accretion discs

It is generally thought that the light coming from the inner plunging region of black hole accretion discs contributes negligibly to the disc’s overall spectrum, i.e. the plunging fluid is swallowed by the black hole before it has time to radiate. In the standard disc model used to fit X-ray observations of accretion discs, the plunging region is assumed to be perfectly dark. However, numerical simulations that include the full physics of the magnetized flow predict that a small fraction of the disc’s total luminosity emanates from this plunging region. In this work, we investigate the observational consequences of this neglected inner light. We compute radiative transfer based disc spectra that correspond to 3D general relativistic magnetohydrodynamic simulated discs (which produce light inside their plunging regions). In the context of black hole spin estimation, we find that this neglected inner light only has a modest effect (this bias is less than typical observational systematic errors). For rapidly spinning black holes, we find that the combined emission from the plunging region produces a weak power law tail at high energies. This indicates that infalling matter is the origin for some of the ‘coronal’ emission observed in the thermal dominant and steep power law states of X-ray binaries.

The Shakura-Sunyaev viscosity prescription with variable α (r)

Almost all hydrodynamic accretion disk models parametrize viscosity with the dimensionless parameter alpha. There is no detailed model for alpha, so it is usually taken to be a constant. However, global simulations of magnetohydrodynamic disks find that alpha varies with distance from the central object. Also, Newtonian simulations tend to find smaller alphas than general relativistic simulations. We seek a one-dimensional model for alpha that can reproduce these two observations. We are guided by data from six general relativistic magnetohydrodynamic accretion disk simulations. The variation of alpha in the inner, laminar regions of the flow results from stretching of mean magnetic field lines by the flow. The variation of alpha in the outer, turbulent regions results from the dependence of the magnetorotational instability on the dimensionless shear rate. We give a one-dimensional prescription for alpha(r) that captures these two effects and reproduces the radial variation of alpha observed in the simulations. For thin disks, the prescription simplifies to the formula alpha(r)=0.025[q(r)/1.5]^6, where the shear parameter, q(r), is an analytical function of radius in the Kerr metric. The coefficient and exponent are inferred from our simulations and will change as better simulation data becomes available. We conclude that the alpha-viscosity prescription can be extended to the radially varying alphas observed in simulations. It is possible that Newtonian simulations find smaller alphas than general relativistic simulations because the shear parameter is lower in Newtonian flows.

A chandra study of the lobe/interstellar medium interactions around the inner radio lobes of centaurus a : Constraints on the temperature structure and transport processes

We present results from deeper Chandra observations of the southwest radio lobe of Centaurus A, first described by Kraft and coworkers. We find that the sharp X-ray surface brightness discontinuity extends around ~75% of the periphery of the radio lobe and detect significant temperature jumps in the brightest regions of this discontinuity nearest to the nucleus. This demonstrates that this discontinuity is indeed a strong shock that is the result of an overpressure that has built up in the entire lobe over time. In addition, we demonstrate that if the mean free path for ions to transfer energy and momentum to the electrons behind the shock is as large as the Spitzer value, the electron and proton temperatures will not have equilibrated along the southwest boundary of the radio lobe where the shock is strongest. Thus, the proton temperature of the shocked gas could be considerably larger than the observed electron temperature, and the total energy of the outburst correspondingly larger as well. We investigate this using a simple one-dimensional shock model for a two-fluid (proton/electron) plasma. We find that for the thermodynamic parameters of the Cen A shock the electron temperature rises rapidly from ~0.29 keV (the temperature of the ambient ISM) to ~3.5 keV, at which point heating from the protons is balanced by adiabatic losses. The proton and electron temperatures do not equilibrate in a timescale less than the age of the lobe. We note that the measured electron temperature of similar features in other nearby powerful radio galaxies in poor environments may considerably underestimate the strength and velocity of the shock.

General relativistic magnetohydrodynamic simulations of Blandford–Znajek jets and the membrane paradigm

Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ∼ 0.3), spinning (0< a∗< 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum effi ciency and uniform fields on the horizon leads to a ∼ 10% overestimate of jet power, while ignoring the accretion disk leads to a further∼ 50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our seco nd result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on t he horizon. This provides intuitive yet rigorous pictures for the black hole energy extraction proc ess. Third, we compute the effective resistance of the load region and show that the load and the black hole achieve near perfect impedance matching. Taken together, these results increase our confidence in the BZ model as the correct description of jets observed from astrophysi cal black holes.