arXiv subjects

Jonathan C. McKinney

Publications and source records attributed to Jonathan C. McKinney.

65 records · Page 4Linked to original sources

arXiv2005

Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics

Conservative numerical schemes for general relativistic magnetohydrodynamics (GRMHD) require a method for transforming between ``conserved'' variables such as momentum and energy density and ``primitive'' variables such as rest-mass density, internal energy, and components of the four-velocity. The forward transformation (primitive to conserved) has a closed-form solution, but the inverse transformation (conserved to primitive) requires the solution of a set of five nonlinear equations. Here we discuss the mathematical properties of the inverse transformation and present six numerical methods for performing the inversion. The first method solves the full set of five nonlinear equations directly using a Newton-Raphson scheme and a guess from the previous timestep. The other methods reduce the five nonlinear equations to either one or two nonlinear equations that are solved numerically. Comparisons between the methods are made using a survey over phase space, a two-dimensional explosion problem, and a general relativistic MHD accretion disk simulation. The run-time of the methods is also examined. Code implementing the schemes is available for download on the web.

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arXiv2005

Total and Jet Blandford-Znajek Power in Presence of Accretion Disk

A rotating black hole probably powers ultrarelativistic jets in gamma-ray bursts, relativistic jets from some active galactic nuclei, and jets from some black hole x-ray binaries. Prior estimates of the power output of a black hole have assumed an infinitely thin disk, a magnetic field based upon a slowly rotating black hole, and have not self-consistently determined the geometry or magnitude of the magnetic field for a realistic accretion disk. We provide useful formulae for the total and jet Blandford-Znajek (BZ) power and efficiency as determined self-consistently from general relativistic magnetohydrodynamic numerical models. Of all jet mechanisms, we suggest that only the BZ mechanism is able to produce an ultrarelativistic jet.

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arXiv2005

Jet Formation in Black Hole Accretion Systems I: Theoretical Unification Model

Two types of relativistic jets are suggested to form near accreting black holes: a potentially ultrarelativistic Poynting-dominated jet and a Poynting-baryon jet. One source of jet matter is electron-positron pair production, which is driven by neutrino annihilation in GRBs and photon annihilation in AGN and x-ray binaries. GRB Poynting-dominated jets are also loaded by electron-proton pairs by the collisional cascade of Fick-diffused free neutrons. We show that, for the collapsar model, the neutrino-driven enthalpy flux (classic fireball model) is probably dominated by the Blandford-Znajek energy flux, which predicts a jet Lorentz factor of $Γ\sim 100-1000$. We show that radiatively inefficient AGN, such as M87, are synchrotron-cooling limited to $Γ\sim 2-10$. Radiatively efficient x-ray binaries, such as GRS1915+105, are Compton-drag limited to $Γ\lesssim 2$, but the jet may be destroyed by Compton drag. However, the Poynting-baryon jet is a collimated outflow with $Γ\sim 1-3$. The jet from radiatively efficient systems, such as microquasar GRS1915+105, may instead be a Poynting-baryon jet that is only relativistic when the disk is geometrically thick. In a companion paper, general relativistic hydromagnetic simulations of black hole accretion with pair creation are used to simulate jet formation in GRBs, AGN, and x-ray binaries.

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arXiv2005

Jet Formation in Black Hole Accretion Systems II: Numerical Models

In a companion theory paper, we presented a unified model of jet formation. We suggested that primarily two types of relativistic jets form near accreting black holes: a potentially ultrarelativistic Poynting-dominated jet and a Poynting-baryon jet. We showed that, for the collapsar model, the neutrino-driven enthalpy flux (classic fireball model) is probably dominated by the Blandford-Znajek energy flux, which predicts a jet Lorentz factor of $Γ\sim 100-1000$. We showed that radiatively inefficient AGN, such as M87, are synchrotron-cooling limited to $Γ\sim 2-10$. Radiatively efficient x-ray binaries, such as GRS1915+105, are Compton-drag limited to $Γ\lesssim 2$, but the jet may be destroyed by Compton drag. However, the Poynting-baryon jet is a collimated outflow with $Γ\sim 1-3$. Here we present general relativistic hydromagnetic simulations of black hole accretion with pair creation used to simulate jet formation in GRBs, AGN, and x-ray binaries. Our collapsar model shows the development of a patchy ``magnetic fireball'' with typically $Γ\sim 100-1000$ and a Gaussian structure. Temporal variability of the jet is dominated by toroidal field instabilities for $\gtrsim 10^2$ gravitational radii. A broader Poynting-baryon jet with $Γ\sim 1.5$ could contribute to a supernova.

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arXiv2004

A Measurement of the Electromagnetic Luminosity of a Kerr Black Hole

Some active galactic nuclei, microquasars, and gamma ray bursts may be powered by the electromagnetic braking of a rapidly rotating black hole. We investigate this possibility via axisymmetric numerical simulations of a black hole surrounded by a magnetized plasma. The plasma is described by the equations of general relativistic magnetohydrodynamics, and the effects of radiation are neglected. The evolution is followed for $2000 G M/c^3$, and the computational domain extends from inside the event horizon to typically $40 G M/c^2$. We compare our results to two analytic steady state models, including the force-free magnetosphere of Blandford & Znajek. Along the way we present a self-contained rederivation of the Blandford-Znajek model in Kerr-Schild (horizon penetrating) coordinates. We find that (1) low density polar regions of the numerical models agree well with the Blandford-Znajek model; (2) many of our models have an outward Poynting flux on the horizon in the Kerr-Schild frame; (3) none of our models have a net outward energy flux on the horizon; and (4) one of our models, in which the initial disk has net magnetic flux, shows a net outward angular momentum flux on the horizon. We conclude with a discussion of the limitations of our model, astrophysical implications, and problems to be addressed by future numerical experiments.

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arXiv2003

Anisotropy of Magnetohydrodynamic Turbulence and the Polarized Spectra of OH Masers

We consider astrophysical maser radiation that is created in the presence of mildly supersonic, magnetohydrodynamic (MHD) turbulence. The focus is on the OH masers for which the magnetic field is strong enough that the separations of the Zeeman components are greater than the spectral linebreadths. A longstanding puzzle has been the absence of the Zeeman $π$ components and the high circular polarization in the observed spectra of these masers. We first argue that the elongation of eddies along the field that has recently been recognized in MHD turbulence will enhance the optical depth parallel to the magnetic field in comparison with that perpendicular to the magnetic field. We then simulate maser emission with a numerical model of MHD turbulence to demonstrate quantitatively how the intensities of the linearly polarized $π$ components are suppressed and the intensities of the nearly circularly polarized $σ$ components are enhanced. This effect is also generic in the sense that most spectral lines in MHD turbulence with Mach number $M\sim 1$ should have larger optical depths parallel to the magnetic field than perpendicular. The effect is reduced considerably when $M<1$. The simulations also demonstrate that the velocity and magnetic field variations due to the turbulence can (but do not necessarily) cause one of the $σ$ components to be much more intense than the other, as is often observed for mainline OH masers.

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arXiv2003

Black Hole Spin Evolution

We consider a subset of the physical processes that determine the spin j = a/M of astrophysical black holes. These include: (1) Initial conditions. Recent models suggest that the collapse of supermassive stars are likely to produce black holes with j ~ 0.7. (2) Major mergers. The outcome of a nearly equal mass black hole-black hole merger is not yet known, but we review the current best guesses and analytic bounds. (3) Minor mergers. We recover the result of Blandford & Hughes that accretion of small companions with isotropically distributed orbital angular momenta results in spindown, with j ~ M^{-7/3}. (4) Accretion. We present new results from fully relativistic magnetohydrodynamic accretion simulations. These show that, at least for one sequence of flow models, spin equilibrium (dj/dt = 0) is reached for j ~ 0.9, far less than the canonical value 0.998 of Thorne that was derived in the absence of MHD effects. This equilibrium value may not apply to all accretion flows, particularly thin disks. Nevertheless, it opens the possibility that black holes that have grown primarily through accretion are not maximally rotating.

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arXiv2003

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.

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arXiv2002

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.

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arXiv2001

Symmetry-breaking and chaos in electron transport in semiconductor superlattices

We study the motion of electrons in a single miniband of a semiconductor superlattice driven by THz electric field polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behaviour and symmetry-breaking. We estimate the magnitudes of dc current and dc voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of modern semiconductor superlattices. This work complements PRL 80(1998)2669 [ cond-mat/9709026 ].

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arXiv1997

Spontaneous DC Current Generation in a Resistively Shunted Semiconductor Superlattice Driven by a TeraHertz Field

We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a dc bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous dc bias is approximately an integer multiple of the ac field frequency.

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