arXiv subjects

Jonathan C. McKinney

Publications and source records attributed to Jonathan C. McKinney.

At least 55 records · Page 3Linked to original sources

arXiv2010

Simulations of Magnetized Disks Around Black Holes: Effects of Black Hole Spin, Disk Thickness, and Magnetic Field Geometry

The standard general relativistic model of a razor-thin accretion disk 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 disks 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 disks, may contain large-scale structures that do not behave like a simple local scalar viscosity. We describe three-dimensional general relativistic magnetohydrodynamic simulations of accretion disks 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 disk in order to match the isotropic turbulence expected in the poloidal plane. For a thin disk 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% relative to the NT model and an excess luminosity from inside the ISCO of 3.5%. The deviations in the case of spinning black holes are of the same order. In addition, the deviations decrease with decreasing |h/r|. We therefore conclude that magnetized thin accretion disks 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% of Eddington where we expect a very small disk thickness |h/r| <~ 0.05. We also discuss how the stress and the luminosity inside the ISCO depend on the assumed initial magnetic field geometry. (abridged)

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arXiv2010

The Submillimeter Bump in Sgr A* from Relativistic MHD Simulations

Recent high resolution observations of the Galactic center black hole allow for direct comparison with accretion disk simulations. We compare two-temperature synchrotron emission models from three dimensional, general relativistic magnetohydrodynamic simulations to millimeter observations of Sgr A*. Fits to very long baseline interferometry and spectral index measurements disfavor the monochromatic face-on black hole shadow models from our previous work. Inclination angles \le 20 degrees are ruled out to 3 σ. We estimate the inclination and position angles of the black hole, as well as the electron temperature of the accretion flow and the accretion rate, to be i=50+35-15 degrees, ξ=-23+97-22 degrees, T_e=(5.4 +/- 3.0)x10^10 K and Mdot=(5+15-2)x10^-9 M_sun / yr respectively, with 90% confidence. The black hole shadow is unobscured in all best fit models, and may be detected by observations on baselines between Chile and California, Arizona or Mexico at 1.3mm or .87mm either through direct sampling of the visibility amplitude or using closure phase information. Millimeter flaring behavior consistent with the observations is present in all viable models, and is caused by magnetic turbulence in the inner radii of the accretion flow. The variability at optically thin frequencies is strongly correlated with that in the accretion rate. The simulations provide a universal picture of the 1.3mm emission region as a small region near the midplane in the inner radii of the accretion flow, which is roughly isothermal and has ν/ν_c ~ 1-20, where ν_c is the critical frequency for thermal synchrotron emission.

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arXiv2010

Magnetohydrodynamic Simulations of Gamma-Ray Burst Jets: Beyond the Progenitor Star

Achromatic breaks in afterglow light curves of gamma-ray bursts (GRBs) arise naturally if the product of the jet's Lorentz factor γand opening angle Θ_j satisfies (γΘ_j) >> 1 at the onset of the afterglow phase, i.e., soon after the conclusion of the prompt emission. Magnetohydrodynamic (MHD) simulations of collimated GRB jets generally give (γΘ_j) <~ 1, suggesting that MHD models may be inconsistent with jet breaks. We work within the collapsar paradigm and use axisymmetric relativistic MHD simulations to explore the effect of a finite stellar envelope on the structure of the jet. Our idealized models treat the jet-envelope interface as a collimating rigid wall, which opens up outside the star to mimic loss of collimation. We find that the onset of deconfinement causes a burst of acceleration accompanied by a slight increase in the opening angle. In our fiducial model with a stellar radius equal to 10^4.5 times that of the central compact object, the jet achieves an asymptotic Lorentz factor γ~ 500 far outside the star and an asymptotic opening angle Θ_j ~ 0.04 rad ~ 2 deg, giving (γΘ_j) ~ 20. These values are consistent with observations of typical long-duration GRBs, and explain the occurrence of jet breaks. We provide approximate analytic solutions that describe the numerical results well.

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arXiv2010

Black Hole Spin and the Radio Loud/Quiet Dichotomy of Active Galactic Nuclei

Radio loud active galactic nuclei (AGN) are on average 1000 times brighter in the radio band compared to radio quiet AGN. We investigate whether this radio loud/quiet dichotomy can be due to differences in the spin of the central black holes that power the radio-emitting jets. Using general relativistic magnetohydrodynamic simulations, we construct steady state axisymmetric numerical models for a wide range of black hole spins (dimensionless spin parameter 0.1 <= a <= 0.9999 and a variety of jet geometries. We assume that the total magnetic flux through the black hole horizon at radius r_H(a) is held constant. If the black hole is surrounded by a thin accretion disk, we find that the total black hole power output depends approximately quadratically on the angular frequency of the hole, P \propto Ω_H^2 \propto (a/r_H)^2. We conclude that, in this scenario, differences in the black hole spin can produce power variations of only a few tens at most. However, if the disk is thick such that the jet subtends a narrow solid angle around the polar axis, then the power dependence becomes much steeper, P \propto Ω_H^4 or even \propto Ω_H^6. Power variations of 1000 are then possible for realistic black hole spin distributions. We derive an analytic solution that accurately reproduces the steeper scaling of jet power with Ω_H, and we provide a numerical fitting formula that reproduces all our simulation results. We discuss other physical effects that might contribute to the observed radio loud/quiet dichotomy of AGN.

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arXiv2010

Numerical Studies of Relativistic Jets

The connection between collimation and acceleration of magnetized relativistic jets is discussed. The focus is on recent numerical simulations which shed light on some longstanding problems.

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arXiv2009

2-D simulations of FU Orionis disk outbursts

We have developed time-dependent models of FU Ori accretion outbursts to explore the physical properties of protostellar disks. Our two-dimensional, axisymmetric models incorporate full vertical structure with a new treatment of the radiative boundary condition for the disk photosphere. We find that FU Ori-type outbursts can be explained by a slow accumulation of matter due to gravitational instability. Eventually this triggers the magnetorotational instability, which leads to rapid accretion. The thermal instability is triggered in the inner disk but this instability is not necessary for the outburst. An accurate disk vertical structure, including convection, is important for understanding the outburst behavior. Large convective eddies develop during the high state in the inner disk. The models are in agreement with Spitzer IRS spectra and also with peak accretion rates and decay timescales of observed outbursts, though some objects show faster rise timescale. We also propose that convection may account for the observed mild-supersonic turbulence and the short-timescale variations of FU Orionis objects.

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arXiv2009

Efficiency of Magnetic to Kinetic Energy Conversion in a Monopole Magnetosphere

Unconfined relativistic outflows from rotating, magnetized compact objects are often well-modeled by assuming the field geometry is approximately a split-monopole at large radii. Earlier work has indicated that such an unconfined flow has an inefficient conversion of magnetic energy to kinetic energy. This has led to the conclusion that ideal magnetohydrodynamical (MHD) processes fail to explain observations of, e.g., the Crab pulsar wind at large radii where energy conversion appears efficient. In addition, as a model for astrophysical jets, the monopole field geometry has been abandoned in favor of externally confined jets since the latter appeared to be generically more efficient jet accelerators. We perform time-dependent axisymmetric relativistic MHD simulations in order to find steady state solutions for a wind from a compact object endowed with a monopole field geometry. Our simulations follow the outflow for 10 orders of magnitude in distance from the compact object, which is large enough to study both the initial "acceleration zone" of the magnetized wind as well as the asymptotic "coasting zone." We obtain the surprising result that acceleration is actually {\it efficient} in the polar region, which develops a jet despite not being confined by an external medium. Our models contain jets that have sufficient energy to account for moderately energetic long and short gamma-ray burst (GRB) events (~10^{51}--10^{52} erg), collimate into narrow opening angles (opening half-angle θ_j \approx 0.03 rad), become matter-dominated at large radii (electromagnetic energy flux per unit matter energy flux σ<1), and move at ultrarelativistic Lorentz factors (γ_j ~ 200 for our fiducial model). (abridged)

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arXiv2009

Stability of Relativistic Jets from Rotating, Accreting Black Holes via Fully Three-Dimensional Magnetohydrodynamic Simulations

Rotating magnetized compact objects and their accretion discs can generate strong toroidal magnetic fields driving highly magnetized plasmas into relativistic jets. Of significant concern, however, has been that a strong toroidal field in the jet should be highly unstable to the non-axisymmetric helical kink (screw) $m=1$ mode leading to rapid disruption. In addition, a recent concern has been that the jet formation process itself may be unstable due to the accretion of non-dipolar magnetic fields. We describe large-scale fully three-dimensional global general relativistic magnetohydrodynamic simulations of rapidly rotating, accreting black holes producing jets. We study both the stability of the jet as it propagates and the stability of the jet formation process during accretion of dipolar and quadrupolar fields. For our dipolar model, despite strong non-axisymmetric disc turbulence, the jet reaches Lorentz factors of $Γ\sim 10$ with opening half-angle $θ_j\sim 5^\circ$ at $10^3$ gravitational radii without significant disruption or dissipation with only mild substructure dominated by the $m=1$ mode. On the contrary, our quadrupolar model does not produce a steady relativistic ($Γ\gtrsim 3$) jet due to mass-loading of the polar regions caused by unstable polar fields. Thus, if produced, relativistic jets are roughly stable structures and may reach up to an external shock with strong magnetic fields. We discuss the astrophysical implications of the accreted magnetic geometry playing such a significant role in relativistic jet formation, and we outline avenues for future work.

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arXiv2008

Three-Dimensional Simulations of Magnetized Thin Accretion Disks around Black Holes: Stress in the Plunging Region

We describe three-dimensional general relativistic magnetohydrodynamic simulations of a geometrically thin accretion disk around a non-spinning black hole. The disk has a thickness $h/r\sim0.05-0.1$ over the radial range $(2-20)GM/c^2$. In steady state, the specific angular momentum profile of the inflowing magnetized gas deviates by less than 2% from that of the standard thin disk model of Novikov & Thorne (1973). Also, the magnetic torque at the radius of the innermost stable circular orbit (ISCO) is only $\sim2%$ of the inward flux of angular momentum at this radius. Both results indicate that magnetic coupling across the ISCO is relatively unimportant for geometrically thin disks.

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arXiv2008

Simulations of Ultrarelativistic Magnetodynamic Jets from Gamma-ray Burst Engines

Long-duration gamma-ray bursts (GRBs) require an engine capable of driving a jet of plasma to ultrarelativistic bulk Lorentz factors of up to several hundred and into narrow opening angles of a few degrees. We use global axisymmetric stationary solutions of magnetically-dominated (force-free) ultrarelativistic jets to test whether the popular magnetic-driving paradigm can generate the required Lorentz factors and opening angles. Our global solutions are obtained via time-dependent relativistic ideal magnetodynamical numerical simulations which follow the jet from the central engine to beyond six orders of magnitude in radius. Our model is primarily motivated by the collapsar model, in which a jet is produced by a spinning black hole or neutron star and then propagates through a massive stellar envelope. We find that the size of the presupernova progenitor star and the radial profile of pressure inside the star determine the terminal Lorentz factor and opening angle of the jet. At the radius where the jet breaks out of the star, our well-motivated fiducial model generates a Lorentz factor $γ\sim 400$ and a half-opening angle $θ_j\sim 2^\circ$, consistent with observations of many long-duration GRBs. Other models with slightly different parameters give $γ$ in the range 100 to 5000 and $θ_j$ from $0.1^\circ$ to $10^\circ$, thus reproducing the range of properties inferred for GRB jets. A potentially observable feature of some of our solutions is that the maximum Poynting flux in the jet is found at $θ\sim θ_j$ with the jet power concentrated in a hollow cone, while the maximum in the Lorentz factor occurs at an angle $θ$ substantially smaller than $θ_j$ also in a hollow cone. [abridged]

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arXiv2007

WHAM: A WENO-based general relativistic numerical scheme I: Hydrodynamics

Active galactic nuclei, x-ray binaries, pulsars, and gamma-ray bursts are all believed to be powered by compact objects surrounded by relativistic plasma flows driving phenomena such as accretion, winds, and jets. These flows are often accurately modelled by the relativistic magnetohydrodynamics (MHD) approximation. Time-dependent numerical MHD simulations have proven to be especially insightful, but one regime that remains difficult to simulate is when the energy scales (kinetic, thermal, magnetic) within the plasma become disparate. We develop a numerical scheme that significantly improves the accuracy and robustness of the solution in this regime. We use a modified form of the WENO method to construct a finite-volume general relativistic hydrodynamics code called WHAM that converges at fifth order. We avoid (1) field-by-field decomposition by adaptively reducing down to 2-point stencils near discontinuities for a more accurate treatment of shocks, and (2) excessive reduction to low order stencils, as in the standard WENO formalism, by maintaining high order accuracy in smooth monotonic flows. Our scheme performs the proper surface integral of the fluxes, converts cell averaged conserved quantities to point conserved quantities before performing the reconstruction step, and correctly averages all source terms. We demonstrate that the scheme is robust in strong shocks, very accurate in smooth flows, and maintains accuracy even when the energy scales in the flow are highly disparate.

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arXiv2007

Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index

The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $Γ$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $Γ$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic equation of state can considerably bear upon the solution when transitions from cold to hot gas (or viceversa) are present. Under these circumstances, a polytropic equation of state can significantly endanger the solution.

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arXiv2006

Disk-Jet Coupling in Black Hole Accretion Systems II: Force-Free Electrodynamical Models

In paper I, we showed that time-dependent general relativistic magnetohydrodynamic (GRMHD) numerical models of accretion disks, although being highly turbulent, have surprisingly simple electromagnetic properties. In particular, the toroidal current density in the disk takes the form $dI_ϕ/dr \propto r^{-5/4}$. Guided by this simplicity, we use a time-dependent general relativistic force-free electrodynamics (GRFFE) code to study an idealized problem in which the accretion disk is replaced by an infinitely thin rotating equatorial current sheet. We consider both an $r^{-5/4}$ current profile and an $r^{-1}$ profile, the latter corresponding to the paraboloidal model of Blandford & Znajek (1977). The force-free magnetosphere we obtain with the $r^{-5/4}$ current sheet matches remarkably well to the Poynting-dominated jet seen in GRMHD numerical models. By comparing to the non-rotating force-free model studied in paper I, rotation is seen to lead to mild decollimation of the jet suggesting that hoop-stress forces nearly cancel centrifugal forces. In order to study the process that generates the corona and disk wind and destroys the ordered field in the corona in GRMHD numerical models, the force-free field with the $r^{-5/4}$ current distribution is embedded in an accretion disk and followed in a GRMHD simulation. Reconnection and magnetic stresses contribute to a magnetized, thermal wind without the aid of an ordered field threading the disk.

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arXiv2006

Disk-Jet Coupling in Black Hole Accretion Systems I: General Relativistic Magnetohydrodynamical Models

General relativistic numerical simulations of magnetized accretion flows around black holes show a disordered electromagnetic structure in the disk and corona and a highly relativistic, Poynting-dominated funnel jet in the polar regions. The polar jet is nearly consistent with the stationary paraboloidal Blandford-Znajek model of an organized field threading the polar regions of a rotating black hole. How can a disordered accretion disk and corona lead to an ordered jet? We show that the polar jet is associated with a strikingly simple angular-integrated toroidal current distribution $dI_ϕ/dr \propto r^{-5/4}$, where $I_ϕ(r)$ is the toroidal current enclosed inside radius $r$. We demonstrate that the poloidal magnetic field in the simulated jet agrees well with the force-free field solution for a non-rotating thin disk with an $r^{-5/4}$ toroidal current, suggesting rotation leads to negligible self-collimation. We find that the polar field is confined/collimated by the corona. The electromagnetic field in the disk also scales as $r^{-5/4}$, which is consistent with some Newtonian accretion models that assume rough equipartition between magnetic and gas pressure. However, the agreement is accidental since toward the black hole the magnetic pressure increases faster than the gas pressure. This field dominance near the black hole is associated with magnetic stresses that imply a large effective viscosity parameter $α\sim 1$, whereas the typically assumed value of $α\sim 0.1$ holds far from the black hole.[abridged]

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arXiv2006

Self-Similar Force-Free Wind From an Accretion Disk

We consider a self-similar force-free wind flowing out of an infinitely thin disk located in the equatorial plane. On the disk plane, we assume that the magnetic stream function $P$ scales as $P\propto R^ν$, where $R$ is the cylindrical radius. We also assume that the azimuthal velocity in the disk is constant: $v_ϕ= Mc$, where $M<1$ is a constant. For each choice of the parameters $ν$ and $M$, we find an infinite number of solutions that are physically well-behaved and have fluid velocity $\leq c$ throughout the domain of interest. Among these solutions, we show via physical arguments and time-dependent numerical simulations that the minimum-torque solution, i.e., the solution with the smallest amount of toroidal field, is the one picked by a real system. For $ν\geq 1$, the Lorentz factor of the outflow increases along a field line as $γ\approx M(z/\Rfp)^{(2-ν)/2} \approx R/R_{\rm A}$, where $\Rfp$ is the radius of the foot-point of the field line on the disk and $R_{\rm A}=\Rfp/M$ is the cylindrical radius at which the field line crosses the Alfven surface or the light cylinder. For $ν< 1$, the Lorentz factor follows the same scaling for $z/\Rfp < M^{-1/(1-ν)}$, but at larger distances it grows more slowly: $γ\approx (z/\Rfp)^{ν/2}$. For either regime of $ν$, the dependence of $γ$ on $M$ shows that the rotation of the disk plays a strong role in jet acceleration. On the other hand, the poloidal shape of a field line is given by $z/\Rfp \approx (R/\Rfp)^{2/(2-ν)}$ and is independent of $M$. Thus rotation has neither a collimating nor a decollimating effect on field lines, suggesting that relativistic astrophysical jets are not collimated by the rotational winding up of the magnetic field.

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arXiv2006

General Relativistic Magnetohydrodynamic Simulations of Jet Formation and Large-Scale Propagation from Black Hole Accretion Systems

The formation and large-scale propagation of Poynting-dominated jets produced by accreting, rapidly rotating black hole systems are studied by numerically integrating the general relativistic magnetohydrodynamic equations of motion to follow the self-consistent interaction between accretion disks and black holes. This study extends previous similar work by studying jets till $t\approx 10^4GM/c^3$ out to $r\approx 10^4GM/c^2$, by which the jet is super- fast magnetosonic and moves at a lab-frame bulk Lorentz factor of $Γ\sim 10$ with a maximum terminal Lorentz factor of $Γ_\infty\lesssim 10^3$. The radial structure of the Poynting-dominated jet is piece-wise self-similar, and fits to flow quantities along the field line are provided. Beyond the \alf surface at $r\sim 10$--$100GM/c^2$, the jet becomes marginally unstable to (at least) current-driven instabilities. Such instabilities drive shocks in the jet that limit the efficiency of magnetic acceleration and collimation. These instabilities also induce jet substructure with $3\lesssimΓ\lesssim 15$. The jet is shown to only marginally satisfy the necessary and sufficient conditions for kink instability, so this may explain how astrophysical jets can extend to large distances without completely disrupting. At large distance, the jet angular structure is Gaussian-like (or uniform within the core with sharp exponential wings) with a half-opening angle of $\approx 5^\circ$ and there is an extended component out to $\approx 27^\circ$. Unlike in some hydrodynamic simulations, the environment is found to play a negligible role in jet structure, acceleration, and collimation as long as the ambient pressure of the surrounding medium is small compared to the magnetic pressure in the jet.

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arXiv2006

General Relativistic Force-Free Electrodynamics: A New Code and Applications to Black Hole Magnetospheres

The force-free limit of magnetohydrodynamics (MHD) is often a reasonable approximation to model black hole and neutron star magnetospheres. We describe a general relativistic force-free (GRFFE) formulation that allows general relativistic magnetohydrodynamic (GRMHD) codes to directly evolve the GRFFE equations of motion. Established, accurate, and well-tested conservative GRMHD codes can simply add a new inversion piece of code to their existing code, while continuing to use all the already-developed facilities present in their GRMHD code. We show how to enforce the $\mathbf{E}\cdot\mathbf{B}=0$ constraint and energy conservation, and we introduce a simplified general model of the dissipation of the electric field to enforce the $B^2-E^2>0$ constraint. We also introduce a simplified yet general method to resolve current sheets, without much reconnection, over many dynamical times. This formulation is incorporated into an existing GRMHD code (HARM), which is demonstrated to give accurate and robust GRFFE results for Minkowski and black hole space-times.

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arXiv2006

Relativistic Force-Free Electrodynamic Simulations of Neutron Star Magnetospheres

The luminosity and structure of neutron star magnetospheres are crucial to our understanding of pulsar and plerion emission. A solution found using the force-free approximation would be an interesting standard with which any model with more physics could be compared. Prior quasi-analytic force-free solutions may not be stable, while prior time-dependent magnetohydrodynamic models used unphysical model parameters. We use a time-dependent relativistic force-free electrodynamics code with no free parameters to find a unique stationary solution for the axisymmetric rotating pulsar magnetosphere in a Minkowski space-time in the case of no surface currents on the star. The solution is similar to the force-free quasi-analytic solution of \citet{cont99} and the numerical magnetohydrodynamic solution of \citet{kom05}. The magnetosphere structure and the usefulness of the classical y-point in the general dissipative regime are discussed. The pulsar luminosity is found to be $L \approx 0.99\pm 0.01 μ^2Ω_\star^4/c^3$ for a dipole moment $μ$ and stellar angular frequency $Ω_\star$.

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