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 $P\propto R^\nu$, where $R$ is the cylindrical radius. We also assume that the azimuthal velocity in the disk is constant: $v_\phi = Mc$, where $M<1$ is a constant. For each choice of the parameters $\nu$ 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 $\nu \geq 1$, the Lorentz factor of the outflow increases along a field line as \gamma \approx M(z/\Rfp)^{(2-\nu)/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 $\nu < 1$, the Lorentz factor follows the same scaling for z/\Rfp < M^{-1/(1-\nu)}, but at larger distances it grows more slowly: \gamma \approx (z/\Rfp)^{\nu/2}. For either regime of $\nu$, the dependence of $\gamma$ 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-\nu)} 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.Comment: 21 pages, 15 figures, accepted to MNRA

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.Comment: 14 pages, 4 figures, accepted for publication in MNRAS Main Journa

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 $L \approx 0.99\pm 0.01 \mu^2\Omega_\star^4/c^3$ for a dipole moment $\mu$ and stellar angular frequency $\Omega_\star$.Comment: 5 pages, 5 figures, accepted for publication in MNRAS LETTER

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 $dI_\phi/dr \propto r^{-5/4}$, where $I_\phi(r)$ 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 $\alpha\sim 1$, whereas the typically assumed value of $\alpha\sim 0.1$ holds far from the black hole.[abridged]Comment: 20 pages, 12 figures, accepted to MNRA

Accretion of low angular momentum material onto black holes: 2D magnetohydrodynamical case

We report on the second phase of our study of slightly rotating accretion flows onto black holes. We consider magnetohydrodynamical (MHD) accretion flows with a spherically symmetric density distribution at the outer boundary, but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum and a weak radial magnetic field. We study accretion flows by means of numerical 2D, axisymmetric, MHD simulations with and without resistive heating. Our main result is that the properties of the accretion flow depend mostly on an equatorial accretion torus which is made of the material that has too much angular momentum to be accreted directly. The torus accretes, however, because of the transport of angular momentum due to the magnetorotational instability (MRI). Initially, accretion is dominated by the polar funnel, as in the hydrodynamic inviscid case, where material has zero or very low angular momentum. At the later phase of the evolution, the torus thickens towards the poles and develops a corona or an outflow or both. Consequently, the mass accretion through the funnel is stopped. The accretion of rotating gas through the torus is significantly reduced compared to the accretion of non-rotating gas (i.e., the Bondi rate). It is also much smaller than the accretion rate in the inviscid, weakly rotating case.Our results do not change if we switch on or off resistive heating. Overall our simulations are very similar to those presented by Stone, Pringle, Hawley and Balbus despite different initial and outer boundary conditions. Thus, we confirm that MRI is very robust and controls the nature of radiatively inefficient accretion flows.Comment: submitted in Ap