4,858 research outputs found

    Self-Similar Force-Free Wind From an Accretion Disk

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    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 PP scales as PRνP\propto R^\nu, where RR is the cylindrical radius. We also assume that the azimuthal velocity in the disk is constant: vϕ=Mcv_\phi = Mc, where M<1M<1 is a constant. For each choice of the parameters ν\nu and MM, we find an infinite number of solutions that are physically well-behaved and have fluid velocity c\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 ν1\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 ν<1\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 ν\nu, the dependence of γ\gamma on MM 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 MM. 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

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    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 EB=0\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 B2E2>0B^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

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    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 L0.99±0.01μ2Ω4/c3L \approx 0.99\pm 0.01 \mu^2\Omega_\star^4/c^3 for a dipole moment μ\mu and stellar angular frequency Ω\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

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    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 dIϕ/drr5/4dI_\phi/dr \propto r^{-5/4}, where Iϕ(r)I_\phi(r) is the toroidal current enclosed inside radius rr. 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 r5/4r^{-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 r5/4r^{-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 α1\alpha\sim 1, whereas the typically assumed value of α0.1\alpha\sim 0.1 holds far from the black hole.[abridged]Comment: 20 pages, 12 figures, accepted to MNRA

    Contributions of Joseph Hardcastle to accounting theory

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    Joseph Hardcastle was one of the foremost authorities on subjects connected with the mathematics of finance and other topics in accounting in the late 19th and early 20th centuries. As a teacher, author, and leader in the profession, he figured prominently in the elevation of accountancy. Hardcastle is relatively unknown in the literature except for having the distinction of scoring the highest grades on the first CPA exam in New York in 1896. However, he was well respected during his time as one of the premier theorists in accounting and was awarded an honorary degree of Master of Letters by New York University. Because of his prolific writings, his teaching of future accountants, and his interactions with members of the Institute of Accounts, he had a strong impact on the science of accounts, the dominant accounting theory in the U.S. at the turn of the century
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