Recollimation Boundary Layers in Relativistic Jets

We study the collimation of relativistic hydrodynamic jets by the pressure of an ambient medium in the limit where the jet interior has lost causal contact with its surroundings. For a jet with an ultrarelativistic equation of state and external pressure that decreases as a power of spherical radius, p \propto r^(-eta), the jet interior will lose causal contact when eta > 2. However, the outer layers of the jet gradually collimate toward the jet axis as long as eta < 4, leading to the formation of a shocked boundary layer. Assuming that pressure-matching across the shock front determines the shape of the shock, we study the resulting structure of the jet in two ways: first by assuming that the pressure remains constant across the shocked boundary layer and looking for solutions to the shock jump equations, and then by constructing self-similar boundary-layer solutions that allow for a pressure gradient across the shocked layer. We demonstrate that the constant-pressure solutions can be characterized by four initial parameters that determine the jet shape and whether the shock closes to the axis. We show that self-similar solutions for the boundary layer can be constructed that exhibit a monotonic decrease in pressure across the boundary layer from the contact discontinuity to the shock front, and that the addition of this pressure gradient in our initial model generally causes the shock front to move outwards, creating a thinner boundary layer and decreasing the tendency of the shock to close. We discuss trends based on the value of the pressure power-law index eta.Comment: 10 pages, 8 figures. Accepted to MNRAS; minor revisions from original submitted versio

The Influence of Magnetic Field Geometry on the Evolution of Black Hole Accretion Flows: Similar Disks, Drastically Different Jets

Because the magneto-rotational instability is capable of exponentially amplifying weak preexisting magnetic fields, it might be hoped that the character of the magnetic field in accretion disks is independent of the nature of the seed field. However, the divergence-free nature of magnetic fields in highly conducting fluids ensures that their large-scale topology is preserved, no matter how greatly the field intensity is changed. By performing global two-dimensional and three-dimensional general relativistic magnetohydrodynamic disk simulations with several different topologies for the initial magnetic field, we explore the degree to which the character of the flows around black holes depends on the initial topology. We find that while the qualitative properties of the accretion flow are nearly independent of field topology, jet-launching is very sensitive to it: a sense of vertical field consistent for at least an inner disk inflow time is essential to the support of strong jets.Comment: 42 pages; 17 figures; Accepted for publication in ApJ (some new discussion and 2 new figures

A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics

We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the magnetic field. A variety of approximate Riemann solvers are implemented to compute the fluxes of the conserved variables. The methods are tested with a comprehensive suite of multidimensional problems. These tests have helped us develop a hierarchy of correction steps that are applied when the integration algorithm predicts unphysical states due to errors in the fluxes, or errors in the inversion between conserved and primitive variables. Although used exceedingly rarely, these corrections dramatically improve the stability of the algorithm. We present preliminary results from the application of these algorithms to two problems in RMHD: the propagation of supersonic magnetized jets, and the amplification of magnetic field by turbulence driven by the relativistic Kelvin-Helmholtz instability (KHI). Both of these applications reveal important differences between the results computed with Riemann solvers that adopt different approximations for the fluxes. For example, we show that use of Riemann solvers which include both contact and rotational discontinuities can increase the strength of the magnetic field within the cocoon by a factor of ten in simulations of RMHD jets, and can increase the spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a factor of 2. This increase in accuracy far outweighs the associated increase in computational cost. Our RMHD scheme is publicly available as part of the Athena code.Comment: 75 pages, 28 figures, accepted for publication in ApJS. Version with high resolution figures available from http://jila.colorado.edu/~krb3u/Athena_SR/rmhd_method_paper.pd