44 research outputs found
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