9 research outputs found
Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure
Shock jump conditions are obtained for steady-state, plane shocks with
oblique magnetic fields and arbitrary flow speeds. For ultrarelativistic and
nonrelativistic shocks, the jump conditions may be solved analytically. For
mildly relativistic shocks, analytic solutions are obtained for isotropic
pressure using an approximation for the adiabatic index that is valid in high
sonic Mach number cases. In the more general case of gyrotropic pressure, the
jump conditions cannot be solved analytically without additional assumptions,
and the effects of gyrotropic pressure are investigated by parameterizing the
distribution of pressure parallel and perpendicular to the magnetic field. Our
numerical solutions reveal that relatively small departures from isotropy
(e.g., about 20%) produce significant changes in the shock compression ratio,
r, at all shock Lorentz factors, including ultrarelativistic ones, where an
analytic solution with gyrotropic pressure is obtained. In particular, either
dynamically important fields or significant pressure anisotropies can incur
marked departures from the canonical gas dynamic value of r=3 for a shocked
ultrarelativistic flow and this may impact models of particle acceleration in
gamma-ray bursts and other environments where relativistic shocks are inferred.
The jump conditions presented apply directly to test-particle acceleration, and
will facilitate future self-consistent numerical modeling of particle
acceleration at oblique, relativistic shocks.Comment: 26 pages with 7 figures, submitted to Ap. J. April 200
Nonlinear Particle Acceleration in Relativistic Shocks
Monte Carlo techniques are used to model nonlinear particle acceleration in
parallel collisionless shocks of various speeds, including mildly relativistic
ones. When the acceleration is efficient, the backreaction of accelerated
particles modifies the shock structure and causes the compression ratio, r, to
increase above test-particle values. Modified shocks with Lorentz factors less
than about 3 can have compression ratios considerably greater than 3 and the
momentum distribution of energetic particles no longer follows a power law
relation. These results may be important for the interpretation of gamma-ray
bursts if mildly relativistic internal and/or afterglow shocks play an
important role accelerating particles that produce the observed radiation. For
shock Lorentz factors greater than about 10, r approaches 3 and the so-called
`universal' test-particle result of N(E) proportional to E^{-2.3} is obtained
for sufficiently energetic particles. In all cases, the absolute normalization
of the particle distribution follows directly from our model assumptions and is
explicitly determined.Comment: Updated version, Astroparticle Physics, in press, 29 pages, 13
figure
Diffusive Shock Acceleration in Unmodified Relativistic, Oblique Shocks
We present results from a fully relativistic Monte Carlo simulation of
diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses
a single algorithmic sequence to smoothly span the range from nonrelativistic
speeds to fully relativistic shocks of arbitrary obliquity, providing a
powerful consistency check. While known results are obtained for
nonrelativistic and ultra-relativistic parallel shocks, new results are
presented for the less explored trans- relativistic regime and for oblique,
fully relativistic shocks. We find, for a wide trans-relativistic range
extending to shock Lorentz factors >30, that the particle spectrum produced by
DSA varies strongly from the canonical f(p) proportional to p^{-4.23} spectrum
known to result in ultra-relativistic shocks. Trans- relativistic shocks may
play an important role in gamma-ray bursts and other sources and most
relativistic shocks will be highly oblique.Comment: Accepted for publication in Astroparticle Physics, August 2004, 22
pages, 14 figure
Nonlinear particle acceleration in relativistic shocks. Astroparticle Phys
Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speeds, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles modifies the shock structure and causes the compression ratio, r, to increase above test-particle values. Modified shocks with Lorentz factors, γ0 � 3, can have compression ratios considerably greater than 3 and the momentum distribution of energetic particles no longer follows a power law relation. These results may be important for the interpretation of gammaray bursts if mildly relativistic internal and/or afterglow shocks play an important role accelerating particles that produce the observed radiation. For γ0 � 10, r approaches 3 and the so-called ‘universal ’ test-particle result of N(E) ∝ E −2.3 is obtained for sufficiently energetic particles. In all cases, the absolute normalization of the particle distribution follows directly from our model assumptions and is explicitly determined. Subject headings: Cosmic rays — acceleration of particles — relativistic shock waves — gamma-ray bursts; PACS: 52.60, 96.40 1