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The exact solution of the Riemann problem in relativistic magnetohydrodynamics with tangential magnetic fields

Published online by Cambridge University Press:  18 November 2005

ROBERTO ROMERO
Affiliation:
Departament d'Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, Spain
JOSÉ M. MARTÍ
Affiliation:
Departament d'Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, Spain
JOSÉ A. PONS
Affiliation:
Departament de Física Aplicada, Universitat d'Alacant, Ap. de correus 99, 03080 Alacant, Spain
JOSÉ M. IBÁÑEZ
Affiliation:
Departament d'Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, Spain
JUAN A. MIRALLES
Affiliation:
Departament de Física Aplicada, Universitat d'Alacant, Ap. de correus 99, 03080 Alacant, Spain

Abstract

We have extended the procedure to find the exact solution of the Riemann problem in relativistic hydrodynamics to a particular case of relativistic magnetohydrodynamics in which the magnetic field of the initial states is tangential to the discontinuity and orthogonal to the flow velocity. The wave pattern produced after the break up of the initial discontinuity is analogous to the non-magnetic case and we show that the problem can be understood as a purely relativistic hydrodynamical problem with a modified equation of state. The new degree of freedom introduced by the non-zero component of the magnetic field results in interesting effects consisting in the change of the wave patterns for given initial thermodynamical states, in a similar way to the effects arising from the introduction of tangential velocities. Secondly, when the magnetic field dominates the thermodynamical pressure and energy, the wave speeds approach the speed of light, leading to fast shocks and fast and arbitrarily thin rarefaction waves. Our approach is the first non-trivial exact solution of a Riemann problem in relativistic magnetohydrodynamics and it can also be of great interest to test numerical codes against known analytical or exact solutions.

Type
Papers
Copyright
© 2005 Cambridge University Press

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