Magnetohydrodynamic Effects in Propagating Relativistic Jets: Reverse Shock and Magnetic Acceleration

We solve the Riemann problem for the deceleration of an arbitrarily magnetized relativistic flow injected into a static unmagnetized medium in one dimension. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization σ (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when σ exceeds a critical value, σc, defined by the balance between the magnetic pressure in the flow and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the flow. We discuss the implications of these results for models of gamma-ray bursts and active galactic nuclei.