The Hydromagnetic Free Expansion of a Relativistic Gas

The one-dimensional plane adiabatic expansion of a relativistic plasma is described under a wide variety of situations, including the presence of a cold background plasma and a frozen-in magnetic field. The relativistic plasma is assumed to be monoenergetic, isotropic, and initially uniform. Synchrotron emission from the expanding plasma always appears to be red shifted (with respect to the initial gas) as seen by an observer at rest, and has a spectrum which depends on the amount of cold plasma present. If little nonrelativistic plasma is present, the observer will also see strong limb darkening and center brightening. Equipartition of magnetic and relativistic thermal energies is not preserved in the expansion. Possible application to extragalactic radio sources is briefly discussed.