The existence of an ultrarelativistic plasma betond the Alfven cylinder of a pulsar

Previous studies of the steady-state magnetohydrodynamic models of pulsar magnetospheres have indicated that at the Alfvenic critical surface of the flow in such magnetospheres there exists a shock discontinuity. In this paper, the relativistic theory of magnetohydrodynamic shocks is employed to determine the state of the plasma across this discontinuity. It is found that an appreciable fraction of the magnetic energy of the plasma which crosses the shock is thermalized, and that to within a first-order approximation, the mean particle energy in the shocked plasma is given by E'approx. =3.7 x 10161X/subv//suby/'B62n6-1eV, where γ' is the Lorentz factor based on the flow velocity of the plasma beyond the Alfven cylinder, v which depends on the thickness of the shock is a factor of the order of unity, and B6 and n6 are the poloidal magnetic field and the particle number density behind the Alfven cylinder in units of 106 gauss and 106 cm-3, respectively. For the estimated values of the parameters at the Alfven cylinder: which in the limiting case of a massless magnetosphere is coincident with the light cylinder: this result agrees both with the brightness temperature of the radio emission from most pulsars and with the upper limit so far established by observations of the cosmic ray energies in the Crab nebula