Potential drops above pulsar polar caps - Ultrarelativistic particle acceleration along the curved magnetic field

Abstract

We investigate the electrostatic acceleration of relativistic particles by pulsars. The model studied is the steady flow of nonneutral plasma along the narrow tube of curved open field lines, well within the light cylinder of a rotating, magnetized, isolated neutron star. We assume negligible binding of the charges in the solid surface. When the magnetic field is strictly dipolar and the magnetic axis is orthogonal to the rotation axis, we obtain large acceleration at high altitudes, with electron energy V e m e c 2 and 1.4 x 10 5 Here 6 C is the opening angle of the polar field lines at the stellar surface, 6 d = (IttRJcP) 112 , R* ae 10 6 cm is the stellar radius, B* is the magnetic field at the magnetic poles of the star, P is the stellar rotation period, and 6* and * are the magnetic colatitude and azimuth, respectively, where a field line cuts the stellar surface. The large electrostatic acceleration is due primarily to the effects of field line curvature. We use this acceleration to find that pair creation may have negligible effects on the potential if P > 0?05(R*/10 12 gauss) 8/17 (0 c /0 d) 22/17 O>/pa) 7 4/17. Here p is the radius of curvature of a field line and p d is the value of p for a perfect dipole. We also investigate the effects of higher multipole moments in the magnetic field. The y-ray luminosity of the neutron star without pair creation is briefly discussed, as well as the total energy available for particle acceleration and the total energy loss from the star. We show that when the magnetic axis and the rotation axis are either aligned or oblique, such that the angle between the axes is less than (tt/2-6 C), no steady (as measured in the corotating frame), unidirectional flow exists when the plasma is completely charge separated. This inconsistency occurs entirely because of the field line curvature. We suggest a possible resolution of the inconsistency , involving the abandonment of unidirectional flow and the formation of steady-state distributions of electrostatically trapped particles on open field lines which bend away from the rotation axis. In this suggested model, large acceleration occurs along open field lines which curve toward the rotation axis, with particle energy similar to that of the orthogonal rotator.