ELECTRODYNAMICS OF MAGNETARS. IV. SELF-CONSISTENT MODEL OF THE INNER ACCELERATOR WITH IMPLICATIONS FOR PULSED RADIO EMISSION

We consider the voltage structure in the open-field circuit and outer magnetosphere of a magnetar. The standard polar cap model for radio pulsars is modified significantly when the polar magnetic field exceeds 1.8 x 10(14) G. Then a surface gap is effectively screened, because resonantly scattered X-rays can convert almost instantaneously to electron-positron pairs. We point out a second possible voltage distribution, in which backflowing charges spawn just enough pairs to compensate the gradient in the corotation charge density. We also examine the gap structure when the magnetic field is somewhat weaker and deduce a voltage 10-30 times larger over a range of surface temperatures. We examine carefully how the flow of charge back to the star above the gap depends on the magnitude of the current, on the curvature of the magnetic field lines, and on resonant drag. The rates of different channels of pair creation are determined self-consistently, including the nonresonant scattering of X-rays and collisions between gamma rays and X-rays. Both circuit solutions are subject to a two-stream instability due to a spatially extended return charge flow. The voltage is high enough to sustain the radio output of strongly magnetic pulsars, but not of the two radio magnetars with active magnetospheres, unless the gap is also present on the closed magnetic field lines. Several properties of the radio magnetars-their rapid variability, broad pulses, and unusually hard radio spectra-are consistent with a third possibility, that the current in the outer magnetosphere is strongly variable and a very high rate of pair creation is sustained by a turbulent cascade.