PULSAR PAIR CASCADES IN MAGNETIC FIELDS WITH OFFSET POLAR CAPS

Abstract

Neutron star magnetic fields may have polar caps (PC) that are offset from\nthe dipole axis, through field-line sweepback near the light cylinder or\nnon-symmetric currents within the star. The effects of such offsets on\nelectron-positron pair cascades are investigated, using simple models of dipole\nmagnetic fields with small distortions that shift the PCs by different amounts\nor directions. Using a Monte Carlo pair cascade simulation, we explore the\nchanges in the pair spectrum, multiplicity and energy flux across the PC, as\nwell as the trends in pair flux and pair energy flux with spin-down luminosity,\nL_{sd}. We also give an estimate of the distribution of heating flux from\nreturning positrons on the PC for different offsets. We find that even modest\noffsets can produce significant increases in pair multiplicity, especially for\npulsars that are near or beyond the pair death lines for centered PCs,\nprimarily because of higher accelerating fields. Pair spectra cover several\ndecades in energy, with the spectral range of millisecond pulsars (MSPs) two\norders of magnitude higher than for normal pulsars, and PC offsets allow\nsignificant extension of all spectra to lower pair energies. We find that the\ntotal PC pair luminosity L_{pair} is proportional to L_{sd}, with L_{pair} ~\n10^{-3} L_{sd} for normal pulsars and L_{pair} ~ 10^{-2} L_{sd} for MSPs.\nRemarkably, the total PC heating luminosity for even large offsets increases by\nless than a factor of two, even though the PC area increases by much larger\nfactors, because most of the heating occurs near the magnetic axis.\n