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Pulsar Pair Cascades in Magnetic Fields with Offset Polar Caps

Neutron star magnetic fields may have polar caps (PC) that are offset from the dipole axis, through field-line sweepback near the light cylinder or non-symmetric currents within the star. The effects of such offsets on electron-positron pair cascades are investigated, using simple models of dipole magnetic fields with small distortions that shift the PCs by different amounts or directions. Using a Monte Carlo pair cascade simulation, we explore the changes in the pair spectrum, multiplicity and energy flux across the PC, as well as the trends in pair flux and pair energy flux with spin-down luminosity, L_{sd}. We also give an estimate of the distribution of heating flux from returning positrons on the PC for different offsets. We find that even modest offsets can produce significant increases in pair multiplicity, especially for pulsars that are near or beyond the pair death lines for centered PCs, primarily because of higher accelerating fields. Pair spectra cover several decades in energy, with the spectral range of millisecond pulsars (MSPs) two orders of magnitude higher than for normal pulsars, and PC offsets allow significant extension of all spectra to lower pair energies. We find that the total PC pair luminosity L_{pair} is proportional to L_{sd}, with L_{pair} ~ 10^{-3} L_{sd} for normal pulsars and L_{pair} ~ 10^{-2} L_{sd} for MSPs. Remarkably, the total PC heating luminosity for even large offsets increases by less than a factor of two, even though the PC area increases by much larger factors, because most of the heating occurs near the magnetic axis.