  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.

High Energy Astrophysical Phenomena