High-energy emission from millisecond pulsars: polar cap models

The viability of polar cap models for high-energy emission from millisecond pulsars is discussed. It is shown that in millisecond pulsars, polar gap a cceleration along the last open field lines is radiation-reaction limited, that is, the maximum energy to which particles can be accelerated is determ ined by balancing the energy-loss rate (due to curvature radiation) with th e gap-acceleration rate. The maximum Lorentz factor is limited by curvature radiation and is not sensitive to the specific acceleration model. However , the distance (from the polar cap) at which the Lorentz factor achieves th e limit is model dependent, and can be between one-hundredth (for the vacuu m gap) and above one-tenth (for the space-charge limited gap) of a stellar radius distant from the polar cap for a pulsar period P=2 ms and a surface magnetic field B*=7.5x10(4) T. Because of the radiation reaction constraint and the relatively weak magnetic field, both the expected multiplicity (nu mber of pairs per primary particle) and the Lorentz factor of the outflowin g one-dimensional magnetospheric e(+/-) plasma from the polar gap are consi derably lower than those for normal pulsars. Assuming space-charge limited flow, the location of the pair production front (PPF) is estimated to occur at about one stellar radius above the polar cap, which is significantly hi gher than that for normal pulsars. If the observed X-ray emission originate s in the region near or above the PPF, the wide hollow-cone can reproduce t he observed wide double-peaked feature of the light curves without using th e aligned rotator assumption.