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 acceleration along the last open field lines is radiation-reaction limited, that is, the maximum energy to which particles can be accelerated is determined by balancing the energy-loss rate (due to curvature radiation) with the 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 the limit is model dependent, and can be between one-hundredth (for the vacuum 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 =7.510⁴ T. Because of the radiation reaction constraint and the relatively weak magnetic field, both the expected multiplicity (number of pairs per primary particle) and the Lorentz factor of the outflowing one-dimensional magnetospheric e^± plasma from the polar gap are considerably 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 higher than that for normal pulsars. If the observed X-ray emission originates in the region near or above the PPF, the wide hollow-cone can reproduce the observed wide double-peaked feature of the light curves without using the aligned rotator assumption.