A sub-population of energetic rotation-powered pulsars show high fluxes of
pulsed non-thermal hard X-ray emission. While this MeV pulsar population
includes some radio-loud pulsars like the Crab, a significant number have no
detected radio or GeV emission, a mystery since gamma- ray emission is a common
characteristic of pulsars with high spin-down power. Their steeply rising hard
X-ray spectral energy distributions (SEDs) suggest peaks at 0.1 - 1 MeV but
they have not been detected above 200 keV. Several upcoming and planned
telescopes may shed light on the MeV pulsars. The Neutron star Interior
Composition ExploreR (NICER) will observe pulsars in the 0.2 - 12 keV band and
may discover additional MeV pulsars. Planned telescopes, such as All-Sky
Medium-Energy Gamma-Ray Observatory (AMEGO) and e-ASTROGAM, will detect
emission above 0.2 MeV and polarization in the 0.2 - 10 MeV band. We present a
model for the spectrum and polarization of MeV pulsars where the X-ray emission
comes from electron- positron pairs radiating in the outer magnetosphere and
current sheet. This model predicts that the peak of the SED increases with
surface magnetic field strength if the pairs are produced in polar cap
cascades. For small inclination angles, a range of viewing angles can miss both
the radio pulse and the GeV pulse from particles accelerating near the current
sheet. Characterizing the emission and geometry of MeV pulsars can thus provide
clues to the source of pairs and acceleration in the magnetosphere.Comment: 8 pages, 5 figures, published in Proceedings of Scienc