  We report on a series of spectroscopic observations of PSR J1311-3430, an
extreme black-widow gamma-ray pulsar with a helium-star companion. In a
previous study we estimated the neutron star mass as M_NS= 2.68+/-0.14M_Sun
(statistical error), based on limited spectroscopy and a basic (direct heating)
light curve model; however, much larger model-dependent systematics dominate
the mass uncertainty. Our new spectroscopy reveals a range of complex source
behavior. The variable He I companion wind emission lines can dominate
broad-band photometry, especially in red filters or near minimum brightness,
and the wind flux should complete companion evaporation in a spin-down time.
The heated companion face also undergoes dramatic flares, reaching 40,000K over
20% of the star; this is likely powered by a magnetic field generated in the
companion. The companion center-of-light radial velocity is now well measured
with K_CoL = 615.4+/-5.km/s. We detect non-sinusoidal velocity components due
to the heated face flux distribution. Using our spectra to excise flares and
wind lines, we generate substantially improved light curves for companion
continuum fitting. We show that the inferred inclination and neutron star mass,
however, remain sensitive to the poorly constrained heating pattern. The
neutron star's mass, M_NS, is likely less than the direct heating value and
could range as low as 1.8M_Sun for extreme equatorial heating concentration.
While we cannot yet pin down M_NS, our data imply that an intrabinary shock
reprocesses the pulsar emission and heats the companion. Improved spectra and,
especially, models that include such shock heating are needed for precise
parameter measurement.
