  Gamma-ray emission in the TeV range has been detected by HESS from two X-ray
binaries: PSR B1259-63 and LS 5039. In both, the early-type star provides large
numbers of target photons for pair-production with TeV gamma-rays. This results
in a modulation of the gamma-ray flux as the relative positions of the
gamma-ray source and companion star change with orbital phase. The lightcurve
and spectrum of absorption provide useful diagnostics for the location and
nature of gamma-ray emission. The expected orbital variations of the absorption
spectrum and flux are calculated for LS 5039, PSR B1259-63 and LSI +61 303, a
system similar to LS 5039 but still undetected at TeV energies. In LS 5039,
emission close to a black hole or a neutron star primary is considered. In both
cases, the flux above 250 GeV drops by more than an order-of-magnitude near
periastron due to absorption. A black hole yields a clear spectral signature in
the average spectrum at 400 GeV. A neutron star yields more variability, with
the spectral feature moving from 200 GeV to 2 TeV. The absorbed fraction of the
flux can be as small as 20%, allowing for an almost direct view of the
intrinsic spectrum. Low variability requires emission on large scales, more
than 0.7 AU away to have <50% absorption in a jet. Such predictions are
essential to distinguish between variability due to the gamma-ray emission
process from that due to absorption. A modulation in LS 5039 would provide a
novel way to constrain the gamma-ray source. Its absence would imply that
gamma-ray emission occurs on large scales.
