  The polarization of X-ray emission is a unique tool used to investigate the
magnetic field structure around astrophysical objects. In this paper, we study
the linear polarization of X-ray emissions from gamma-ray binary systems based
on pulsar scenarios. We discuss synchrotron emissions from pulsar wind
particles accelerated by a standing shock. We explore three kinds of
axisymmetric magnetic field structures: (i) toroidal magnetic fields, (ii)
poloidal magnetic fields, and (iii) tangled magnetic fields. Because of the
axisymmetric structure, the polarization angle of integrated emission is
oriented along or perpendicular to the shock-cone axis projected on the sky and
swings by 360? in one orbit. For the toroidal case, the polarization angle is
always directed along the shock cone axis and smoothly changes along the
orbital phase. For the poloidal/tangled magnetic field, the direction of the
polarization angle depends on the system parameters and orbital phase. In one
orbit, the polarization degree for the toroidal case can reach the maximum
value of the synchrotron radiation (? 70%), while the maximum polarization
degree for poloidal/tangled field cases is several 10%. We apply our model to
bright gamma-ray binary LS 5039 and make predictions for future observations.
With the expected sensitivity of the Imaging X-ray Polarimetry Explorer, linear
polarization can be detected by an observation of several days if the magnetic
field is dominated by the toroidal magnetic field. If the magnetic field is
dominated by the poloidal/tangled field, significant detection is expected with
an observation longer than 10 days.
