  We study an influence of X-ray photo-ionization from an accreting neutron
star in a high mass X-ray binary. Our aim is to unveil a new principle
governing X-ray luminosities of X-ray binaries, with a simple analysis of fluid
equations simulating line-driven wind flow under influence of X-ray
irradiation. In this study, we solve equation of motion of the accretion flow
taking into account the line-driven acceleration and X-ray photo-ionization.
Under the influence of X-ray irradiation, we find the flow equations take two
types of solutions. The first solution is characterized by a slow wind velocity
which causes a large accretion rate. The second solution is a fast wind flow
which results in a small accretion rate. We find that only the solution with a
fast wind and faint X-ray luminosity is a steady solution. On the other hand,
slow wind solution with a large X-ray luminosity is not a realizable solution.
In bright X-ray binary systems, X-ray luminosity would increase until strong
X-ray reduces the line-driven acceleration and causes a stagnation of the wind.
This result implies an important consequence that the X-ray luminosity of the
wind-fed, X-ray emitting binary will be settled by the wind stagnation limit.
At the same time, the fast wind solution with small X-ray luminosity also can
be a steady state. Bright X-ray sources, such as Vela X-1, would have limiting
luminosities of wind stagnation, while faint systems such a quiescent Super
giant Fast X-ray Transients could be on the faint solutions.
