X-ray binaries with neutron stars at different accretion stages

Different accretion regimes onto magnetized NSs in HMXBs are considered: wind-fed supersonic (Bondi) regime at high accretion rates g s^-1, subsonic settling regime at lower and supercritical disc accretion during Roche lobe overflow. In wind-fed stage, NSs in HMXBs reach equilibrium spin periods P _* proportional to binary orbital period P_b. At supercritical accretion stage, the system may appear as a pulsating ULX. Population synthesis of Galactic HMXBs using standard assumptions on the binary evolution and NS formation is presented. Comparison of the model P _* - P_b (the Corbet diagram), P_* - L_x and P_b - L_x distributions with those for the observed HMXBs (including Be X-ray binaries) and pulsating ULXs suggests the importance of the reduction of P^* in non-circular orbits, explaining the location of Be X-ray binaries in the model Corbet diagram, and the universal parameters of pulsating ULXs depending only on the NS magnetic fields.