The Orbit of X Per and Its Neutron Star Companion
  We have observed the Be/X-ray pulsar binary system X Per/4U 0352+30 on 61 occasions spanning an interval of 600 days with the PCA instrument on RXTE. Pulse timing analyses of the 837-s pulsations yield strong evidence for the presence of orbital Doppler delays. We confirm the Doppler delays by using measurements made with the RXTE All-Sky Monitor. We obtain an orbital period of 250 days, a projected semimajor axis of the neutron star of 454 lt-s, a mass function of 1.61 solar masses, and a modest eccentricity of 0.11. We discuss the formation of the system in the context of the standard evolutionary scenario for Be/X-ray binaries with consideration of the possibility that the birth of the neutron star was accompanied by a kick of the type often inferred from the velocity distribution of isolated radio pulsars. The orbital eccentricity just after the supernova explosion was almost certainly virtually the same as at present, because the Be star is much smaller than the orbital separation. We find that the system most likely formed from a pair of massive progenitor stars, and probably involved a quasi-stable and nearly conservative transfer of mass from the primary to the secondary. We find that the He star remnant of the primary most likely had a mass less than 6 solar masses after mass transfer. Finally, we speculate that there may be a substantial population of neutron stars formed with little or no kick. 
Hugo Delgado-Marti, Alan M. Levine, Eric Pfahl, and Saul A. Rappaport