The orbit of X Persei 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 board the Rossi X-Ray Timing Explorer (RXT E). 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 All Sky Monitor (ASM) on RXTE. We infer that the orbit is characterized by a period P-orb = 250 days, a projected semimajor axis of the neutron ax sin i = 454 lt-s, a mass function f(M) = 1.61 M-., and a modest eccentricity e = 0.11. The measured orbital parameters, together with the known properties of the classical Be star X Per, imply a semimajor axis a = 1.8-2.2 AU and an orbital inclination i similar to 26 degrees -33 degrees. We discuss the formation of the system in the context of the standard evolutionary scenario for Be/X-ray binaries. 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 or similar to6 M. after mas transfer. If the supernova explosion was completely symmetric, then the present orbital eccentricity indicates that less than or similar to4 M-. was ejected from the binary. If on the other hand, the neutron star received at birth a kick of the type often inferred from the velocity distribution of isolated radio pulsars, then the resultant orbital eccentricity would likely have been substantially larger than 0.11. We have carried out a Monte Carlo study of the effects of such natal kicks and find that there is less than a 1% probability of a system like that of X Per forming with an orbital eccentricity e less than or similar to 0.11. We speculate that there may be a substantial population of neutron stars formed with little or no kick. Finally, we discuss the connected topics of the wide orbit and accretion by the neutron star from a stellar wind.