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 ( 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 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 star a x 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 ~ 26°-33°. 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 ≲6 M ☉ after mass transfer. If the supernova explosion was completely symmetric, then the present orbital eccentricity indicates that ≲4 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 ≲ 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.