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 o ccasions 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 delay s. We confirm the Doppler delays by using measurements made with the All Sk y Monitor (ASM) on RXTE. We infer that the orbit is characterized by a peri od P-orb = 250 days, a projected semimajor axis of the neutron ax sin i = 4 54 lt-s, a mass function f(M) = 1.61 M-., and a modest eccentricity e = 0.1 1. The measured orbital parameters, together with the known properties of t he classical Be star X Per, imply a semimajor axis a = 1.8-2.2 AU and an or bital inclination i similar to 26 degrees -33 degrees. We discuss the formation of the system in the context of the standard evolu tionary 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 qua si-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 exp losion was completely symmetric, then the present orbital eccentricity indi cates 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 oft en inferred from the velocity distribution of isolated radio pulsars, then the resultant orbital eccentricity would likely have been substantially lar ger than 0.11. We have carried out a Monte Carlo study of the effects of su ch natal kicks and find that there is less than a 1% probability of a syste m like that of X Per forming with an orbital eccentricity e less than or si milar to 0.11. We speculate that there may be a substantial population of n eutron stars formed with little or no kick. Finally, we discuss the connect ed topics of the wide orbit and accretion by the neutron star from a stella r wind.