Orbital decay in LMC X-4

We report on the results of observations of the binary X-ray pulsar LMC X-4 with the Rossi X-Ray Timing Explorer. Our analysis of the Doppler delays of the 13.5 s X-ray pulsations yields the most accurate determination of the LMC X-4 orbital parameters available to date. The epoch of orbital phase zero for the 1.4 day orbit is determined with an uncertainty of similar to 20 s and is combined with five earlier determinations of the epoch of phase zero to obtain the rate of change in the orbital period: (P)over-dot(orb)/(P)(orb) = (-9.8 +/- 0.7) x 10(-7) yr(-1). This is the first high significance measurement of the rate of change of the orbital period in LMC X-4. We present data on one of three strong X-ray flares as well as energy-dependent pulse profiles for both nonflaring and flaring time intervals. The pulse profiles during the nonflaring time intervals are typically strikingly different from the hare profiles but at other times can be similar. Possible origins of the flaring behavior are discussed. We reconsider the orbital decay of LMC X-4 in the context of tidal evolution. We find that while the orbital decay is most likely driven by tidal interactions, the asynchronism between the orbit and the rotation of the companion star is probably maintained by the evolutionary expansion of the companion star, just as is thought to be the case for Cen X-3 and SMC X-l. For LMC X-4, we find that the evidence favors the companion star being in a late stage of its evolution on the main sequence. The orbital decay timescale of about 1,000,000 yr implies that the Roche lobe will move catastrophically deep into the atmosphere of the companion within a few times 10(4) yr. This short X-ray lifetime must be similar to the lifetimes of SMC X-1 and Cen X-3 which have decay timescales of 300,000 and 550,000 yr, respectively, and may be typical of all massive X-ray binaries in Roche lobe or near Roche lobe contact.