Determination of parameters of long-term variability of the X-ray pulsar LMC X-4

We have investigated the temporal variability of the X-ray flux measured from the high-mass Xray binary LMCX-4 on time scales from several tens of days to tens of years, i.e., exceeding considerably the orbital period (1.408 days). In particular, we have investigated the 30-day cycle of modulation of the X-ray emission from the source (superorbital or precessional variability) and refined the orbital period and its first derivative. We show that the precession period in the time interval 1991--2015 is near its equilibrium value $P_{sup} = 30.370$ days, while the observed historical changes in the phase of this variability can be interpreted in terms of the "red noise" model. We have obtained an analytical law from which the precession phase can be determined to within 5\% in the entire time interval under consideration. Using archival data from several astrophysical observatories, we have found 43 X-ray eclipses in LMC X-4 that, together with the nine eclipses mentioned previously in the literature, have allowed the parameters of the model describing the evolution of the orbital period to be determined. As a result, the rate of change in the orbital period $\dot P_{orb}/P_{orb}=(1.21\pm0.07)\times10^{-6}$ yr$^{-1}$ has been shown to be higher than has been expected previously.