A comprehensive study of orbital evolution of LMC X-4: existence of a second derivative of the orbital period

Abstract

ABSTRACT We report here results from pulse arrival time delay analysis of the eclipsing high-mass X-ray binary (HMXB) pulsar LMC X-4 using observations made with the Rossi X-ray Timing Explorer, XMM–Newton, NuSTAR (Nuclear Spectroscopic Telescope ARray), and AstroSat. Combining the orbital parameters determined from these observations with the historical measurements dating back to 1998, we have extended the Tπ/2 epoch history of LMC X-4 by about 4600 binary orbits spanning about 18 yr. We also report mid-eclipse time measurements (Tecl) using data obtained from wide-field X-ray monitors of MAXI-GSC (Monitor of All-sky X-ray Image – Gas Slit Camera) and Swift-BAT (Burst Alert Telescope). Combining the new Tπ/2 and Tecl estimates with all the previously reported values, we have significantly improved the orbital evolution measurement, which indicates that the orbital period is evolving at a time-scale ($P_{\rm orb}/\dot{P}_{\rm orb}$) of about 0.8 Myr. For the first time in an accreting X-ray pulsar system, we confirm the existence of a second derivative of the orbital period, having an evolution time-scale ($\dot{P}_{\mathrm{ orb}}/\ddot{P}_{\mathrm{ orb}}$) of about 55 yr. Detection of a second derivative of the orbital period in LMC X-4 makes its orbital evolution time-scale more uncertain, which may also be true for other HMXBs. Independent solutions for the orbital evolution measurement using the mid-eclipse data and the pulse timing data are consistent with each other, and help us put an upper limit of 0.009 on the eccentricity of the binary system.