Long-term evolution of cyclotron line energy in an eclipsing pulsar 4U 1538-522

We present the timing and spectral analysis of the high-mass X-ray binary source 4U 1538-522 using Nuclear Spectroscopic Telescope Array (NuSTAR) observations. One of the observations partially covers the X-ray eclipse of the source along with eclipse ingress. The source is found to spin down at the rate of 0.163 ± 0.002 s yr^-1 between ~54973 and 58603 MJD. It is evident that at time ~58620 MJD, a torque reversal occurred; thereafter, the source exhibited a spin-up trend at the rate -(0.305 ± 0.018) s yr^-1 until 59275 MJD. A recent NuSTAR observation finds the pulse period of the source: (526.2341 ± 0.0041) s. The pulse profile exhibits a transition from double-peaked to single-peaked nature above ~30 keV. We analysed the overall trend of the temporal evolution of fundamental cyclotron resonance scattering feature, E_cyc, incorporating recent NuSTAR measurements. Initially, during the time span ~50452.16-55270.8 MJD, the cyclotron line energy is found to increase at a rate of 0.11 ± 0.03 keV yr^-1, which is further followed by a decrease at a rate -0.14 ± 0.01 keV yr^-1 between 55270.8 and 59267 MJD. The combined measurements in the time span 50452.16-59267 MJD reveal that the cyclotron line energy is increasing linearly at a rate of 0.08 ± 0.02 keV yr^-1.