Torque reversal and cyclotron absorption feature in HMXB 4U 1538-522

We present a comprehensive timing and spectral analysis of the HMXB 4U 1538-522 by using the Nuclear Spectroscopic Telescope Array (NuSTAR) observatory data. Using three archived observations made between 2019 and 2021, we have detected $\sim $ 526 s coherent pulsations up to 60 keV. We have found an instantaneous spin-down rate of $\dot{P} = 6.6_{-6.0}^{+2.4} \times 10^{-6}$ s s$^{-1}$ during the first observation. The pulse profiles had a double peaked structure consisting of a broad primary peak and an energy dependent, weak secondary peak. We have also analysed the long-term spin-period evolution of 4U 1538-522 from data spanning more than four decades, including the data from Fermi/GBM. Based on the recent spin trends, we have found that the third torque reversal in 4U 1538-522 happened around MJD 58800. The source is currently spinning up with $\dot{P} = -1.9(1) \times 10^{-9}$ s s$^{-1}$. We also report a periodic fluctuation in the spin-period of 4U 1538-522. The broad-band persistent spectra can be described with a blackbody component and either powerlaw or Comptonization component along with a Fe K$_{\alpha}$ line at 6.4 keV and a cyclotron absorption feature around 22 keV. We have also found a relatively weak absorption feature around 27 keV in the persistent spectra of 4U 1538-522 in all three observations. We have estimated a magnetic field strength of $1.84_{-0.06}^{+0.04} (1+z) \times 10^{12}$ and $2.33_{-0.24}^{+0.15} (1+z) \times 10^{12}$ G for the two features, respectively.
Comment: Accepted for publication in MNRAS