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Long-term evolution of cyclotron resonant scattering features in the accreting pulsar Vela X-1: A pulse-to-pulse approach

We investigated the long-term evolution of the cyclotron line energy, as well as the relationship between cyclotron line energy and luminosity in the high-mass X-ray binary Vela X-1, based on archival Swift/BAT monitoring from 2005 to 2024 and pulse-to-pulse analysis of nine NuSTAR observations from 2012 to 2024. Our results provide the first confirmation that the long-term decay of the harmonic line energy ($E_{\rm cyc,H}$) in Vela X-1 has ended. We further report the first detection of a transient increase in $E_{\rm cyc,H}$ between 2020 and 2023, which suggests a sudden and significant change in the magnetic field configuration or accretion geometry. In addition, $E_{\rm cyc,H}$ shows slightly lower values at low luminosities and tends to flatten at higher luminosities, in the range of $(0.13\text{--}1.21) \times10^{37} $erg $\rm{s}^{-1}$. The fundamental line energy ($E_{\rm cyc,F}$) exhibits no significant variation with time or luminosity, remaining stable at approximately 25 keV.