Long-term evolutions of the cyclotron line energies in Her X-1, Vela X-1, and Cen X-3 as observed with Swift/BAT

We study the long-term evolution of the centroid energy of cyclotron lines - often referered to as cyclotron resonance scattering features (CRSFs) - in Her X-1, Vela X-1, and Cen X-3, using survey observations of the Burst Alert Telescope onboard Swift. We find a significant decrease of the fundamental CRSF energy in Her X-1 and the first harmonic line energy in Vela X-1 since the launch of Swift in 2004 and until 2010 and 2012, respectively. In both sources, the decreases stopped at some time, with a quite stable centroid energy thereafter. Unlike in Her X-1 and Vela X-1, the CRSF energy in Cen X-3 does not show a long-term decrease. It is observed not to change for at least the past 14 yr. The long-term variation of the line energy is a direct way to investigate the magnetic field structure in the polar regions of pulsars. Our results may stimulate the development of theoretical models, especially regarding how the accreted mass accumulates in the accretion mound or how the magnetic field distorts around the polar cap.