Cyclotron line energy in Hercules X-1: stable after the decay

We summarize the results of a dedicated effort made between 2012 and 2019 to follow the evolution of the cyclotron line in Her X-1 through repeated NuSTAR observations. The previously observed nearly 20-year-long decay of the cyclotron line energy has ended in 2012: from then on, the pulse-phase-averaged flux-corrected cyclotron line energy has remained stable and constant at an average value of E_(cyc) = (37.44 ± 0.07) keV (normalized to a flux level of 6.8 RXTE/ASM-cts s⁻¹). The flux dependence of E_(cyc) discovered in 2007 is now measured with high precision, giving a slope of (0.675 ± 0.075) keV/(ASM-cts s⁻¹), corresponding to an increase of 6.5% of E_(cyc) for an increase in flux by a factor of two. We also find that all line parameters as well as the continuum parameters show a correlation with X-ray flux. While a correlation between E_(cyc) and X-ray flux (both positive and negative) is now known for several accreting binaries with various suggestions for the underlying physics, the phenomenon of a long-term decay has so far only been seen in Her X-1 and Vela X-1, with far less convincing explanations.