The centroid energy E cyc of the cyclotron line in the spectrum of the binary X-ray pulsar Her X-1 has been found to decrease with time on a time scale of a few tens of years -surprisingly short in astrophysical terms. This was found for the pulse phase-averaged line centroid energy using observational data from various X-ray satellites over the time period 1996 to 2012, establishing a reduction of ∼4 keV. Here we report on the result of a new observation by NuSTAR performed in August 2015. The earlier results are confirmed and strengthened with respect to both the dependence of E cyc on flux (it is still present after 2006) and the dependence on time: the long-term decay continued with the same rate, corresponding to a reduction of ∼5 keV in 20 yr.

Context. X-ray spectra of accreting pulsars are generally observed to vary with their X-ray luminosity. In particular, the hardness of the X-ray continuum is found to depend on luminosity. In a few sources, the correlation between the energy of the cyclotron resonance scattering feature (CRSF) and the luminosity is clear. Different types (signs) of the correlation are believed to reflect different accretion modes. Aims. We analyse two NuSTAR observations of the transient accreting pulsar Cep X-4 during its 2014 outburst. Our analysis is focused on a detailed investigation of the dependence of the CRSF energy and of the spectral hardness on X-ray luminosity, especially on short timescales. Methods. To investigate the spectral changes as a function of luminosity within each of the two observations, we used the intrinsic variability of the source on the timescale of individual pulse cycles (tens of seconds) , the so-called pulse-to-pulse variability. Results. We find that the NuSTAR spectrum of Cep X-4 contains two CRSFs: the fundamental line at~30 keV and its harmonic at~55 keV. We find for the first time that the energy of the fundamental CRSF increases and the continuum becomes harder with increasing X-ray luminosity not only between the two observations, that is, on the long timescale, but also within an individual observation, on the timescale of a few tens of seconds. We investigate these dependencies in detail including their non-linearity. We discuss a possible physical interpretation of the observed behaviour in the frame of a simple one-dimensional model of the polar emitting region with a collisionless shock formed in the infalling plasma near the neutron star surface. With this model, we are able to reproduce the observed variations of the continuum hardness ratio and of the CRSF energy with luminosity.

We present the results of the pulse-amplitude-resolved spectroscopy of the accreting pulsar V 0332+53 using the NuSTAR observations of the source in 2015 and 2016. We investigate the dependence of the energy of the cyclotron resonant scattering feature (CRSF) as a function of X-ray luminosity on timescales comparable with the spin period of the pulsar within individual observations, and the behavior on longer timescales within and between the two observed outbursts. We confirm that in both cases the CRSF energy is negatively correlated with flux at luminosities higher than the critical luminosity and is positively correlated at lower luminosities. We also confirm the recently reported gradual decrease in the line energy during the giant outburst in 2015. Using the NuSTAR data, we find that this decrease was consistent with a linear decay throughout most of the outburst, and flattened or even reversed at the end of the 2015 outburst, approximately simultaneously with the transition to the subcritical regime. We also confirm that by the following outburst in 2016 the line energy rebounded to previous values. The observed behavior of the CRSF energy with time is discussed in terms of changes in the geometry of the CRSF forming region caused by changes in the effective magnetospheric radius.