A NuSTAR confirmation of the 36 ks hard X-ray pulse-phase modulation in the magnetar 1E 1547.0 - 5408

This paper describes an analysis of the NuSTAR data of the fastest-rotating magnetar 1E 1547 - 5408, acquired in 2016 April for a time lapse of 151 ks. The source was detected with a 1-60 keV flux of 1.7 × 10^-11 erg s^-1 cm^-2, and its pulsation at a period of 2.086710(5) s. In 8-25 keV, the pulses were phase-modulated with a period of T = 36.0 ± 2.3 ks, and an amplitude of ∼0.2 s. This reconfirms the Suzaku discovery of the same effect at $T=36.0 ^{+4.5}_{-2.5}$ ks, made in the 2009 outburst. These results strengthen the view derived from the Suzaku data, that this magnetar performs free precession as a result of its axial deformation by ∼0.6 × 10^-4, possibly caused by internal toroidal magneti fields (MFs) reaching ∼10¹⁶ G. Like in the Suzaku case, the modulation was not detected in energies below ∼8 keV. Above 10 keV, the pulse-phase behaviour, including the 36 ks modulation parameters, exhibited complex energy dependencies: at ∼22 keV, the modulation amplitude increased to ∼0.5 s, and the modulation phase changed by ∼65° over 10-27 keV, followed by a phase reversal. Although the pulse significance and pulsed fraction were originally very low in >10 keV, they both increased noticeably, when the arrival times of individual photons were corrected for these systematic pulse-phase variations. Possible origins of these complex phenomena are discussed, in terms of several physical processes that are specific to ultrastrong MFs.