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

TL;DR

This study confirms a 36 ks pulse-phase modulation in the magnetar 1E 1547.0$-$5408 using NuSTAR data, supporting the idea of free precession caused by internal magnetic deformation, with complex energy-dependent behaviors.

Contribution

It provides the first NuSTAR confirmation of the 36 ks modulation, strengthening the precession hypothesis and revealing detailed energy-dependent pulse-phase phenomena in this magnetar.

Findings

Confirmed 36 ks pulse-phase modulation with NuSTAR data

Detected complex energy dependence of modulation parameters

Supported internal magnetic field deformation as the cause

Abstract

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 $1.7 \times 10^{-11}$ ergs s$^{-1}$ cm$^{-2}$, and its pulsation at a period of $2.086710(5)$ sec. In 8-25 keV, the pulses were phase-modulated with a period of $T=36.0 \pm 2.3$ ks, and an amplitude of $\sim 0.2$ sec. 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 $\sim 0.6 \times 10^{-4}$, possibly caused by internal toroidal magnetic fields reaching $\sim 10^{16}$ G. Like in the Suzaku case, the modulation was not detected in energies below $\sim 8$ keV. Above 10 keV, the pulse-phase behaviour, including the 36 ks modulation parameters, exhibited complex energy dependences: at $\sim 22$ keV, the modulation amplitude increased to $\sim 0.5$ sec, and the modulation phase changed by $\sim 65^\circ$ 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 ultra-strong magnetic fields.