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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.
The Suzaku data of the highly variable magnetar 1E 1547.0$-$5408, obtained during the 2009 January activity, were reanalyzed. The 2.07 s pulsation of the 15--40 keV emission detected with the HXD was found to be phase modulated, with a period of $36.
Archival NuSTAR data of the magnetar 4U0142+61, acquired in 2014 March for a total time span of 258 ks, were analyzed. This is to reconfirm the 55 ks modulation in the hard X-ray pulse phases of this source, found with a Suzaku observation in 2009 (M
A bright burst, followed by an X-ray tail lasting ~10 ks, was detected during an XMM-Newton observation of the magnetar 1E 1547.0-5408 carried out on 2009 February 3. The burst, also observed by SWIFT/BAT, had a spectrum well fit by the sum of two bl
We present the evolution of the X-ray emission properties of the magnetar 1E 1547.0-5408 since February 2004 over a time period covering three outbursts. We analyzed new and archival observations taken with the Swift, NuSTAR, Chandra and XMM-Newton X
The fastest-rotating magnetar 1E 1547.0-5408 was observed in broad-band X-rays with Suzaku for 33 ks on 2009 January 28-29, 7 days after the onset of its latest bursting activity. After removing burst events, the absorption-uncorrected 2-10 keV flux