Discovery of a 36 ks Phase Modulation in the Hard X-ray Pulses from the Magnetar 1E 1547.0$-$5408

The Suzaku data for the highly variable magnetar 1E 1547.0−5408, obtained during the 2009 January activity, were reanalyzed. The 2.07 s pulsation, detected in the 15–40 keV HXD data, was found to exhibit phase modulation, which can be modeled by a sinusoid with a period of $36.0^{+4.5}_{-2.5}\:$ks and an amplitude of 0.52 ± 0.14 s. While the effect is also seen in the 10–14 keV XIS data, the modul...