Discovery of 40.5 ks Hard X-ray Pulse-Phase Modulations from SGR 1900+14

X-ray timing properties of the magnetar SGR 1900+14 were studied, using the data taken with Suzaku in 2009 and NuSTAR in 2016, for a time lapse of 114 ks and 242 ks, respectively. On both occasions, the object exhibited the characteristic two-component spectrum. The soft component, dominant in energies below $\sim 5$ keV, showed a regular pulsation, with a period of $P=5.21006$ s as determined with the Suzaku XIS, and $P=5.22669$ with NuSTAR. However, in $\gtrsim 6$ keV where the hard component dominates, the pulsation became detectable with the Suzaku HXD and NuSTAR, only after the data were corrected for periodic pulse-phase modulation, with a period of $T=40-44$ ks and an amplitude of $\approx 1$ s. Further correcting the two data sets for complex energy dependences in the phase-modulation parameters, the hard X-ray pulsation became fully detectable, in 12-50 keV with the HXD, and 6-60 keV with NuSTAR, using a common value of $T=40.5 \pm 0.8$ ks. Thus, SGR 1900+14 becomes a third example, after 4U 0142+61 and 1E 1547$-$5408, to show the hard X-ray pulse-phase modulation, and a second case of energy dependences in the modulation parameters. The neutron star in this system is inferred to perform free precession, as it is axially deformed by $\approx P/T =1.3 \times 10^{-4}$ presumably due to $\sim 10^{16}$ G toroidal magnetic fields. As a counter example, the Suzaku data of the binary pulsar 4U 1626-67 were analyzed, but no similar effect was found. These results altogether argue against the accretion scenario for magnetars.