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 and 242 ks, respectively. On both occasions, the object exhibited the characteristic two-component spectrum. The soft component, dominant in energies below ∼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 ≳ 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 ≈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 ± 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 ≈ P/T = 1.3 × 10−4, presumably due to ∼ 1016 G toroidal magnetic fields. As a counterexample, 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.

Oscillations of 2D ESTER models

Context. Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula. In parallel, recent studies have revealed the presence of regular pulsation frequency patterns in rapidly rotating δ Scuti stars that seem to match theoretical expectations. Aims. In this context, a key question is whether strong gradients or discontinuities can adversely affect the asymptotic frequency pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings. Methods. In order to address these questions, we numerically calculate stellar pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D Evolution STEllaire en Rotation (ESTER) code. This code self-consistently calculates the rotation profile based on baroclinic effects and uses a spectral multi-domain approach, thus making it possible to introduce discontinuities at the domain interfaces without loss of numerical accuracy. The pulsation calculations are carried out using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is then used to confirm the high numerical accuracy of the pulsation frequencies and to derive an integral formula for the generalised rotational splittings. Acoustic glitch theory, combined with ray dynamics, is applied to the discontinuous models in order to interpret their pulsation spectra. Results. Our results show that the generalised rotational splittings are very well approximated by the integral formula, except for modes involved in avoided crossings. This potentially allows the application of inverse theory for probing the rotation profile. We also show that glitch theory applied along the island mode orbit can correctly predict the periodicity of the glitch frequency pattern produced by the discontinuity or Γ1 dip related to the He II ionisation zone in some of the models. Furthermore, the asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.