A systematic study of soft X-ray pulse profiles of magnetars in quiescence

Magnetars are neutron stars with extremely high surface magnetic fields. They show diverse X-ray pulse profiles in the quiescent state. We perform a systematic Fourier analysis of their soft X-ray pulse profiles. We find that most magnetars have a single-peaked profile and hence have low amplitudes of the second Fourier harmonic (A2). On the other hand, the pulsed fraction (PF) spreads over a wide range. We compared the results with theoretical profiles assuming various surface hotspot asymmetries, viewing geometries, and beaming functions. We found that a single value of the intensity ratio r between two antipodal hotspots is unable to reproduce the observed distribution of A2 and PF for all magnetars. The inferred r is probably anticorrelated with the thermal luminosity, implying that high-luminosity magnetars tend to have two symmetric hotspots. Our results are consistent with theoretical predictions, for which the existence of an evolving toroidal magnetic field breaks the symmetry of the surface temperature