Unveiling the thermal and magnetic map of neutron star surfaces though their X-ray emission: method and lightcurves analysis

Recent Chandra and XMM-Newton observations of a number of X-ray ``dim'' pulsating neutron stars revealed quite unexpected features in the emission from these sources. Their soft thermal spectrum, believed to originate directly from the star surface, shows evidence for a phase-varying absorption line at some hundred eVs. The pulse modulation is relatively large (pulsed fractions in the range ~12%-35%), the pulse shape is often non-sinusoidal, and the hard X-ray color appears to be anti-correlated in phase with the total emission. Moreover, the prototype of this class, RX J0720.4-3125, has been found to undergo rather sensible changes both in its spectral and timing properties over a timescale of a few years. All these new findings seem difficult to reconcile with the standard picture of a cooling neutron star endowed with a purely dipolar magnetic field, at least if surface emission is produced in an atmosphere on top of the crust. In this paper we explore how a dipolar+quadrupolar star-centered field influence the properties of the observed lightcurves. The phase-resolved spectrum has been evaluated accounting for both radiative transfer in a magnetized atmosphere and general relativistic ray-bending. We computed over 78000 lightcurves varying the quadrupolar components and the viewing geometry. A comparison of the data with our model indicate that higher order multipoles are required to reproduce the observations.