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. 
Silvia Zane (MSSL, Univ. College London, UK), Roberto Turolla (Dept.   of Physics, Univ. of Padua, Italy)