Anomalous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs) are two small classes of X-ray sources strongly suspected to host a magnetar, i.e. an ultra-magnetized neutron star with $Bapprox 10^14-10^15 G. Many SGRs/AXPs are known to be variable, and recently the existence of genuinely transient magnetars was discovered. Here we present a comprehensive study of the pulse profile and spectral evolution of the two transient AXPs (TAXPs) XTE J1810-197 and CXOU J164710.2-455216. Our analysis was carried out in the framework of the twisted magnetosphere model for magnetar emission. Starting from 3D Monte Carlo simulations of the emerging spectrum, we produced a large database of synthetic pulse profiles which was fitted to observed lightcurves in different spectral bands and at different epochs. This allowed us to derive the physical parameters of the model and their evolution with time, together with the geometry of the two sources, i.e. the inclination of the line-of-sight and of the magnetic axis with respect to the rotation axis. We then fitted the (phase-averaged) spectra of the two TAXPs at different epochs using a model similar to that used to calculate the pulse profiles ntzang in XSPEC) freezing all parameters to the values obtained from the timing analysis, and leaving only the normalization free to vary. This provided acceptable fits to XMM-Newton data in all the observations we analyzed. Our results support a picture in which a limited portion of the star surface close to one of the magnetic poles is heated at the outburst onset. The subsequent evolution is driven both by the cooling/varying size of the heated cap and by a progressive untwisting of the magnetosphere.
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