Constraints on the emission and viewing geometry of the transient anomalous X-ray pulsar XTE J1810-197

The temporal decay of the flux components of the transient anomalous X-ray pulsar XTE J1810-197 following its 2002 outburst presents a unique opportunity to probe the emission geometry of a magnetar. Toward this goal, we model the magnitude of the pulsar's modulation in narrow spectral bands over time. Following previous work, we assume that the postoutburst flux is produced in two distinct thermal components arising from a hot spot and a warm concentric ring. We include general relativistic effects on the blackbody spectra due to gravitational redshift and light bending near the stellar surface, which strongly depend on radius. This affects the model fits for the temperature and size of the emission regions. For the hot spot, the observed temporal and energy-dependent pulse modulation is found to require an anisotropic, pencil-beamed radiation pattern. We are able to constrain an allowed range for the angles that the line of sight (psi) and the hot spot pole (xi) make with respect to the spin axis. Within errors, this is defined by the locus of points in the xi-psi plane that lie along the line vertical bar xi + beta(R)] [psi +beta(R)] approximate to const, where beta(R) is a function of the radius R of the star. For a canonical value of R - 12 km, the viewing parameters range from psi - xi - 37 degrees to (psi,xi) - (85 degrees, 15 degrees). We discuss our results in the context of magnetar emission models.