Timing Properties of Magnetars

We study the pulse morphologies and pulse amplitudes of thermally emittingneutron stars with ultrastrong magnetic fields. The beaming of the radiationemerging from a magnetar was recently shown to be predominantly non-radial,with a small pencil and a broad fan component. We show that the combination ofthis radiation pattern with the effects of strong lensing in the gravitationalfield of the neutron star yields pulse profiles that show a qualitativelydifferent behavior compared to that of the radially-peaked beaming patternsexplored previously. Specifically, we find that: (i) the pulse profiles ofmagnetars with a single hot emission region on their surface exhibit 1-2 peaks,whereas those with an antipodal emission geometry have 1-4 peaks, depending onthe neutron star compactness, the observer's viewing angle, and the size of thehot regions; (ii) the energy dependence of the beaming pattern may give rise toweakly or strongly energy-dependent pulse profiles and may introduce phase lagsbetween different energy bands; (iii) the non-radial beaming pattern can giverise to high pulsed fractions even for very relativistic neutron stars; (iv)the pulsed fraction may not vary monotonically with neutron star compactness;(v) the pulsed fraction does not decrease monotonically with the size of theemitting region; (vi) the pulsed fraction from a neutron star with a single hotpole has, in general, a very weak energy dependence, in contrast to the case ofan antipodal geometry. Comparison of these results to the observed propertiesof anomalous X-ray pulsars strongly suggests that they are neutron stars with asingle hot region of ultrastrong magnetic field.Comment: 22 pages, 13 color figures, ApJ in pres