Inferring the Magnetic Fields of Magnetars from their X-ray Spectra

We present the first self-consistent theoretical models of magnetar spectra that take into account the combined effects of the stellar atmosphere and its magnetosphere. We find that the proton cyclotron lines that are already weakened by atmospheric effects become indistinguishable from the continuum for moderate scattering optical depths in the magnetosphere. Furthermore, the hard excess becomes more pronounced due to resonant scattering and the resulting spectra closely resemble the observed magnetar spectra. We argue that while the absence of proton cyclotron lines in the observed spectra are inconclusive about the surface field strengths of magnetars, the continuum carries nearly unique signatures of the field strength and can thus be used to infer this quantity. We fit our theoretical spectra with a phenomenological two-blackbody model and compare our findings to source spectra with existing two-blackbody fits. The field strengths that we infer spectroscopically are in remarkable agreement with the values inferred from the period derivative of the sources assuming a dipole spindown. These detailed predictions of line energies and equivalent widths may provide an optimal opportunity for measuring directly the surface field strengths of magnetars with future X-ray telescopes such as Constellation-X.