Electrodynamics of magnetars: Implications for the persistent X-ray emission and spin-down of the soft gamma repeaters and anomalous X-ray pulsars

We consider the structure of neutron star magnetospheres threaded by large-scale electrical currents and the effect of resonant Compton scattering by the charge carriers ( both electrons and ions) on the emergent X-ray spectra and pulse profiles. In the magnetar model for the soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs), these currents are maintained by magnetic stresses acting deep inside the star, which generate both sudden disruptions (SGR outbursts) and more gradual plastic deformations of the rigid crust. We construct self-similar force-free equilibria of the current-carrying magnetosphere with a power-law dependence of magnetic field on radius, Bproportional tor(-(2+p)), and show that a large-scale twist of field lines softens the radial dependence of the magnetic field to p<1. The spin-down torque acting on the star is thereby increased in comparison with an orthogonal vacuum dipole. We comment on the strength of the surface magnetic field in the SGR and AXP sources, as inferred from their measured spin-down rates, and the implications of this model for the narrow measured distribution of spin periods. A magnetosphere with a strong twist [B phi/B theta = O(1) at the equator] has an optical depth similar to 1 to resonant cyclotron scattering, independent of frequency ( radius), surface magnetic field strength, or charge/mass ratio of the scattering charge. When electrons and ions supply the current, the stellar surface is also heated by the impacting charges at a rate comparable to the observed X-ray output of the SGR and AXP sources, if B(dipole)similar to 10(14) G. Redistribution of the emerging X-ray flux at the cyclotron resonance will strongly modify the emerging pulse pro le and, through the Doppler effect, generate a nonthermal tail to the X-ray spectrum. We relate the sudden change in the pulse pro le of SGR 1900+14 following the 1998 August 27 giant flare to an enhanced optical depth at the electron cyclotron resonance resulting from a sudden twist imparted to the external magnetic field during the are. The self-similar structure of the magnetosphere should generate frequency-independent profiles; more complicated pulse profiles may reflect the presence of higher multipoles, ion cyclotron scattering, or possibly nonresonant Compton scattering of O-mode photons by pair-loaded currents.