Electrodynamics of Magnetars: Implications for the Persistent X-ray Emission and Spindown of the Soft Gamma Repeaters and Anomalous X-ray Pulsars

(ABBREVIATED) 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 SGRs and AXPs, these currents are maintained by magnetic stresses acting deep inside the star. We construct self-similar, force-free equilibria of the current-carrying magnetosphere with a power-law dependence of magnetic field on radius, B ~ r^(-2-p), and show that a large-scale twist softens the radial dependence to p < 1. The spindown torque acting on the star is thereby increased in comparison with a vacuum dipole. We comment on the strength of the surface magnetic field in the SGR and AXP sources, 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 ~ 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} ~ 10^{14} G. Redistribution of the emerging X-ray flux at the ion and electron cyclotron resonances will significantly modify the emerging pulse profile and, through the Doppler effect, generate a non-thermal tail to the X-ray spectrum. The sudden change in the pulse profile of SGR 1900+14 after the 27 August 1998 giant flare is related to an enhanced optical depth to electron cyclotron scattering, resulting from a sudden twist imparted to the external magnetic field.