High energy (>250 keV) emission has been detected persisting for several
tens of seconds after the initial spike of magnetar giant flares. It has been
conjectured that this emission might arise via inverse Compton scattering in a
highly extended corona generated by super-Eddington outflows high up in the
magnetosphere. In this paper we undertake a detailed examination of this model.
We investigate the properties of the required scatterers, and whether the
mechanism is consistent with the degree of pulsed emission observed in the tail
of the giant flare. We conclude that the mechanism is consistent with current
data, although the origin of the scattering population remains an open
question. We propose an alternative picture in which the emission is closer to
that star and is dominated by synchrotron radiation. The RHESSI observations
of the December 2004 flare modestly favor this latter picture. We assess the
prospects for the Fermi Gamma-Ray Space Telescope to detect and characterize a
similar high energy component in a future giant flare. Such a detection should
help to resolve some of the outstanding issues.Comment: 20 pages, 14 figure