We use the relativistic hydrodynamics code Cosmos++ to model the evolution of the radio nebula triggered by the 2004 December 27 giant flare event of SGR 1806-20. We primarily focus on the rebrightening and centroid motion occurring subsequent to day 20 following the flare event. We model this period as a mildly relativistic (γ ~ 1.07-1.67) jetted outflow expanding into the ISM. We demonstrate that a jet with total energy ~1046 ergs confined to a half opening angle ~20° fits the key observables of this event, e.g., the flux light curve, emission map centroid position, and aspect ratio. In particular, we find excellent agreement with observations if the rebrightening is due to the jet, moving at 0.5c and inclined ~0°-40° toward the observer, colliding with a density discontinuity in the ISM at a radius of several times 1016 cm. We also find that a jet with a higher velocity, 0.7c, and larger inclination, 70°, moving into a uniform ISM can fit the observations in general but tends to miss the details of rebrightening. The latter, uniform ISM model predicts an ISM density more than 100 times lower than that of the former model and thus suggests an independent test that might discriminate between the two. One of the strongest constraints of both models is that the data seem to require a nonuniform jet in order to be well fitted.
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