Numerical Modeling of the Radio Nebula from the 2004 December 27 Giant Flare of SGR 1806−20

We use the relativistic hydrodynamics code Cosmos++ to model the evolution ofthe radio nebula triggered by the Dec. 27, 2004 giant flare event of soft gammarepeater 1806-20. We primarily focus on the rebrightening and centroid motionoccurring subsequent to day 20 following the flare event. We model this periodas a mildly relativistic (gamma ~ 1.07 - 1.67) jetted outflow expanding intothe interstellar medium (ISM). We demonstrate that a jet with total energy ~10^46 ergs confined to a half opening angle ~ 20 degrees fits the keyobservables of this event, e.g. the flux lightcurve, emission map centroidposition, and aspect ratio. In particular, we find excellent agreement withobservations if the rebrightening is due to the jet, moving at 0.5c andinclined ~ 0 - 40 degrees toward the observer, colliding with a densitydiscontinuity in the ISM at a radius of several 10^16 cm. We also find that ajet with a higher velocity, >~ 0.7c, and larger inclination, >~ 70 degrees,moving into a uniform ISM can fit the observations in general, but tends tomiss the details of rebrightening. The latter, uniform ISM model predicts anISM density more than 100 times lower than that of the former model, and thussuggests an independent test which might discriminate between the two. One ofthe strongest constraints of both models is that the data seems to require anon-uniform jet in order to be well fit.