Diagnosing the Outflow from the SGR 1806−20 Giant Flare with Radio Observations

On 2004 Dec. 27, the soft gamma repeater (SGR) 1806-20 emitted the brightestgiant flare (GF) ever detected from an SGR, with an (isotropic) energy release$\sim 100$ times greater than the only two other known SGR GFs. It was followedby a very bright, fading radio afterglow. Extensive follow-up radioobservations provided a wealth of information with unprecedented astrometricprecision, revealing the temporal evolution of the source size, along withdensely sampled light curves and spectra. Here we expand on our previous workon this source, by explaining these observations within one self-consistentdynamical model. In this scenario, the early radio emission is due to theoutflow ejected during the GF energizing a thin shell surrounding apre-existing cavity, where the observed steep temporal decay of the radioemission seen beginning on day 9 is attributed to the adiabatic cooling of theshocked shell. The shocked ejecta and external shell move outward together,driving a forward shock into the ambient medium, and are eventually deceleratedby a reverse shock. As we show in Gelfand et al. (2005), the radio emissionfrom the shocked external medium naturally peaks when significant decelerationoccurs, and then decays relatively slowly. The dynamical modeling of thecollision between the ejecta and the external shell together with the observedevolution of the source size (which is nicely reproduced in our model) suggestthat most of the energy in the outflow was in mildly relativistic material,with an initial expansion velocity $v/c \lesssim 0.7d_{15}$, for a distance of$15d_{15}$ kpc to SGR 1806-20. An initially highly relativistic outflow wouldnot have produced a long coasting phase at a mildly relativistic expansionvelocity, as was observed.Comment: 15 pages, 2 figures, clearer and more elaborate version; ApJ, in pres