The Broadband Afterglow of GRB 980329

We present radio observations of the afterglow of the bright gamma-ray burstGRB980329 made between one month and several years after the burst, are-analysis of previously published submillimeter data, and late-time opticaland near-infrared (NIR) observations of the host galaxy. From the absence of aspectral break in the optical/NIR colors of the host galaxy, we exclude theearlier suggestion that GRB980329 lies at a redshift of z >~5. We combine ourdata with the numerous multi-wavelength observations of the early afterglow,fit a comprehensive afterglow model to the entire broadband dataset, and derivefundamental physical parameters of the blast-wave and its host environment.Models for which the ejecta expand isotropically require both a highcircumburst density and extreme radiative losses from the shock. No low densitymodel (n << 10 cm^{-3}) fits the data. A burst with a total energy of ~ 10^{51}erg, with the ejecta narrowly collimated to an opening angle of a few degrees,driven into a surrounding medium with density ~ 20 cm^{-3}, provides asatisfactory fit to the lightcurves over a range of redshifts.Comment: 27 pages, incl. 6 figures, minor revisions (e.g. added/updated references) Accepted by Ap