Radio Supernova SN 1998bw and Its Relation to GRB 980425

SN 1998bw is an unusual Type Ic supernova that may be associated with the$\gamma$-ray burst GRB 980425. We use a synchrotron self-absorption model forits radio emission to deduce that the synchrotron-emitting gas is expandinginto a circumstellar medium of approximately $r^{-2}$ density profile, at aspeed comparable to the speed of light. We assume that the efficiencies ofproduction of relativistic electrons and magnetic field are constant throughthe evolution. The circumstellar density is consistent with that expectedaround the massive star core thought to be the progenitor of SN 1998bw. Theexplosion energy in material moving with velocity $>0.5c$ is $\sim 10^{49}-3\times 10^{50}$ ergs, with some preference for the high values. The rise inthe radio light curves observed at days 20-40 is inferred to be the result of arise in the energy of the blast wave by a factor $\sim 2.5$. Interaction with ajump in the ambient density is not consistent with the observed evolution. Weinfer that the boost in energy is from a shell of matter from the explosionthat catches up with the decelerating shock front. Both the high explosionenergy and the nature of the energy input to the blast wave are difficult toreconcile with energy input from the shock-accelerated high velocity ejectafrom a supernova. The implication is that there is irregular energy input froma central engine, which is the type of model invoked for normal $\gamma$-raybursts. The link between SN 1998bw and GRB 980425 is thus strengthened.Comment: 21 pages, 9 figures, revised version to appear in Ap