4 SN 1998bw and GRB 980425

 

The equivalence of these two events continues to be debated. We believe they were one and the same; indeed the collapsar model predicts every GRB (long enough to trigger Beppo-Sax) should be accompanied by a Type Ib/c supernovae. That the supernova should be as bright as SN 1998bw (which implies an exceptional quantity of ⁵⁶Ni) was not anticipated, but in retrospect is not too surprising. Considerable mass falls into high temperature and is then ejected. It should be clear though that, in SN 1998bw as well as other GRBs, we are dealing with an unusual sort of supernova. Probably 99% of SN Ib/c are made in $3 - 4\, M\hbox{$\odot$}$ helium cores that leave neutron stars and make no GRB. Of the remaining 1%, the vast majority beam their GRB in a direction that is not seen. So one should look for supernovae in GRB error boxes, but not expect GRBs in SN Ib/c boxes.

GRB 980425 was faint because the explosion ejected far less energy in the form of relativistic matter than other GRBs. It takes about 10 s in the collapsar model from iron core collapse until the full development of a very relativistic jet. Moreover, the energy of the jet depends in a very non-linear way on the accretion rate. An accretion rate of $0.05\, M\hbox{$\odot$}\, {\rm s}^{-1}$ produces, in the neutrino model, orders of magnitude less energy than an accretion rate of $0.1 \,M\hbox{$\odot$}\ {\rm s}^{-1}$. Perhaps an energetic jet failed to develop or died before 10 s was up. One would still get a supernova though and high ejection velocities along the rotational axis.

It is also possible that a very energetic jet developed, but, owing to poor collimation properties, was loaded with too much matter to become highly relativistic. Mildly relativistic matter would still be ejected as the jet powered shock wave moved down the density gradient at the surface of the star (McKee & Colgate 1973). A supernova of 10⁵² erg with its initial explosion focused into 10% of the sky would eject about 10²⁵ g of matter having $\Gamma = 5$ (Woosley et al. 1998) in 10% of the sky. Running into circumstellar material at a radius of about $5 \ 10^{12}$ cm, this would produce a GRB that peaked at about 5 s ($t_{\rm peak} =2000\, E_{48} A_{11}^{-1} \Gamma^{-4}$ s for a wind density that fell as 10¹¹ A₁₁ r₁₂^-2 helium nuclei cm^-3; Sari & Piran 1997a,b; Sari 1998, private communication).

At later times, the shock of the jet passage moves around the star and the explosion becomes more symmetric. There is also a lot more matter and energy moving at $\Gamma \sim 1 - 2$ that could contribute to X-ray, radio, and optical afterglows. In summary, in order to produce a supernova like SN 1998bw with kinetic energy well in excess of 10⁵² erg (Iwamoto et al. 1998; Woosley et al. 1998) powered by black hole formation and asymmetric mass ejection, one expects a GRB very much like 970425.

Acknowledgements

We are grateful to Alex Heger, John Danziger, Chris Fryer, Jonathon Katz, Bob Popham, and Re'em Sari for valuable discussions of the collapsar model at the meeting and afterwards. This reasearch was supported by the NSF (AST AST-97-31569), NASA (MIT SC A292701), and by the Humboldt Foundation.