Second-type self-similar solutions to the ultrarelativistic strong explosion problem

The well-known Blandford-McKee solution describes the ultrarelativistic flo w in a spherical blast wave enclosed by a strong shock. It is valid when th e density of the external medium into which the shock propagates varies wit h the distance r from the origin as r(-k), for k < 4. These are first-type self-similar solutions in which the shock Lorentz factor Gamma varies as Ga mma(2)proportional to t(-m), where m=3-k to ensure energy conservation. New second-type self-similar solutions, valid for k > 5-root 3/4 approximate t o 4.13, are presented. In these solutions Gamma varies as Gamma(2)proportio nal to t(-m) with m=(3-2 root 3)k-4(5-3 root 3) so that the shock accelerat es and the fraction of the flow energy contained in the vicinity of the sho ck decreases with time. The new solutions are shown to be in excellent agre ement with numerical simulations of the flow equations. It is proved that n o second-type self-similar solutions exist for k < 5-root 3/4 approximate t o 4.13. (C) 2000 American Institute of Physics. [S1070-6631(00)02906-8].