Jets, Structured Outflows, and Energy Injection in GRB Afterglows: Numerical Modelling

We investigate numerically the ability of three models (jet, structured outflow, energy injection) to accommodate the optical light-curve breaks observed in 10 GRB afterglows (980519, 990123, 990510, 991216, 000301c, 000926, 010222, 011211, 020813, and 030226), and the relative intensities of the radio, optical, and X-ray emissions of these afterglows. We find that the jet and structured outflow models fare much better than the energy injection model in accommodating the multiwavelength data of the above 10 afterglows. For the first two models, a uniform circumburst medium provides a better fit to the optical light-curve break than a wind-like medium with a r^{-2} stratification. However, in the only two cases where the energy injection model may be at work, a wind medium is favoured (an energy injection is also possible in a third case, the afterglow 970508, whose optical emission exhibited a sharp rise but not a steepening decay). The best fit parameters obtained with the jet model indicate an outflow energy of 2-6 E50 ergs and a jet opening of 2-3 degrees. Structured outflows with a quasi-uniform core have a core angular size of 0.7-1.0 degrees and an energy per solid angle of 0.5-3 E53 erg/sr, surrounded by an envelope where this energy falls-off roughly as theta^{-2} with angle from the outflow axis, requiring thus the same energy budget as jets. Circumburst densities are found to be typically in the range 0.1-1 per cc, for either model. We also find that the reverse shock emission resulting from the injection of ejecta into the decelerating blast wave at about 1 day after the burst can explain the slowly decaying radio light-curves observed for the afterglows 990123, 991216, and 010222.