Gamma-Ray Burst Afterglows with Energy Injection: Homogeneous Versus Wind External Media

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Abstract
Assuming an adiabatic evolution of a gamma-ray burst (GRB) fireball interacting with an external medium, we calculate the hydrodynamics of the fireball with an energy injection from a strongly magnetic millisecond pulsar through magnetic dipole radiation, and obtain the light curve of the optical afterglow from the fireball by synchrotron radiation. The results are given both for an homogeneous external medium and for a wind ejected by GRB progenitor. Our calculations are also available in both ultra-relativistic and non-relativistic phases. Furthermore, the observed R-band light curve of GRB000301C can be well fitted in our model, which might provide a probe of the properties of GRB progenitors.