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2 Ju n 20 01 Gamma-Ray Burst Afterglows with Energy Injection : Homogeneous Versus Wind External Media 0

Assuming an adiabatic evolution of a gamma-ray burst (GRB) fireball interacting with an external medium, we calculate the hydrodynamics of the fireball with 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. Results are given both for a 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. Since the measurement of the redshift of GRB970508, gamma-ray bursts(GRBs) as the cosmological origin are confirmed. [1] Thus, one of the most important issues is the nature of the central engine. The popular theoretical explanation of their radiation properties has been commonly thought to be the fireball model [2] , in which GRBs result from the dissipation of the kinetic energy of the relativistically expanding fireballs. Two main ideas have been proposed to realize the dissipation: the internal and external shock model. In present letter, we will consider the external shock model which reproduces very well the delayed emission at lower energy. A number of afterglows from GRBs have been observed at X-ray, optical and radio wavelengths, whose major features can be explained by simple standard models. [3,4] We consider a newborn millisecond pulsar with a strong magnetic field at the center of the fireball, [5] which may be formed by several models: accretion-induced collapse of magnetized white dwarfs, [6] merge of two neutron stars, [7] and accretion-induced phase transitions of neutron stars to strange stars. [8,9] It has been proposed that very strongly magnetized pulsars may be the central engine of GRBs. [5] It is natural to expect that if a GRB results from the birth of a strongly magnetic millisecond pulsar, then after the main GRB, the