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Gamma-ray burst afterglows and evolution of postburst fireballs with energy injection from strongly magnetic millisecond pulsars

Millisecond pulsars with strong magnetic fields may be formed through several processes, e.g. accretion-induced collapse of magnetized white dwarfs, merger of two neutron stars, and accretion-induced phase transitions of neutron stars. During the birth of such a pulsar, an initial fireball available for a gamma-ray burst (GRB) may occur. We here study evolution of a postburst relativistic fireball with energy injection from the pulsar through magnetic dipole radiation, and find that the magnitude of the optical afterglow from this fireball first decreases with time, subsequently flattens, and finally declines again. This may provide a natural explanation for the behavior of the lightcurve of the afterglow of GRB970228 if this burst resulted from the birth of a strongly magnetic millisecond pulsar.