GRB Afterglows with Energy Injection from a spinning down NS

Aims. We investigate a model for the shallow decay phases of Gammaray Burst (GRB) afterglows discovered by Swift /XRT in the first hours following a GRB event. In the context of the firebal l scenario, we consider the possibility that long-lived ene rgy injection from a millisecond spinning, ultramagnetic neutron star (m agnetar) powers afterglow emission during this phase. Methods. We consider the energy evolution in a relativistic shock sub ject to both radiative losses and energy injection from a spi nning down magnetar in spherical symmetry. We model the energy inj ection term through magnetic dipole losses and discuss an ap proximate treatment for the dynamical evolution of the blastwave. We o btain an analytic solution for the energy evolution in the sh ock and associated lightcurves. To fully illustrate the potential of our solution we calculate lightcurves for a few selected X -ray afterglows observed by Swift and fit them using our theoretical lightcur ves. Results. Our solution naturally describes in a single picture the pro pe ties of the shallow decay phase and the transition to the s ocalled normal decay phase. In particular, we obtain remarka bly good fits to X-ray afterglows for plausible parameters of the magnetar. Even though approximate, our treatment provides a step forw ard ith respect to previously adopted approximations and p rovides additional support to the idea that a millisecond spinning ( 1-3 ms), ultramagnetic (B ∼ 1014− 1015 G) neutron star loosing spin energy through magnetic dipole radiation can explain the luminosi ty, durations and shapes of X-ray GRB afterglows.