The First Day in the Life of a Magnetar: Evolution of the Inclination Angle, Magnetic Dipole Moment and Braking Index of Millisecond Magnetars During Gamma-Ray Burst Afterglows

Abstract

The afterglow emission of some gamma-ray bursts (GRBs) show a shallow decay (plateau) phase implying continuous injection of energy. The source of this energy is very commonly attributed to the spin-down power of a nascent millisecond magnetar. The magnetic dipole radiation torque is considered to be the mechanism causing the spin-down of the neutron star. This torque has a component working for the alignment of the angle between rotation and magnetic axis, i.e., inclination angle, which has been neglected in modelling GRB afterglow light curves. Here, we demonstrate the evolution of the inclination angle and magnetic dipole moment of nascent magnetars associated with GRBs. We constrain the initial inclination angle, magnetic dipole moment and rotation period of seven magnetars by modelling the seven long-GRB afterglow light curves. We find that, in its first day, the inclination angle of a magnetar decreases rapidly. The rapid alignment of the magnetic and rotation axis may address the lack of persistent radio emission from mature magnetars. We also find that in three cases the magnetic dipole moments of magnetars decrease exponentially to a value a few times smaller than the initial value. The braking index of nascent magnetars, as a result of the alignment and magnetic dipole moment decline, is variable during the afterglow phase and always greater than three.