Short-duration gamma-ray bursts with extended emission from protomagnetar spin-down

Evidence is growing for a class of gamma-ray bursts (GRBs) characterized by an initial ~0.1-1 s spike of hard radiation followed, after a ~3-10 s lull in emission, by a softer period of extended emission lasting ~10-100 s. In a few well-studied cases, these `short GRBs with extended emission' show no evidence for a bright associated supernova (SN). We propose that these events are produced by the formation and early evolution of a highly magnetized, rapidly rotating neutron star (a `protomagnetar') which is formed from the accretion-induced collapse (AIC) of a white dwarf (WD), the merger and collapse of a WD-WD binary or perhaps, the merger of a double neutron star binary. The initial emission spike is powered by accretion on to the protomagnetar from a small disc that is formed during the AIC or merger event. The extended emission is produced by a relativistic wind that extracts the rotational energy of the protomagnetar on a time-scale ~10-100 s. The ~10 s delay between the prompt and extended emission is the time required for the newly formed protomagnetar to cool sufficiently that the neutrino-heated wind from its surface becomes ultrarelativistic. Because a protomagnetar ejects little or no⁵⁶Ni (< 10^-3M_solar), these events should not produce a bright SN-like transient. We model the extended emission from GRB060614 using spin-down calculations of a cooling protomagnetar, finding reasonable agreement with observations for a magnetar with an initial rotation period of ~1 ms and a surface dipole field of ~3 × 10¹⁵ G. If GRBs are indeed produced by AIC or WD-WD mergers, they should occur within a mixture of both early- and late-type galaxies and should not produce strong gravitational wave emission. An additional consequence of our model is the existence of X-ray flashes unaccompanied by a bright SN and not associated with massive star formation.