Short Duration Gamma-Ray Bursts with Extended Emission from Proto-Magnetar 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 ``proto-magnetar'') 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 onto the proto-magnetar from a small disk 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 proto-magnetar on a timescale ~10-100 s. The ~3-10 s delay between the prompt and extended emission is the time required for the newly-formed proto-magnetar to cool sufficiently that the neutrino-heated wind from its surface becomes ultra-relativistic. Because a proto-magnetar ejects little or no Ni56 (< 1e-3 M_sun), these events should not produce a bright SN-like transient. We model the extended emission from GRB060614 using spin-down calculations of a cooling proto-magnetar, finding reasonable agreement with observations for a magnetar with an initial rotation period of ~1 ms and a surface dipole field of ~3e15 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.