Magnetar spin-down, hyperenergetic supernovae, and gamma-ray bursts

The Kelvin-Helmholtz cooling epoch, lasting tens of seconds after the birth of a neutron star in a successful core-collapse supernova, is accompanied by a neutrino-driven wind. For magnetar-strength (∼10¹⁵ G) large-scale surface magnetic fields, this outflow is magnetically dominated during the entire cooling epoch. Because the strong magnetic field forces the wind to corotate with the proto-neutron star, this outflow can significantly affect the neutron star's early angular momentum evolution, as in analogous models of stellar winds. If the rotational energy is large in comparison with the supernova energy and the spin-down timescale is short with respect to the time required for the supernova shock wave to traverse the stellar progenitor, the energy extracted may modify the supernova shock dynamics significantly. This effect is capable of producing hyperenergetic supernovae and, in some cases, provides conditions favorable for gamma-ray bursts. We estimate spin-down timescales for magnetized, rotating proto-neutron stars and construct steady state models of neutrino-magnetocentrifugally driven winds. We find that if magnetars are born rapidly rotating, with initial spin periods (P) of ∼1 ms, then of order 10⁵¹-10⁵² ergs of rotational energy can be extracted in ∼10 s. If magnetars are born slowly rotating (P ≳ 10 ms), they can spin down to periods of ∼1 s on the Kelvin-Helmholtz timescale.