Long duration gamma-ray bursts (GRBs) originate from the core collapse of massive stars, but the identity of the central engine remains elusive. Previous work has shown that rapidly spinning, strongly magnetized protoneutron stars (‘millisecond protomagnetars’) produce outflows with energies, time-scales and magnetizations σ0 (maximum Lorentz factor) that are consistent with those required to produce long duration GRBs. Here we extend this work in order to construct a self-consistent model that directly connects the properties of the central engine to the observed prompt emission. Just after the launch of the supernova shock, a wind heated by neutrinos is driven from the protomagnetar. The outflow is collimated into a bipolar jet by its interaction with the progenitor star. As the magnetar cools, the wind becomes ultrarelativistic and Poynting flux dominated (σ0≫ 1) on a time-scale comparable to that required for the jet to clear a cavity through the star. Although the site and mechanism of the prompt emission are debated, we calculate the emission predicted by two models: magnetic dissipation and shocks.
Magnetic reconnection may occur near the photosphere if the outflow develops an alternating field structure due to e.g. magnetic instabilities or a misalignment between the magnetic and rotation axes. Shocks may occur at larger radii because the Lorentz factor of the wind increases with time, such that the faster jet at late times collides with slower material released earlier. Our results favour magnetic dissipation as the prompt emission mechanism, in part because it predicts a relatively constant ‘Band’ spectral peak energy Epeak with time during the GRB. The baryon loading of the jet decreases abruptly when the neutron star becomes transparent to neutrinos at s. Jets with ultrahigh magnetization cannot effectively accelerate and dissipate their energy, which suggests this transition ends the prompt emission. This correspondence may explain both the typical durations of long GRBs and the steep decay phase that follows. Residual rotational or magnetic energy may continue to power late time flaring or afterglow emission, such as the X-ray plateau. We quantify the emission predicted from protomagnetars with a wide range of physical properties (initial rotation period, surface dipole field strength and magnetic obliquity) and assess a variety of phenomena potentially related to magnetar birth, including low-luminosity GRBs, very luminous GRBs, thermal-rich GRBs/X-ray flashes, very luminous supernovae and short-duration GRBs with extended emission.