Constraints on millisecond magnetars as the engines of prompt emission in gamma-ray bursts

We examine millisecond magnetars as central engines of gamma-ray bursts' (GRBs) prompt emission. Using the protomagnetar wind model of Metzger et al., we estimate the temporal evolution of the magnetization and power injection at the base of the GRB jet and apply these to different prompt emission models to make predictions for the GRB energetics, spectra and light curves. We investigate both shock and magnetic reconnection models for the particle acceleration, as well as the effects of energy dissipation across optically thick and thin regions of the jet. The magnetization at the base of the jet, σ₀, is the main parameter driving the GRB evolution in the magnetar model and the emission is typically released for 100 ≲σ₀ ≲3000. Given the rapid increase in σ₀ as the protomagnetar cools and its neutrino-driven mass loss subsides, the GRB duration is typically limited to ≲100 s. This low baryon loading at late times challenges magnetar models for ultralong GRBs, though black hole models likely run into similar difficulties without substantial entrainment from the jet walls. The maximum radiated gamma-ray energy is ≲5 × 10⁵¹ erg, significantly less than the magnetar's total initial rotational energy and in strong tension with the high end of the observed GRB energy distribution. However, the gradual magnetic dissipation model applied to a magnetar central engine, naturally explains several key observables of typical GRBs, including energetics, durations, stable peak energies, spectral slopes and a hard to soft evolution during the burst.