The early evolution of magnetar rotation -- II. Rapidly rotating magnetars: Implications for Gamma-Ray Bursts and Super Luminous Supernovae

Abstract: Rapidly rotating magnetars have been associated with gamma-ray bursts (GRBs) and super-luminous supernovae (SLSNe). Using a suite of 2D magnetohydrodynamic simulations at fixed neutrino luminosity and a couple of evolutionary models with evolving neutrino luminosity and magnetar spin period, we show that magnetars are viable central engines for powering GRBs and SLSNe. We also present analytic estimates of the energy outflow rate from the proto-neutron star (PNS) as a function of polar magnetic field strength $B_0$, PNS angular velocity $\Omega_{\star}$, PNS radius $R_{\star}$ and mass outflow rate $\dot{M}$. We show that rapidly rotating magnetars with spin periods $P_{\star}\lesssim 4$ ms and polar magnetic field strength $B_0\gtrsim 10^{15}$ G can release $10^{50}-5\times 10^{51}$ ergs of energy during the first $\sim2$ s of the cooling phase. Based on this result, it is plausible that sustained energy injection by magnetars through the relativistic wind phase can power GRBs. We also show that magnetars with moderate field strengths of $B_0\lesssim 5\times 10^{14}$ G do not release a large fraction of their rotational kinetic energy during the cooling phase and hence, are not likely to power GRBs. Although we cannot simulate to times greater than $\sim 3-5$ s after a supernova, we can hypothesize that moderate field strength magnetars can brighten the supernova light curves by releasing their rotational kinetic energy via magnetic dipole radiation on timescales of days to weeks, since these do not expend most of their rotational kinetic energy during the early cooling phase.