The early evolution of magnetar rotation - II. Rapidly rotating magnetars: implications for gamma-ray bursts and superluminous supernovae

Rapidly rotating magnetars have been associated with gamma-ray bursts (GRBs) and superluminous supernovae (SLSNe). Using a suite of two-dimensional 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 analytical 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 (M)over dot. We show that rapidly rotating magnetars with spin periods P-star less than or similar to 4 ms and polar magnetic field strength B-0 greater than or similar to 10(15) G can release 10(50) to 5 x 10(51) erg of energy during the first similar to 2 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 less than or similar to 5 x 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 similar to 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 time-scales of days to weeks, since these do not expend most of their rotational kinetic energy during the early cooling phase.