A global model of the magnetorotational instability in protoneutron stars

Abstract

Context. Magnetars are isolated neutron stars characterized by their variable high-energy emission, which is powered by the dissipation of enormous internal magnetic fields. The measured spin-down of magnetars constrains the magnetic dipole to be in the range of 1014 − 1015 G. The magnetorotational instability (MRI) is considered to be a promising mechanism to amplify the magnetic field in fast-rotating protoneutron stars and form magnetars. This scenario is supported by many local studies that have shown that magnetic fields could be amplified by the MRI on small scales. However, the efficiency of the MRI at generating a dipole field is still unknown. Aims. To answer this question, we study the MRI dynamo in an idealized global model of a fast rotating protoneutron star with differential rotation. Methods. Using the pseudo-spectral code MagIC, we performed three-dimensional incompressible magnetohydrodynamics simulations in spherical geometry with explicit diffusivities where the differential rotation is forced at the outer boundary. We performed a parameter study in which we varied the initial magnetic field and investigated different magnetic boundary conditions. These simulations were compared to local shearing box simulations performed with the code Snoopy. Results. We obtain a self-sustained turbulent MRI-driven dynamo, whose saturated state is independent of the initial magnetic field. The MRI generates a strong turbulent magnetic field of B ≥ 2 × 1015 G and a nondominant magnetic dipole, which represents systematically about 5% of the averaged magnetic field strength. Interestingly, this dipole is tilted toward the equatorial plane. By comparing these results with shearing box simulations, we find that local models can reproduce fairly well several characteristics of global MRI turbulence such as the kinetic and magnetic spectra. The turbulence is nonetheless more vigorous in the local models than in the global ones. Moreover, overly large boxes allow for elongated structures to develop without any realistic curvature constraint, which may explain why these models tend to overestimate the field amplification. Conclusions. Overall, our results support the ability of the MRI to form magnetar-like large-scale magnetic fields. They furthermore predict the presence of a stronger small-scale magnetic field. The resulting magnetic field could be important to power outstanding stellar explosions, such as superluminous supernovae and gamma-ray bursts.