Non-linear evolution of the elliptical instability in the presence of weak magnetic fields

We investigate whether the elliptical instability is important for tidal dissipation in gaseous planets and stars. In a companion paper, we found that the conventional elliptical instability results in insufficient dissipation because it produces long-lived vortices that then quench further instability. Here, we study whether the addition of a magnetic field prevents those vortices from forming, and hence leads to enhanced dissipation. We present results from magnetohydrodynamic simulations that evolve the elliptical instability in a local patch of a rotating planet or star, in the presence of a weak magnetic field.We find that magnetic fields do indeed prevent vortices from forming, and hence greatly enhance the steady-state dissipation rate. In addition, the resulting turbulence acts as a small-scale dynamo, amplifying the initially weak field. The inferred tidal dissipation is potentially important at short orbital periods. For example, it can circularize hot Jupiters with orbital periods shorter than 2.5 d and synchronize their spins with their orbits out to 6 d. However, it appears unable to account for the hot Jupiters that appear to have been circularized out to 6-10 d orbital periods. It also cannot account for the inferred circularization of many close binary stars.