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Dynamical instabilities in protoneutron stars may produce gravitational waveswhose observation could shed light on the physics of core-collapse supernovae.When born with sufficient differential rotation, these stars are susceptible toa shear instability (the "low-T/|W| instability"), but such rotation can alsoamplify magnetic fields to strengths where they have a considerable impact onthe dynamics of the stellar matter. Using a new magnetohydrodynamics module forthe Spectral Einstein Code, we have simulated a differentially-rotating neutronstar in full 3D to study the effects of magnetic fields on this instability.Though strong toroidal fields were predicted to suppress the low-T/|W|instability, we find that they do so only in a small range of field strengths.Below 4e13 G, poloidal seed fields do not wind up fast enough to have an effectbefore the instability saturates, while above 5e14 G, magnetic instabilitiescan actually amplify a global quadrupole mode (this threshold may be even lowerin reality, as small-scale magnetic instabilities remain difficult to resolvenumerically). Thus, the prospects for observing gravitational waves from suchsystems are not in fact diminished over most of the magnetic parameter space.  Additionally, we report that the detailed development of the low-T/|W|instability, including its growth rate, depends strongly on the particularnumerical methods used. The high-order methods we employ suggest that growthmight be considerably slower than found in some previous simulations.

Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars