Low-T/|W| instabilities in differentially rotating protoneutron stars with magnetic fields

Recent hydrodynamical simulations have shown that differentially rotating neutron stars formed in core-collapse supernovae may develop global non-axisymmetric instabilities even when T/|W| (the ratio of the rotational kinetic energy T to the gravitational potential energy |W|) is relatively small (less than 0.1). Such low-T/|W| instability can give rise to efficient gravitational wave emission from the protoneutron star. We investigate how this instability is affected by magnetic fields using a cylindrical stellar model. Wave absorption at the corotation resonance plays an important role in facilitating the hydrodynamic low-T/|W| instability. In the presence of a toroidal magnetic field, the corotation resonance is split into two magnetic resonances where wave absorptions take place. We show that the toroidal magnetic field suppresses the low-T/|W| instability when the total magnetic energy, W-B, is of the order of 0.2 T or larger, corresponding to toroidal fields of a few x1016 G or stronger. Although poloidal magnetic fields do not influence the instability directly, they can affect the instability by generating toroidal fields through linear winding of the initial poloidal field and magnetorotational instability. We show that an initial poloidal field with strength as small as 1014 G may suppress the low-T/|W| instability.