Low-$T/|W|$ instabilities in differentially rotating proto-neutron stars with magnetic fields

TL;DR

This study explores how magnetic fields influence low-$T/|W|$ instabilities in differentially rotating proto-neutron stars, revealing that strong toroidal and poloidal fields can suppress these instabilities, affecting gravitational wave emission.

Contribution

It demonstrates the impact of magnetic fields, especially toroidal and poloidal, on the suppression of low-$T/|W|$ instabilities in proto-neutron stars, extending understanding of magnetic effects in stellar dynamics.

Findings

Toroidal magnetic fields suppress the instability when $W_B \,\sim\, 0.2 T$ or larger.

Poloidal magnetic fields as small as $10^{14}$ G can suppress the instability.

Wave absorption at magnetic resonances influences the development of the instability.

Abstract

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 proto-neutron 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 $W_{\rm B}$ is of order $0.2\,T$ or larger, corresponding to toroidal fields of a few $\times 10^{16}$ 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 magneto-rotational instability. We show that an initial poloidal field with strength as small as $10^{14}$ G may suppress the low-$T/|W|$ instability.