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

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 $W_{\mathrm{B}}$ is of order $0.2T$ 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.

arXiv comment12 pages, 6 figures; submitted to MNRAS

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• An Optically Targeted Search for Gravitational Waves emitted by Core-Collapse Supernovae during the First and Second Observing Runs of Advanced LIGO and Advanced Virgo
• The One-Armed Spiral Instability in Neutron Star Mergers and its Detectability in Gravitational Waves
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• Astrophysical science metrics for next-generation gravitational-wave detectors
• Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars
• Insights into non-axisymmetric instabilities in three-dimensional rotating supernova models with neutrino and gravitational-wave signatures
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• Dynamics of the Innermost Accretion Flows Around Compact Objects: Magnetosphere-Disc Interface, Global Oscillations and Instabilities
• Magnetized stars with differential rotation and a differential toroidal field
• Properties of rapidly rotating hot neutron stars within Brueckner theory