Simulations show the low-T/|W| instability develops robustly across five nuclear EOS in a rapidly rotating 35 M⊙ progenitor, with dominant GW frequency correlating to PNS compactness and stiffness.
The intimate relation between the low T/W instability and the co-rotation point
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abstract
We study the low T/W instability associated with the f-mode of differentially rotating stars. Our stellar models are described by a polytropic equation of state and the rotation profile is given by the standard j-constant law. The properties of the relevant oscillation modes, including the instability growth time, are determined from time evolutions of the linearised dynamical equations in Newtonian gravity. In order to analyse the instability we monitor also the canonical energy and angular momentum. Our results demonstrate that the l=m=2 f-mode becomes unstable as soon as a co-rotation point develops inside the star (i.e. whenever there is a point where the mode's pattern speed matches the bulk angular velocity). Considering various degrees of differential rotation, we show that the instability grows faster deep inside the co-rotation region and deduce an empirical relation that correlates the mode frequency and the star's parameters, which captures the main features of the l=m=2 f-mode growth time. This function is proportional to the product of the kinetic to gravitational energy ratio and the gradient of the star's spin, strengthening further the relationship between the co-rotation point and the low T/W instability. We briefly consider also the l=m=2 r-mode and demonstrate that it never moves far inside the co-rotation region even for significant differential rotation.
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Numerical post-merger waveforms indicate that planned 3rd-generation GW detector networks can detect rotational instabilities in BNS remnants at distances up to 200 Mpc with a high-frequency design, and the main post-merger peak at 40 Mpc with upgraded HLV.
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Impact of the equation of state on core collapse supernovae I: the low-$T/|W|$ instability
Simulations show the low-T/|W| instability develops robustly across five nuclear EOS in a rapidly rotating 35 M⊙ progenitor, with dominant GW frequency correlating to PNS compactness and stiffness.
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Exploring the Potential for Detecting Rotational Instabilities in Binary Neutron Star Merger Remnants with Gravitational Wave Detectors
Numerical post-merger waveforms indicate that planned 3rd-generation GW detector networks can detect rotational instabilities in BNS remnants at distances up to 200 Mpc with a high-frequency design, and the main post-merger peak at 40 Mpc with upgraded HLV.