A general framework for incorporating arbitrary nonequilibrium corrections into linear non-radial relativistic stellar perturbations without specifying constitutive relations.
Radial Oscillations of Viscous Stars
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abstract
Oscillation modes of neutron stars, a key target for third-generation gravitational wave detectors, encode key information about their constituent nuclear matter. In this work, we study the effect of viscosity on oscillations of cold, polytropic, spherically symmetric neutron stars. We focus on purely radial oscillations and work perturbatively to linear order within two hydrodynamic frameworks: the acausal covariant generalization of the Navier-Stokes equations proposed by Eckart, and the causal generalization formulated by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). We find that viscosity damps the radial modes on millisecond timescales and induces fractional shifts in the oscillation frequency which increase both with the compactness and viscosity of the star, reaching up to the percent level for the fundamental mode with bulk viscosities $\zeta\sim10^{30}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. For more viscous stars, the oscillation frequency decreases, becoming zero (i.e., an overdamped mode) for $\zeta\gtrsim10^{31}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. We also study the linear threshold of gravitational collapse. Consistent with recent analytic results in the zero heat conductivity limit, we find that viscosity in Eckart theory cannot stabilize an unstable inviscid star. We provide numerical evidence that viscosity in BDNK theory is similarly unable to prevent gravitational collapse, but it slightly modifies the threshold of collapse. Overall, our results advance our understanding of the impact of viscosity on the oscillation modes of neutron stars, a key component of viscous asteroseismology with next-generation gravitational wave detectors.
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Heat diffusion introduces a distinct thermal mode sector in viscous star oscillations that transitions to propagating behavior above a critical overtone, realizing finite-size relativistic second sound.
Causal viscous relativistic hydrodynamics applied to neutron stars yields new axial mode families without perfect-fluid counterparts, including mode avoidance and long-lived modes.
A finite-volume scheme for causal viscoresistive relativistic MHD is developed with an extra correction needed in the ultra-relativistic limit, plus a primitive recovery method validated on benchmarks and 2D simulations.
citing papers explorer
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Out-of-Equilibrium Effects in Non-Radial Relativistic Stellar Perturbations: A Model-Agnostic Formulation and Mode Analysis
A general framework for incorporating arbitrary nonequilibrium corrections into linear non-radial relativistic stellar perturbations without specifying constitutive relations.
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Radial Oscillations of Viscous Stars at Finite Temperature
Heat diffusion introduces a distinct thermal mode sector in viscous star oscillations that transitions to propagating behavior above a critical overtone, realizing finite-size relativistic second sound.
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Axial Oscillations of Viscous Neutron Stars
Causal viscous relativistic hydrodynamics applied to neutron stars yields new axial mode families without perfect-fluid counterparts, including mode avoidance and long-lived modes.
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Finite-volume scheme for first-order viscoresistive relativistic magnetohydrodynamics
A finite-volume scheme for causal viscoresistive relativistic MHD is developed with an extra correction needed in the ultra-relativistic limit, plus a primitive recovery method validated on benchmarks and 2D simulations.