Suppression of composition $g$-modes in chemically-equilibrating warm neutron stars

TL;DR

This work analyzes how finite-temperature chemical equilibration and the resulting bulk viscosity affect non-radial oscillations in warm neutron stars, focusing on composition-driven $g$-modes whose frequencies can be resonantly damped when beta-relaxation rates $ extgamma$ match mode frequencies $ extomega$. The authors introduce the dynamical sound speed $c_{ m dy}^2$, a complex, frequency-dependent quantity that encapsulates both the restoring forces and dissipative effects of bulk viscosity, and compute complex mode frequencies using microphysical Urca reaction rates across three EOSs. They find that bulk viscosity becomes increasingly important with temperature, potentially suppressing $g$-modes, while the $f$-mode remains largely insensitive to these dissipative effects. The results underscore the sensitivity of $g$-mode behavior to thermal structure, weak reaction rates, and the EOS, and establish $c_{ m dy}^2$ as a useful descriptor for dissipative neutron-star matter in oscillation analyses. These insights have implications for the gravitational-wave signatures from protoneutron stars and post-merger remnants where MeV-scale temperatures prevail.

Abstract

We investigate the impact of chemical equilibration and the resulting bulk viscosity on non-radial oscillation modes of warm neutron stars at temperatures up to $T\approx 5$ MeV, relevant for protoneutron stars and neutron-star post-merger remnants. In this regime, the relaxation rate of weak interactions becomes comparable to the characteristic frequencies of composition $g$-modes in the core, resulting in resonant damping. To capture this effect, we introduce the dynamical sound speed, a complex, frequency-dependent generalization of the adiabatic sound speed that encodes both the restoring force and the dissipative effects of bulk compression. Using realistic weak reaction rates and three representative equations of state, we compute the complex frequencies of composition $g$-modes with finite-temperature profiles. We find that bulk viscous damping becomes increasingly significant with temperature and can completely suppress composition $g$-modes. In contrast, the $f$-mode remains largely unaffected by bulk viscosity due to its nearly divergence-free character. Our results highlight the sensitivity of $g$-mode behavior to thermal structure, weak reaction rates, and the equation of state, and establish the dynamical sound speed as a valuable descriptor characterizing oscillation properties in dissipative neutron star matter.

Figures (14)

• Figure 1: Left (main) panel shows the beta equilibration relaxation rate $\gamma$ defined in Eq. (\ref{['eq:gamma_def']}) for QMC-RMF3, IUFSU and IOPB-I EOSs at temperatures $T=1$ MeV (dot-dashed) and $T=3$ MeV (dashed). The solid (dashed) lines in the top right panel represent the $g$-mode ($f$-mode) frequency of cold NSs with various central baryon densities $n_{\rm B}^c$. The sharp jump in the rate is due to the onset of the direct Urca threshold.
• Figure 2: Real (left panels) and imaginary (right panels) part of the dynamical sound speed squared for the QMC-RMF3 EOS. For the real part, the equilibrium sound speed squared is used as a reference. The black dashed line represents the difference between adiabatic and equilibrium squared sound speeds. The upper two panels correspond to fixed temperature $T=5$ MeV while varying frequency $\omega= [200,400,1000,2000]$ s$^{-1}$; the bottom two panels represent fixed frequency $\omega=1000$ s$^{-1}$ while varying temperature from 3 to 7 MeV. Note the different scales of y-axes in real and imaginary parts.
• Figure 3: Same as Fig. \ref{['fig:cs2dy']}, but for the IOPB-I EOS.
• Figure 4: The dashed contour shows the maximum (across all densities) of the imaginary part of the dynamical sound speed squared for QMC-RMF3 (top) and IOPB-I (bottom). The dark blue region corresponds to the resonant peak, where bulk viscosity is most effective at damping oscillations. The horizontal brown and red bands represent typical $f$-mode and $g_1$-mode frequencies (at zero temperature) for NSs of various masses, with the central line corresponding to a 1.4 ${\rm M}_{\odot}$ NS.
• Figure 5: Real and imaginary parts of the frequencies of the fundamental and the first three overtone $g$-modes for a $1.4~{\rm M}_{\odot}$ neutron star versus varying temperature for the QMC-RMF3 EOS. The imaginary part of the full GR calculation (dotted) largely overlaps with that of the calculation with Cowling approximation (dashed), and the real parts of the full GR calculation (dash-dotted) and Cowling approximation (solid) are also very similar. We define the ordering of $g$-modes by their smooth asymptotic eigenmode at zero temperature.