Gravitational wave interactions with a viscous fluid: Core collapse supernova, binary neutron star merger, and accretion around a black hole merger

TL;DR

This paper extends the study of gravitational-wave interactions with matter by moving from Minkowski (and Schwarzschild) backgrounds to a general static, non-vacuum, spherically symmetric spacetime. It develops a numerical framework within the Bondi-Sachs formalism to compute GW damping and viscous heating in a multi-layer fluid shell, capturing how a background curvature enhances energy transfer via the shear viscosity. Applied to core-collapse supernovae, post-merger binary neutron stars, and accretion around binary black hole mergers, the results show damping and heating can be orders of magnitude larger than in flat space, with possible complete damping and heating strong enough to influence thermal and potentially electromagnetic outcomes. The study highlights the importance of more realistic backgrounds and calls for future work using numerical relativity and Kerr geometries to refine the estimates and assess observational consequences.

Abstract

The interaction of gravitational waves (GWs) with matter is normally treated as being insignificant. However, recent work has shown that the interaction with a viscous fluid may be astrophysically important when the distance between the matter and GW source is somewhat smaller than the GW wavelength. Previous work has mainly considered perturbations on a Minkowski background, and here these results are extended to the case that the background is a general, non-vacuum, static, spherically symmetric spacetime. Expressions are obtained for GW damping and the consequent heating of the fluid, and implemented in computer code. The results are applied to astrophysical scenarios: Core collapse supernovae, the post-merger signal from a binary neutron star merger, and matter accreting at a binary black hole merger. It is found that, compared to the Minkowski case, the damping and heating effects increase, in some cases by several orders of magnitude. It is possible for a GW signal to be completely damped, and for the heating to be such that a gamma-ray burst occurs.

Figures (5)

• Figure 1: Errors in background quantities when the Schwarzschild interior solution applies.
• Figure 2: Comparisons between the Schwarzschild code and the matter code with negligible density shell. The parameter $\nu=0.1355$, corresponding to a frequency of $72.5$Hz when $M=60M_\odot$. The left panel plots on a $\log_{10}$ scale the differences between the metric quantities indicated for the two codes. The right panel plots $\log_{10}(f_E)$ as calculated by the two codes as well as in the Minkowski background case (Eq. \ref{['e-fEM']}).
• Figure 3: H damp (left) and $\log_{10}(\Delta T)$ (K) (right) plotted against distance (km) for the CCSN model.
• Figure 4: H damp (left) and $\log_{10}(\Delta T)$ (K) (right) plotted against distance (km) for the BNS post-merger model.
• Figure 5: $\log_{10}(\Delta T)$ (K) plotted against radial distance (km) for the model of an accretion disk around merging black holes. Plots for both the Schwarzschild background and Minkowski background codes are shown, at both the equator ($\theta=\pi/2$) and the poles ($\theta=0,\pi$)