TIDAL AND TIDAL-RESONANT EFFECTS IN COALESCING BINARIES

TL;DR

This paper investigates tidal and tidal-resonant effects in coalescing compact binaries by directly integrating the full equations of motion, including orbital dynamics, stellar oscillations, tidal coupling, and radiation reaction, for polytropic neutron-star models. It shows that energy transfer is dominated by non-resonant $f$-modes, with $g$-mode resonances possible but generally subdominant, and that resonant coupling occurs mainly at late inspiral when the mode frequencies become commensurate with the orbital frequency. The gravitational-wave phasing accumulates large dephasings in the 100--1000 Hz window, reaching about $21\pi$ for certain models and $14\pi$ for others, with roughly 90% of the total phase difference generated in the final inspiral. These tidal effects can even drive a tidally induced plunge without radiation reaction, underscoring the importance of extended-body waveform templates for accurate parameter estimation and inference of neutron-star radii and compactness.

Abstract

Tidal and tidal-resonant effects in coalescing compact binary systems are investigated by direct numerical integration of the equations of motion. For the stars polytropic models are used. The tidal effects are found to be dominated by the (non-resonant) $f$-modes. The effect of the $g$-mode-tidal resonances is obtained. The tidal interaction is shown to be of interest especially for low-mass binaries. There exists a characteristic final plunge orbit beyond which the system cannot remain stable even if radiation reaction is not taken into account; in agreement with results obtained by Lai et al. \shortcite{Lai93}. The importance of the investigated effects for the observation of gravitational waves on Earth is discussed.