Fisher Forecast of Finite-Size Effects with Future Gravitational Wave Detectors

We use Fisher information theory to forecast the bounds on the finite-size effects of astrophysical compact objects with next-generation gravitational wave detectors, including the ground-based Cosmic Explorer (CE) and Einstein Telescope (ET), as well as the space-based Laser Interferomet Space Antenna (LISA). Exploiting the worldline effective field theory (EFT) formalism, we first characterize three types of quadrupole finite-size effects: the spin-induced quadrupole moments, the conservative tidal deformations, and the tidal heating. We then derive the corresponding contributions to the gravitational waveform phases for binary compact objects in aligned-spin quasi-circular orbits. We separately estimate the constraints on these finite-size effects for black holes using the power spectral densities (PSDs) of the CE+ET detector network and LISA observations. For the CE+ET network, we find that the bounds on the mass-weighted spin-independent dissipation number $H_0$ are of the order $O(1)$, while the bounds on the mass-weighted tidal Love number $\tilde{\Lambda}$ are of the order $O(10)$. For high-spin binary black holes with dimensionless spin $\chi \simeq 0.8$, the bounds on the symmetric spin-induced quadrupole moment $\kappa_s$ are of the order $O(10^{-1})$. LISA observations of supermassive black hole mergers offer slightly tighter constraints on all three finite-size parameters. Additionally, we perform a Fisher analysis for a binary neutron star merger within the CE+ET network. The bounds on the tidal parameter $H_0$ and on $\tilde \Lambda$ are around two orders of magnitude better than the current LIGO-Virgo-KAGRA (LVK) bounds.