Constraining the environment of compact binary mergers with self-lensing signatures

TL;DR

This paper investigates how gravitational self-lensing signatures in gravitational wave signals can reveal the environments of binary black hole mergers, analyzing probabilities and detectability across different astrophysical settings.

Contribution

It quantifies the likelihood of self-lensing effects in various environments and assesses their detectability with current and future gravitational wave detectors.

Findings

Low probability of self-lensing in star clusters

Detectability of lensing imprints is limited for stellar-mass lenses

Higher probability and detectable signals from supermassive black hole lenses

Abstract

Gravitational waves (GWs) from coalescing binary black holes (BBHs) can come from different environments. GWs interact gravitationally with astrophysical objects, which makes it possible to use gravitational lensing by objects in the same gravitational system (self-lensing) to learn about their environments. We quantify the probability of self-lensing through the optical depth $\tau$ for the main channels of detectable GWs at frequencies $f_{\rm GW}\sim (1-10^3)\,{\rm Hz}$. We then analyze the detectability of the lensing effect (imprint). In star clusters, the probability of self-lensing by stellar-mass black holes (BHs) is low, $\tau\simeq10^{-7}$, even when taking into account nearby BHs in resonant interactions, $\tau\simeq 10^{-5}$. Additionally, the lensing imprint of a stellar-mass lens (diffraction and interference) is too marginal to be detectable by the LIGO-Virgo-KAGRA detectors and most Einstein Telescope signals. For a massive BH lens in the center of a cluster, the probability can reach $\tau\simeq 10^{-4}$ either via von Zeipel-Lidov-Kozai induced mergers of BBHs orbiting a central massive BH, or BBHs formed as GW captures in single-single interactions in the Bahcall-Wolf cusp of a nuclear cluster. For self-lensing by a supermassive BH for BBHs in the migration trap of an active galactic nucleus (AGN) disk, $\tau \simeq 10^{-2}$. The imprint of these massive lenses are multiple images that are already detectable. Moreover, self-lensed signals from AGN disks have a distinct linear polarization. The probability depends on the extent of the detectability through the threshold impact parameter $y_{\rm max}$, which can increase for future detectors. We conclude that constraining the environment of BBHs is possible by combining self-lensing imprints with other waveform signatures such as eccentricity and polarization.