A multi-parameter expansion for the evolution of asymmetric binaries in astrophysical environments

TL;DR

This work develops a two-parameter perturbative framework to model the evolution and gravitational-wave emission of highly asymmetric binaries embedded in general, low-density matter environments. By expanding around the Schwarzschild spacetime in the small parameters $q$ (mass ratio) and $\epsilon$ (environmental density relative to the BH), the authors derive axial and polar perturbation equations that closely resemble the vacuum Regge–Wheeler and Zerilli formalisms, augmented by matter-source terms. The approach yields master equations for both vacuum-like and matter-coupled perturbations, provides explicit pathways to reconstruct metric and fluid perturbations, and delivers GW flux formulas that include environmental contributions. This semi-analytical framework enables realistic waveform modeling for EMRIs/IMRIs in astrophysical environments, with potential applications for LISA and multi-messenger studies, while outlining clear directions to extend to spinning primaries and more complex fluids.

Abstract

Compact binaries with large mass asymmetries - such as Extreme and Intermediate Mass Ratio Inspirals - are unique probes of the astrophysical environments in which they evolve. Their long-lived and intricate dynamics allow for precise inference of source properties, provided waveform models are accurate enough to capture the full complexity of their orbital evolution. In this work, we develop a multi-parameter formalism, inspired by vacuum perturbation theory, to model asymmetric binaries embedded in general matter distributions with both radial and tangential pressures. In the regime of small deviations from the Schwarzschild metric, relevant to most astrophysical scenarios, the system admits a simplified description, where both metric and fluid perturbations can be cast into wave equations closely related to those of the vacuum case. This framework offers a practical approach to modeling the dynamics and the gravitational wave emission from binaries in realistic matter distributions, and can be modularly integrated with existing results for vacuum sources.