Line-of-sight acceleration in compact binaries with higher harmonics and eccentricity

Direct detections of gravitational waves provide a unique opportunity to probe the astrophysical origin of compact binary mergers. The formation channels of these systems remain highly debated, and a fraction may originate in dynamical environments or active galactic nuclei. Binaries formed in such environments are expected to experience line-of-sight acceleration from their surroundings, which can imprint characteristic signatures on the observed gravitational-wave signal. Here, we re-derive the line-of-sight acceleration effects and implement them in state-of-the-art quasi-circular waveform models with precession and higher-order modes. We also implement the corrections in eccentric waveform models, applying them consistently to all contributing harmonics. Using this model, we investigate the impact of these effects on the inference of line-of-sight acceleration and analyze a few interesting GWTC events observed during the third observing run of LIGO and Virgo. We find no substantial evidence for line-of-sight acceleration in these events. We also show that an inconsistent treatment of line-of-sight acceleration between higher harmonics can lead to biased conclusions. Our model provides a robust framework for uncovering line-of-sight acceleration in current and future gravitational-wave observations, enabling more accurate probes of environmental signatures in compact-binary formation.