Joint inference of line-of-sight acceleration and orbital eccentricity in neutron-star--black-hole binaries

Abstract: A line-of-sight acceleration (LOSA) of a compact-binary center of mass, imparted for example by a nearby tertiary perturber, imprints a Doppler modulation on the gravitational-wave signal and provides a single-event diagnostic of dynamical formation environments. Waveform-modeling systematics -- missing higher-order modes, spin precession, or orbital eccentricity -- can mimic or mask a non-zero LOSA, making waveform accuracy a leading concern for LOSA inference. We implement LOSA corrections directly in the time domain as a remap of the strain: the treatment applies uniformly to all mode content, spin precession, and orbital eccentricity, and integrates naturally with time-domain inspiral-merger-ringdown models that best capture these effects. We deploy it in the SEOBNRv6EHM (aligned-spin eccentric) and SEOBNRv5PHM (precessing quasi-circular) models, and validate the implementation on simulated signals; we find that SEOBNRv6EHM recovers LOSA correctly on both eccentric and spin-precessing injections, while SEOBNRv5PHM yields a spurious LOSA measurement on eccentric signals. Motivated by the eccentricity hints in the neutron-star--black-hole (NSBH) event GW200105_162426 and the favorable low-mass regime of these sources, we jointly infer LOSA and orbital eccentricity for the five NSBH events in the LIGO-Virgo-KAGRA catalog, reporting the first LOSA constraints on three of them. All five events are consistent with a vanishing LOSA, $Γ\equiv a_\parallel/c = 0$; for GW200105_162426, the joint $(Γ, e)$ posterior nonetheless disfavors both $Γ$ and $e$ being zero simultaneously at 90% credibility, supporting the eccentricity hints reported in previous analyses.