Line-of-sight Acceleration Driven Effects in Eccentric Compact Binary Coalescences

Abstract

The line-of-sight acceleration (LOSA) effect, imprinted in the gravitational wave (GW) signal of an inspiralling compact binary by an external gravitational potential, is one of the most promising means of probing the environment of compact binaries on a single-event basis. However, this effect is potentially degenerate with other low-frequency effects, particularly the binary's orbital eccentricity. LOSA effects and orbital eccentricity can mimic each other if only one or the other (but not both) are accounted for in the waveform template. In this work, we present the (2, 2) mode, leading eccentric harmonic, frequency-domain phase correction incurred by an accelerating eccentric compact binary, and discuss inconsistencies pertaining to this phase correction in the literature. We show that the degeneracy between LOSA and orbital eccentricity can be resolved if both effects are modeled in the template. To demonstrate this, we inject a GW170817-like signal, with eccentricity and LOSA added to it, and recover the parameters of the injected signal assuming an A+ like noise power spectral density (PSD) of the LVK detector network. We find that the true LOSA and eccentricity parameters, along with other binary parameters, are recovered within the $90\%$ credible interval (CI). This study highlights the importance of incorporating LOSA in eccentric waveform models to robustly and reliably estimate LOSA and eccentricity.