Detecting accelerating eccentric binaries in the LISA band

Many gravitational wave (GW) sources in the LISA band are expected to have non-negligible eccentricity. Furthermore, many of them can undergo acceleration because they reside in the presence of a tertiary. Here we develop analytical and numerical methods to quantify how the compact binary's eccentricity enhances the detection of its peculiar acceleration. We show that the general relativistic precession pattern can disentangle the binary's acceleration-induced frequency shift from the chirp-mass -induced frequency shift in GW template fitting, thus relaxing the signal-to-noise ratio requirement for distinguishing the acceleration by a factor of 10'' 100. Moreover, by adopting the GW templates of the accelerating eccentric compact binaries, we can enhance the acceleration measurement accuracy by a factor of-100, compared to the zero-eccentricity case, and detect the source's acceleration even if it does not change during the observational time. For example, a stellar-mass binary black hole (BBH) with moderate eccentricity in the LISA band yields an error of the acceleration measurement-10-7 m center dot s-2 for SNR 1/4 20 and observational time of 4 yr. In this example, we can measure the BBHs' peculiar acceleration even when it is-1 pc away from a 4 x 106M0 supermassive black hole. Our results highlight the importance of eccentricity to the LISA-band sources and show the necessity of developing GW templates for accelerating eccentric compact binaries.

Automated summary

This paper investigates the non-negligible eccentricity of gravitational wave sources in the LISA band and the potential acceleration they can undergo due to the presence of a tertiary. The study develops analytical and numerical methods to quantify how the eccentricity of a compact binary enhances the detection of its acceleration. The results show that the general relativistic precession pattern can separate the acceleration-induced frequency shift from the chirp-mass-induced frequency shift, reducing the signal-to-noise ratio requirement for distinguishing the acceleration by a factor of 10-100. Moreover, by adopting GW templates for accelerating eccentric compact binaries, the accuracy of the acceleration measurement can be enhanced by a factor of 100 compared to the zero-eccentricity case, and the source's acceleration can be detected even if it remains constant during the observational time.