Space-borne atom interferometric gravitational wave detections. Part III. Eccentricity on dark sirens

Eccentricity of the inspiraling compact binaries can greatly improve the distance inference and source localization of dark sirens. In this paper, we continue the research for the space-borne atom interferometric gravitational-wave detector AEDGE and investigate the effects of eccentricity on the dark sirens observed by AEDGE in the mid-band. We simulate five types of typical compact binaries with component mass ranging from $1-100~M_{\odot}$. The largest improvement for both distance inference and localization can be as much as 1.5--3 orders of magnitude. We then construct the catalogs of dark sirens observed by AEDGE in five years. We find eccentricity is crucial to the detection of golden binary black holes (BBH) whose host galaxy can be uniquely identified. With only 5--10 golden dark BBHs one can obtain a 2 percent precision measurement of $H_0$ which is sufficient to arbitrate the Hubble tension. Regardless of eccentricity, AEDGE can also observe tens of golden binary neutron stars (BNS) and neutron star--black hole binaries (NSBH) with unique host galaxies. These golden dark sirens can serve as early warnings for the follow-up observations of gravitational waves in the high frequency band as well as the search of their electromagnetic counterparts. Our results show eccentricity is a crucial factor in the detection, data analysis, and application of GWs with the atom interferometers in the mid-band.