The Eccentric and Accelerating Stellar Binary Black Hole Mergers in Galactic Nuclei: Observing in Ground and Space Gravitational-wave Observatories

We study the stellar binary black holes (BBHs) inspiraling/merging in galactic nuclei based on our numerical method GNC. We find that 3%-40% of all newborn BBHs will finally merge due to various dynamical effects. In a five-year mission, up to 10(4), 10(5), and similar to 100 of BBHs inspiraling/merging in galactic nuclei can be detected with signal-to-noise ration >8 in Advanced LIGO (aLIGO), Einstein/DECIGO, and TianQin/LISA/TaiJi, respectively. Roughly tens are detectable in both LISA/TaiJi/TianQin and aLIGO. These BBHs have two unique characteristics. (1) Significant eccentricities: 1%-3%, 2%-7%, or 30%-90% of them have e ( i ) > 0.1 when they enter into aLIGO, Einstein, or space observatories, respectively. Such high eccentricities provide a possible explanation for that of GW190521. Most highly eccentric BBHs are not detectable in LISA/Tianqin/TaiJi before entering into aLIGO/Einstein, as their strain becomes significant only at f (GW) greater than or similar to 0.1 Hz. DECIGO becomes an ideal observatory to detect those events, as it can fully cover the rising phase. (2) Up to 2% of BBHs can inspiral/merge at distances less than or similar to 10(3) r (SW) from the massive black hole, with significant accelerations, such that the Doppler phase drift of similar to 10-10(5) of them can be detected with signal-to-noise ratio >8 in space observatories. The energy density of the gravitational-wave backgrounds (GWBs) contributed by these BBHs deviates from the power-law slope of 2/3 at f (GW) less than or similar to 1 mHz. The high eccentricity, significant accelerations, and the different profile of the GWB of these sources make them distinguishable, and thus interesting for future gravitational-wave detections and tests of relativities.