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) inspiralling/merging in
galactic nuclei based on our numerical method GNC. We find that $3-40\%$ of all
new born BBHs will finally merge due to various dynamical effects. In a five
year's mission, up to $10^4$, $10^5$, $\sim100$ of BBHs inspiralling/merging in
galactic nuclei can be detected with SNR$>8$ in aLIGO, Einstein/DECIGO,
TianQin/LISA/TaiJi, respectively. About 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 is with
$e_i>0.1$ when they enter into aLIGO, Einstein, or space observatories,
respectively. Such high eccentricities provide a possible explanation for that
of GW 190521. Most highly-eccentric BBHs are not detectable in
LISA/Tianqin/TaiJi before entering into aLIGO/Einstein as their strain become
significant only at $f_{\rm GW}\gtrsim0.1$ Hz. DECIGO become 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 $\lesssim10^3 r_{\rm SW}$
from the massive black hole (MBH), with significant accelerations, such that
the Doppler phase drift of $\sim10-10^5$ of them can be detectable with SNR$>8$
in space observatories. The energy density of the gravitational wave
backgrounds (GWB) contributed by these BBHs deviate from the powerlaw slope of
$2/3$ at $f_{\rm GW}\lesssim 1$mHz. The high eccentricity, significant
accelerations and different profile of GWB of these sources make them
distinguishable, thus interesting for future GW detections and tests of
relativities.
