  Mergers of binary black holes on eccentric orbits are among the targets for
second-generation ground-based gravitational-wave detectors. These sources may
commonly form in galactic nuclei due to gravitational-wave emission during
close flyby events of single objects. We determine the distributions of initial
orbital parameters for a population of these gravitational-wave sources. Our
results show that the initial dimensionless pericenter distance systematically
decreases with the binary component masses and the mass of the central
supermassive black hole, and its distribution depends sensitively on the
highest possible black hole mass in the nuclear star cluster. For a multi-mass
black hole population with masses between 5 Msun and 80 Msun, we find that
between 43-69% (68-94%) of 30 Msun - 30 Msun (10 Msun - 10 Msun) sources have
an eccentricity greater than 0.1 when the gravitational-wave signal reaches 10
Hz, but less than 10% of the sources with binary component masses less than 30
Msun remain eccentric at this level near the last stable orbit (LSO). The
eccentricity at LSO is typically between 0.005-0.05 for the lower-mass BHs, and
0.1 - 0.2 for the highest-mass BHs. Thus, due to the limited low-frequency
sensitivity, the six currently known quasi-circular LIGO/Virgo sources could
still be compatible with this originally highly eccentric source population.
However, at the design sensitivity of these instruments, the measurement of the
eccentricity and mass distribution of merger events may be a useful diagnostic
to identify the fraction of GW sources formed in this channel.
