  Aims: We investigate the orbital and phase space properties of loss cone
stars that interact strongly with a hard, high-redshift binary supermassive
black hole (SMBH) system formed in a cosmological scenario. Methods: We use a
novel hybrid integration approach that combines the direct N-body code
$\varphi$-GRAPE with ETICS, a collisionless code that employs the
self-consistent field method for force calculation. The hybrid approach shows
considerable speed-up over direct summation for particle numbers $> 10^6$,
while retaining accuracy of direct N-body for a subset of particles. During the
SMBH binary evolution we monitor individual stellar interactions with the
binary in order to identify stars that noticeably contribute to the SMBH binary
hardening. Results: We successfully identify and analyze in detail the
properties of stars that extract energy from the binary. We find that the
summed energy changes seen in these stars match very well with the overall
binary energy change, demonstrating that stellar interactions are the primary
drivers of SMBH binary hardening in triaxial, gas-poor systems. The slight
triaxiality of our system results in efficient loss cone refilling, avoiding
the final parsec problem. We distinguish three different populations of
interactions based on their apocenter. We find a clear prevalence of
interactions co-rotating with the binary. Nevertheless, retrograde interactions
are the most energetic, contributing only slightly less than the prograde
population to the overall energy exchange. The most energetic interactions are
also likely to result in a change of sign in the angular momentum of the star.
We estimate the merger timescale of the binary to be $\approx 20$
$\mathrm{Myr}$, a value larger by a factor of two than the timescale reported
in a previous study.
