Properties of loss cone stars in a cosmological galaxy merger remnant

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 utilize 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 integration method. 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 which extract energy from the binary. We identify stars on centrophilic orbits that repopulate the loss cone and estimate that $76\%$ of the centrophilic orbits are possible only in a triaxial system. We distinguish three different populations of interactions, based on their apocenter and investigate their contribution to the SMBH binary hardening. We find a clear prevalence of interactions co-rotating with the binary. While smaller in number, 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 sign-flip change in the angular momentum of the star. We show that even slight triaxiality results in a roughly constant hardening rate of the binary, avoiding the Final Parsec Problem. 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.