Extreme mass ratio inspirals from the Hills mechanism, The eccentricity distribution of Hills EMRIs in LISA

Abstract

Extreme mass ratio inspirals (EMRIs) are promising sources for future space-based gravitational-wave detectors. We investigate EMRIs produced through the Hills mechanism, in which a stellar-mass black-hole binary (BBH) is tidally separated by a massive black hole (MBH), leaving one component bound to it. We present the first self-consistent modelling of this channel, combining an orbit-averaged Fokker-Planck treatment of the nuclear star cluster (NSC), three-body modelling of the binary-MBH encounter, Monte Carlo evolution of captured black holes (BHs), and fully relativistic EMRI trajectories to follow the evolution from binary supply down to final plunge. We find that Hills EMRIs are substantially more circular than classical EMRIs formed through two-body relaxation. For an MBH of $4 \times 10^6 M_\odot$ and circular, equal-mass BBHs of $20 M_\odot$ with initial separation of $0.1$ AU, EMRI mean eccentricities are approximately $0.097$ at our adopted LISA-band entry threshold and $0.034$ at plunge, compared with $0.478$ and $0.228$, respectively, for classical EMRIs. Of the initial BBHs, approximately $0.4$ per cent become EMRIs, whereas approximately $60$ per cent of captured BHs do. For comparable NSC initial compact-object mass, we find approximately $1.6 \times 10^{-8}$ Hills EMRIs per year per galaxy, approximately $12$ per cent of the classical EMRI yield. The Hills channel contribution to the overall eccentricity distribution depends strongly on the binary mass fraction in NSCs. We discuss implications for identifying EMRI formation channels with LISA and for quasi-periodic eruptions.