The difficult path to coalescence: massive black hole dynamics in merging low mass dark matter haloes and galaxies

We present a high-resolution numerical study of the sinking and merging of massive black holes (MBHs) with masses in the range of 10³ - 10⁷ \, M_ in multiple minor mergers of low-mass dark matter haloes without and with galaxies (4× 10⁸ \, M_ Mₕₐₗₒ 2× 10¹⁰ \, M₎. The ketju simulation code, a combination of the gadget tree solver with accurate regularized integration, uses unsoftened forces between the star/dark matter components and the MBHs for an accurate treatment of dynamical friction and scattering of dark matter/stars by MBH binaries or multiples. Post-Newtonian corrections up to order 3.5 for MBH interactions allow for coalescence by gravitational wave emission and gravitational recoil kicks. Low-mass MBHs (10⁵ \, M_) hardly sink to the centre or merge. Sinking MBHs have various complex evolution paths – binaries, triplets, free-floating MBHs, and dynamically or recoil ejected MBHs. Collisional interactions with dark matter alone can drive MBHs to coalescence. The highest mass MBHs of 10⁶ \, M_ mostly sink to the centre and trigger the scouring of dark matter and stellar cores. The scouring can transform a centrally baryon-dominated system into a dark-matter-dominated system. Our idealized high-resolution study highlights the difficulty to bring in and keep low-mass MBHs in the centres of low-mass haloes/galaxies – a remaining challenge for merger assisted MBH seed growth mechanisms.