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 10( 3)- 10( 7) Me e in multiple minor mergers of low-mass dark matter haloes without and with galaxies (4 x 10( 8) Me e < M halo < 2 x 10( 10 )Me). e ). 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 (< < 10( 5) M-circle dot ) 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 > 10( 6) M-circle dot 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.