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

Abstract

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 halos without and with galaxies (4 × 108 M⊙ ≲ Mhalo ≲ 2 × 1010 M⊙). The Ketju simulation code, a combination of the Gadget tree solver with accurate regularised 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 $\gtrsim 10^6 \, \rm M_\odot$ 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 halos/galaxies – a remaining challenge for merger assisted MBH seed growth mechanisms.