Dynamical friction modelling of massive black holes in cosmological simulations and effects on merger rate predictions

In this work, we establish and test methods for implementing dynamical friction (DF) for massive black hole pairs that form in large volume cosmological hydrodynamical simulations that include galaxy formation and black hole growth. We verify our models and parameters both for individual black hole dynamics and for the black hole population in cosmological volumes. Using our model of DF from collisionless particles, black holes can effectively sink close to the galaxy centre, provided that the black hole's dynamical mass is at least twice that of the lowest mass resolution particles in the simulation. Gas drag also plays a role in assisting the black holes' orbital decay, but it is typically less effective than that from collisionless particles, especially after the first billion years of the black hole's evolution. DF from gas becomes less than 1{{ rm per cent}} of DF from collisionless particles for BH masses >107 Mpdbl. Using our best DF model, we calculate the merger rate down to z = 1.1 using an Lbox = 35 Mpc h-1 simulation box. We predict ∼2 mergers per year for z > 1.1 peaking at z ∼2. These merger rates are within the range obtained in previous work using similar resolution hydrodynamical simulations. We show that the rate is enhanced by factor of ∼2 when DF is taken into account in the simulations compared to the no-DF run. This is due to {gt}40{{ rm per cent}} more black holes reaching the centre of their host halo when DF is added.