Supermassive black hole pairs in clumpy galaxies at high redshift: delayed binary formation and concurrent mass growth

Massive gas-rich galaxy discs at $z \sim 1-3$ host massive star-forming clumps with typical baryonic masses in the range $10^7-10^8$~M$_{\odot}$ which can affect the orbital decay and concurrent growth of supermassive black hole (BH) pairs. Using a set of high-resolution simulations of isolated clumpy galaxies hosting a pair of unequal-mass BHs, we study the interaction between massive clumps and a BH pair at kpc scales, during the early phase of the orbital decay. We find that both the interaction with massive clumps and the heating of the cold gas layer of the disc by BH feedback tend to delay significantly the orbital decay of the secondary, which in many cases is ejected and then hovers for a whole Gyr around a separation of 1--2 kpc. In the envelope, dynamical friction is weak and there is no contribution of disc torques: these lead to the fastest decay once the orbit of the secondary BH has circularised in the disc midplane. In runs with larger eccentricities the delay is stronger, although there are some exceptions. We also show that, even in discs with very sporadic transient clump formation, a strong spiral pattern affects the decay time-scale for BHs on eccentric orbits. We conclude that, contrary to previous belief, a gas-rich background is not necessarily conducive to a fast BH decay and binary formation, which prompts more extensive investigations aimed at calibrating event-rate forecasts for ongoing and future gravitational-wave searches, such as with Pulsar Timing Arrays and the future evolved Laser Interferometer Space Antenna.