RABBITS IV: Stellar feedback and SMBH merging time-scales in the sub-Milky Way mass regime

Merging supermassive black holes (SMBHs) in low- and intermediate-mass galaxies are important sources for future millihertz gravitational-wave observatories such as LISA. Predicting the delay between galaxy coalescence and SMBH merger is therefore critical for modelling the observable SMBH merger population. Using the KETJU code, we perform 16 equal-mass galaxy merger simulations as part of the Resolving supermAssive Black hole Binaries In galacTic hydrodynamical Simulations (RABBITS) series to investigate SMBH binary evolution in galaxies with stellar masses below M 10 10, M. We systematically vary the strength of stellar feedback by altering the supernova outflow velocity by a factor of about4, while still producing galaxies consistent with observed scaling relations. We find post-hardening SMBH merger time-scales spanning about30 - 500, Myr, with stronger stellar feedback producing systematically longer merger delays through its impact on the central stellar density of the merger remnants. Across our suite, merging time-scales vary by more than an order of magnitude, demonstrating that uncertainties in stellar feedback alone can translate into large uncertainties in SMBH merger delays. At the onset of hardening, the binary evolution remains consistent with stellar-dynamical hardening models based on the local stellar density and velocity dispersion near the binary sphere of influence. Using KETJU as a benchmark, we show that merging time-scales can be recovered with useful accuracy when these nuclear stellar properties are extrapolated from scales up to about 100,R infl. These results provide a promising route for modelling SMBH mergers in cosmological simulations.