KETJU -- resolving small-scale supermassive black hole dynamics in GADGET-4

We present the new public version of the KETJU supermassive black hole (SMBH) dynamics module, as implemented into GADGET-4. KETJU adds a small region around each SMBH where the dynamics of the SMBHs and stellar particles are integrated using an algorithmically regularised integrator instead of the leapfrog integrator with gravitational softening used by GADGET-4. This enables modelling SMBHs as point particles even during close interactions with stellar particles or other SMBHs, effectively removing the spatial resolution limitation caused by gravitational softening. KETJU also includes post-Newtonian corrections, which allows following the dynamics of SMBH binaries to sub-parsec scales and down to tens of Schwarzschild radii. Systems with multiple SMBHs are also supported, with the code also including the leading non-linear cross terms that appear in the post-Newtonian equations for such systems. We present tests of the code showing that it correctly captures, at sufficient mass resolution, the sinking driven by dynamical friction and binary hardening driven by stellar scattering. We also present an example application demonstrating how the code can be applied to study the dynamics of SMBHs in mergers of multiple galaxies and the effect they have on the properties of the surrounding galaxy. We expect that the presented KETJU SMBH dynamics module can also be straightforwardly incorporated into other codes similar to GADGET-4, which would allow coupling small-scale SMBH dynamics to the rich variety of galactic physics models that exist in the literature.