Post-Newtonian dynamical modeling of supermassive black holes in
  galactic-scale simulations
  We present KETJU, a new extension of the widely-used smoothed particle
hydrodynamics simulation code GADGET-3. The key feature of the code is the
inclusion of algorithmically regularized regions around every supermassive
black hole (SMBH). This allows for simultaneously following global
galactic-scale dynamical and astrophysical processes, while solving the
dynamics of SMBHs, SMBH binaries and surrounding stellar systems at sub-parsec
scales. The KETJU code includes Post-Newtonian terms in the equations of
motions of the SMBHs which enables a new SMBH merger criterion based on the
gravitational wave coalescence timescale pushing the merger separation of SMBHs
down to $\sim 0.005$ pc. We test the performance of our code by comparison to
NBODY7 and rVINE. We set up dynamically stable multi-component merger
progenitor galaxies to study the SMBH binary evolution during galaxy mergers.
In our simulation sample the SMBH binaries do not suffer from the final-parsec
problem, which we attribute to the non-spherical shape of the merger remnants.
For bulge-only models, the hardening rate decreases with increasing resolution,
whereas for models which in addition include massive dark matter halos the SMBH
binary hardening rate becomes practically independent of the mass resolution of
the stellar bulge. The SMBHs coalesce on average 200 Myr after the formation of
the SMBH binary. However, small differences in the initial SMBH binary
eccentricities can result in large differences in the SMBH coalescence times.
Finally, we discuss the future prospects of KETJU, which allows for a
straightforward inclusion of gas physics in the simulations.
