Post-Newtonian Dynamical Modeling of Supermassive Black Holes in Galactic-scale Simulations

Abstract

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 PostNewtonian 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 ∼ 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.

Galaxy mergers in eagle do not induce a significant amount of black hole growth yet do increase the rate of luminous AGN

“…For eagle, the coalescence of two BHs is not a resolved process, and we therefore implement broad conditions for this process to occur: the two BHs must be within each others smoothing kernel and their relative velocity to one another must be less than the circular velocity at that distance. It is likely that these conditions merge the BHs earlier than they should (e.g., Rantala et al 2017), which would potentially result in a rightward shifting of the excess peaks in Figure 8 (i.e., the peak of AGN activity would lag further behind the coalescence of the two galaxies). However, we do not anticipate any of the overall behaviour or trends of this study would be affected by this, with the majority of the triggered AGN activity still occurring post-coalescence (of the galaxy nuclei).…”

mstar – a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates

“…The time-step H is then adjusted accordingly, to bring the k where convergence is expected to the optimal value (Press et al 2007). Finally, it should be noted that the extrapolation algorithm used in AR-CHAIN described above is serial in nature, even though the particle accelerations in the individual leapfrog sequences can be computed in parallel as in (Rantala et al 2017). Thus, computing a large number of subsequent subdivision counts or reaching the maximum subdivision count k max without convergence and restarting with a smaller time-step H/2 can be very time-consuming.…”

“…With non-zero external tidal perturbations f i the derivative of the binding energy B depends on the particle velocities, but the dependence is only linear and can thus be analytically integrated over the time-step (see e.g. the Appendix A and B of Rantala et al 2017). An explicit leapfrog algorithm cannot be constructed if the post-Newtonian accelerations g i (v) are non-zero.…”

“…typically provides sufficiently accurate results, especially when the time interval ∆t is short. In our AR-CHAIN implementation (Rantala et al 2017) we begin the regularised integration by estimating the amount of fictitious time ∆s based on the smallest Keplerian time-scale P Kepler of the system. Using Eq.…”

“…This algorithmic regularisation (AR) method is faster than the previous regularisation methods and more accurate, especially in the case of large mass ratios between particles in an N-body system. Many current direct summation codes (Harfst et al 2008;Aarseth 2012) and regularised tree codes (Rantala et al 2017) use an implementation of the AR-CHAIN integrator (Mikkola & Merritt 2006 to resolve the small-scale dynamics around SMBHs.…”