Collisionless loss-cone refilling: there is no final parsec problem

Abstract

Coalescing massive black hole binaries, formed during galaxy mergers, are expected to be a primary source of low frequency gravitational waves. Yet in isolated gas-free spherical stellar systems, the hardening of the binary stalls at parsec-scale separations owing to the inefficiency of relaxation-driven loss-cone refilling. Repopulation via collisionless orbit diffusion in triaxial systems is more efficient, but published simulation results are contradictory. While sustained hardening has been reported in simulations of galaxy mergers with N ∼ 10 6 stars and in early simulations of rotating models, in isolated non-rotating triaxial models the hardening rate continues to fall with increasing N , a signature of spurious two-body relaxation.We present a novel approach for studying loss cone repopulation in galactic nuclei. Since loss cone repopulation in triaxial systems owes to orbit diffusion, it is a purely collisionless phenomenon and can be studied with an approximated force calculation technique, provided the force errors are well behaved and sufficiently small. We achieve this using an accurate fast multipole method and define a proxy for the hardening rate that depends only on stellar angular momenta. We find that the loss cone is efficiently replenished even in very mildly triaxial models (with axis ratios 1 : 0.9 : 0.8). Such triaxiality is unavoidable following galactic mergers and can drive binaries into the gravitational wave regime. We conclude that there is no 'final parsec problem'.

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

“…Berczik et al 2006). We find that this result is in good agreement with the previous work of Gualandris et al (2016).…”

“…The halo-including sample H5 has far fewer stellar particles at velocities v < w, which explains the lowest hardening rate, even though more stellar mass interacts with the SMBH binary for this simulation sample. We find that this picture is consistent with the study of Gualandris et al (2016): mergers without a DM halo result in a merger remnant in which the SMBH binary evolution depends on the particle number used when N < 10 7 . However, we note that while Khan et al (2011) andPreto et al (2011) reported resolution-independent SMBH binary hardening in mergers without a DM halo, we find resolution-independent hardening rates only in the merger simulations, which use multi-component ICs including a DM halo.…”

“…Recent state-of-the-art direct summation studies (e.g. Khan et al 2013;Vasiliev et al 2014) utilizing φGRAPE-based codes (Harfst et al 2007(Harfst et al , 2008) have employed particle numbers up to N ∼ 10 6 , but as demonstrated by Vasiliev et al (2015) and Gualandris et al (2016) even simulations with these high particle numbers are affected by spurious relaxation effects. Instead, our main goal here is to demonstrate that KETJU can reproduce NBODY7 results in simulation setups which are possible to run using NBODY7 in a reasonable wallclock time.…”

“…However, even in simulations that avoid the final-parsec problem the loss-cone filling rate is affected by the enhanced two-body relaxation timescale, especially in simulations with N 10 6 particles (Vasiliev et al 2015). Recently, Gualandris et al (2016) also studied the collisionless loss-cone repopulation in triaxial galaxies without SMBHs using an accurate fast multipole method and found that for particle numbers N < 10 7 , the loss-cone filling rate is mildly N -dependent, whereas the rate becomes practically independent of N for particle numbers above N ∼ 10 7 . Recent observations show that even early-type galaxies have non-negligible gas reservoirs of cold gas in their central regions (Young et al 2011;Davis et al 2013).…”

“…The performance of normal GADGET-3 can be substandard in situations that require high dynamical precision due to the insufficient precision of the tree force calculation (see e.g. Gualandris et al 2016). Some of these problems can be mitigated by setting the internal accuracy parameters of GADGET-3 to very high values, significantly beyond their usual nominal values.…”