The Final Parsec Problem

When two galaxies merge, their central supermassive black holes sink toward the center of the merged system through dynamical friction, forming a bound binary at separations of roughly a parsec. At this point, the binary has ejected all stars on intersecting orbits and can no longer efficiently lose energy through stellar dynamical friction — the so-called final parsec problem. Without a mechanism to harden the binary below a parsec, the two black holes would take longer than the Hubble time to merge via gravitational wave emission alone, yet observations confirm that SMBH mergers do occur and that the nanohertz gravitational wave background detected by pulsar timing arrays requires a substantial population of such mergers. ΛCDM-based explanations invoke gas dynamics, triaxial potentials, or a third black hole perturber, but no single mechanism is universally accepted.

Successive Collision Theory resolves the final parsec problem through the angular momentum inheritance mechanism combined with the pre-existing compact object populations from the colliding pockets. In SCT, the SMBH seeds present in the pre-collision pockets did not form at the centers of fully assembled galactic halos — they existed in a more chaotic, pre-thermalization environment with a richer phase space of stellar and compact-object orbits. When these seeds merged in the post-collision debris field, they were surrounded by compact object populations on highly eccentric orbits set by the inherited angular momentum distribution, rather than the smooth, isotropic stellar distributions that ΛCDM binary hardening models assume. These compact objects — neutron stars, stellar-mass black holes, white dwarfs — on angular-momentum-selected orbits efficiently scatter off the SMBH binary, removing energy and hardening the binary well below the final parsec without requiring an implausible gap in the loss cone.

The tensor mesh dissipation mechanism provides an additional hardening channel unique to SCT. As the gravitational potential of the host galaxy's parent frame hierarchy slowly weakens through orbital decay, the effective tidal field experienced by the SMBH binary changes secularly, introducing a time-varying perturbation to the binary's orbital energy budget. This is a coherent, directed perturbation rather than a stochastic noise source, and it contributes to binary hardening at a rate proportional to the local mesh dissipation rate. The SCT prediction is therefore that SMBH binary merger timescales are systematically shorter than ΛCDM estimates — consistent with the observed nanohertz background amplitude — and that the merger rate correlates with the local tensor mesh dissipation rate, which in turn correlates with large-scale structure environment.