The Erratic Path to Coalescence of LISA Massive Black Hole Binaries in Subparsec-resolution Simulations of Smooth Circumnuclear Gas Disks

We perform high-resolution simulations to follow the orbital decay of 5 105 and 107 M o˙ massive black hole (MBH) pairs embedded in a circumnuclear gas disk (CND), from the CND scale (100 pc) down to 0.1-0.01 pc, the scale at which a circumbinary disk (CBD) could form. The MBHs' erratic orbital evolution is characterized by three stages: (i) a slow initial decay that leads to some circularization; (ii) a fast-migration phase, analogous to type III migration for massive planets in protoplanetary disks, in which angular momentum is efficiently drained by disk-driven torques arising from the co-orbital region of the secondary MBH, at a distance of 1-3 Hill radii; and (iii) a very slow decay phase, in which orbital angular momentum can even increase. In this last stage, a CBD forms when the parsec-scale decay rate becomes small enough to allow sufficient time for a cavity to be carved. When this happens, the MBH separation nearly stalls in our higher-resolution run. We suggest an empirically modified gap-opening criterion that takes into account such timescale effects, as well as other deviations from standard assumptions. Interestingly, a CBD does not form in the lower-resolution runs, resulting in a faster subparsec decay. Our findings show that the subparsec MBH pairing in gaseous disks is a stochastic and fragile process. Additional mechanisms, such as the stellar-driven hardening, may be necessary to guarantee that the gravitational wave emission phase is entered and the MBHs become accessible to future detectors such as the Laser Interferometer Space Antenna.