Unequal Mass Binary Evolution Driven by High Mach Circumbinary Disks

Abstract

We present a study of the gas-driven orbital evolution of unequal mass black hole binaries with circumbinary gas disks (CBDs), varying Mach number and viscosity (nu). Using two-dimensional grid-based hydrodynamics simulations spanning a thousand binary orbits at fixed separation, we explore low to moderate mass ratios (q = 0.05-1.0) and examine how variations in Mach and q affect the torques and component accretion rates exerted by the CBD and consequently the binary evolution. Equal mass binary systems receive positive torques in low-mach disks but transition to negative torques for Mach >25. As q decreases, the transition moves to higher Mach numbers. For q<0.1, we find no torque sign reversal below Mach~52, except in sufficiently low-viscosity disks. We find that the secondary black hole cannot effectively repel the CBD, it instead accretes most of the inflowing gas from the CBD; these low mass ratio binaries in high viscosity disks therefore tend to outspiral, although inspiral can occur in less viscous environments. We also find that binaries with mass ratios in the range of 0.25 - 0.5 can show preferential accretion favoring the primary when the gas viscosity is low, exemplifying an exception to the established rule of thumb that accretion favors the secondary. We discuss differences between our results and those reported in the literature on the orbital evolution and preferential accretion, and emphasize that our simulations extend into a regime that remains largely unexplored. Overall, our results suggest that intermediate mass ratio inspirals (IMRIs) in CBDs may be less frequent, but this depends sensitively on the interplay between mass ratio, disk temperature, and viscosity.

Figures (18)

• Figure 1: Plot of the two-dimensional surface density for a thin disk around an MBHB with mass ratio $q=1.0$ (left) and $q=0.1$ (right), accreting from a CBD. The image is from a simulation snapshot, using Sailfish, taken well after the disk is viscously relaxed. The axes show the $x-y$ plane in units of the binary separation $a$.
• Figure 2: Plot of the dimensionless torque parameter, $\ell$, as a function of Mach number, $\mathcal{M}$, for an MBHB with mass ratio $q = 1.0$. Results are compared with those from Tiede2020, Penzlin2022 and Dittmann2024. At higher Mach numbers, the torques become increasingly negative, in agreement with the trends reported in these previous studies.
• Figure 3: Plot of the dimensionless torque parameter, $\ell$, as a function of Mach number, $\mathcal{M}$, for MBHBs with mass ratio in the range $q = 0.05-1.0$. Results shown here are for the highest resolution tested ($\Delta x = 0.005 a$).
• Figure 4: Plot of the two-dimensional surface density for MBHBs with varying Mach numbers and mass ratios. From top to bottom, rows show decreasing mass ratio in the range $q=0.05-1.0$. From left to right, columns show increasing Mach number in the range $\mathcal{M} = 13-52$.
• Figure 5: Plot of the dimensionless torque parameter, $\ell$, as a function of Mach number, $\mathcal{M}$, for an MBHB with varying mass ratio. The plot is similar to Fig. \ref{['fig:ell-q']} but with lower viscosity. The color for each line corresponds to the mass ratio of the binary, same as in Fig. \ref{['fig:ell-q']}.