What factors impact how long it takes for a supermassive black hole binary to merge? New research investigates the influence of orbital inclination on the population of merging black holes in our universe.
One Merger Leads to Another
This image from the Hubble Space Telescope shows NGC 6240, the result of a three-galaxy merger that contains three nuclei, two of which appear to have active supermassive black holes. [NASA, ESA, the Hubble Heritage (STScI/AURA)-ESA/Hubble Collaboration, and A. Evans (University of Virginia, Charlottesville/NRAO/Stony Brook University)]
With observational evidence for supermassive black hole mergers taking shape, theorists are exploring the details of these mergers. One aspect of this process that hasn’t yet been examined fully is how the relative inclination of the merging galaxies impacts the time it takes for their central black holes to merge — a factor that has the potential to shape the demographics of merging supermassive black holes across our universe.
Ready, Set, Spiral
Sena Ghobadi (Georgia Institute of Technology) and collaborators used 3D dynamical models to explore how the angle at which galaxies collide — and therefore how the black holes’ orbits are tilted relative to one another — impacts the time it takes the supermassive black holes at their centers to merge.
In the simulations, Ghobadi’s team placed a 106–108-solar-mass black hole at the center of a disk galaxy. Then, they sent a second, smaller black hole spiraling toward it from a distance of 1 kiloparsec (3,300 light-years).
The team varied the inclination of the incoming black hole’s orbit relative to the disk of the target galaxy from 0 to 75 degrees. They also explored the impact of changing the black hole masses and the galaxy’s central gas density, disk rotation speed, and gas mass fraction. For each simulation, they recorded how long it took for the incoming smaller black hole to get within 10 parsecs of the larger black hole.
Simulated orbits of black holes with initial inclinations of 0 (top), 25 (center), and 45 (bottom) degrees. For the 0-degree simulation, the black holes merge in 5.75 billion years. For the 25-degree simulation, the merger occurs at 7.90 billion years. The 45-degree simulation fails to merge within the lifetime of the universe. [Adapted from Ghobadi et al. 2026]
(Dis)inclined to Merge
The simulations showed a clear trend with changing inclination: a black hole with an orbital inclination greater than 20 degrees took longer to merge than those with inclinations of 0–20 degrees. For black holes approaching the merger on slightly inclined orbits, dynamical friction between the black hole and the stars and gas of the galaxy worked to drag the black hole down into the disk, decreasing its inclination over time and guiding it toward a merger. Aside from the influence of inclination, the team also found that higher-mass supermassive black holes and more rapidly rotating galactic disks tended to lead to faster mergers.
For inclinations greater than roughly 45 degrees, a dramatic transition took place, with the orbits of the incoming black holes becoming more inclined over time rather than settling down into the disk. These simulated black holes failed to merge in the allotted time of 14 billion years.
With highly inclined binaries failing to merge within the lifetime of the universe, this suggests that the dual active galactic nuclei and the supermassive black hole binaries that produce gravitational waves in the universe today are the result of binaries with initial inclinations of 20 degrees or less.
Citation
“Evolution of Supermassive Black Hole Pairs on Inclined Orbits in Postmerger Galaxies,” Sena Ghobadi et al 2026 ApJ 999 131. doi:10.3847/1538-4357/ae40bc