Three black holes, changing partners: a new model follows mergers inside simulated galaxies

A third massive black hole can complicate a merger already in progress: it may change the eventual partners, help drive a coalescence or leave one object on a wider orbit. A study available as an arXiv preprint extends the RAMCOAL model to represent these possibilities inside simulations that follow both galaxies and their gas. The manuscript reports acceptance by Monthly Notices of the Royal Astronomical Society (MNRAS) on 5 November 2026; the version discussed here is the arXiv manuscript, not a final journal publication.

The arXiv submission history records the original submission on 5 July 2026 at 05:18:18 UTC, followed by the third version on 5 November 2026. These are distinct from the journal’s receipt and acceptance dates.

Kunyang Li, Ricarda S. Beckmann, Yohan Dubois and Marta Volonteri describe a bridge between two scales that are difficult to calculate together. Galaxy simulations follow large-scale flows of gas, stars and dark matter, but cannot resolve the final, extremely close orbits of merging massive black holes. RAMCOAL supplies simplified physical rules for that unresolved evolution.

Keeping a close encounter distinct from a merger

In a conventional simulation, two black-hole particles may be combined when they become closer than the numerical resolution allows. That computational event does not necessarily mean the real black holes would have merged.

RAMCOAL instead preserves their separate identities within a shared numerical particle. Its subgrid model—a description of processes smaller than the simulation can resolve—continues following their relative motion.

The model separates the evolution into stages. Initially, black holes move through the resolved galaxy. At smaller separations, dynamical friction, the drag associated with gravitational wakes in surrounding matter, can bring them together. Once a bound binary forms under the model’s criteria, encounters with stars and interactions with gas can tighten its orbit. Eventually, gravitational waves, ripples in spacetime that carry away orbital energy, drive the final inspiral.

Crucially, RAMCOAL updates its environmental inputs during the galaxy simulation rather than assigning the entire merger delay afterwards. It also tracks gas accretion, meaning the capture of surrounding material, and black-hole spin.

Replacing chaotic encounters with weighted outcomes

The extension adds systems containing three massive black holes. An inner pair may coexist with a third object on a wider orbit. If the outer object meets the model’s capture and orbital-evolution conditions, RAMCOAL activates its chaotic three-body treatment.

It does not calculate every close gravitational encounter directly. Instead, it selects an outcome from a library based on earlier numerical scattering experiments. The selection probabilities depend on the primary black hole’s mass and two mass ratios. Seven channels cover different merging pairs, ejections and stalled systems.

The authors checked this selection procedure with 100 independent random draws for one fixed configuration. The recovered frequencies agreed with the input probabilities within the expected counting scatter. That checks whether the software samples its table correctly; it does not independently establish that the table describes every galactic environment. At fixed input masses and ratios, the outcome probabilities have no explicit dependence on the host galaxy.

Different starting orbits, different merging pairs

Three controlled experiments used one isolated, gas-containing galaxy. In the first, with initial orbits in the galactic plane, black holes labelled 1 and 2 merged at a simulation time of about 3.51 billion years. The third remained on a wide orbit.

In the second, the incoming black hole followed an inclined orbit. Black holes 1 and 3 instead formed the merging pair, coalescing at about 290 million years. Neither experiment activated the chaotic subgrid triplet treatment: their contrast demonstrates sensitivity to the initial orbital configuration even before that regime is reached. It does not show that inclined encounters generally merge faster. Each geometry was tested in a single realization, so the comparison does not capture the full scatter in possible outcomes.

A third, more compact experiment used three black holes of approximately three million solar masses each. It progressed into the active triplet regime. The sampled outcome replaced the original inner pairing with a merger between an inner member and the incoming object, leaving the third black hole bound to the remnant.

Fast calculations, approximate timing

The timing of that compact example requires particular caution. The tests use an arbitrary 100-year timer to execute a sampled chaotic outcome, not a calibrated physical interaction duration. The paper treats the selected merger as effectively immediate. A separate reconstruction of a gravitational-wave-only inspiral lasts about 0.9 billion years, underscoring that the scheduled event is not a directly resolved merger clock.

Other assumptions also matter. Close three-body dynamics and surrounding gas discs remain unresolved; accretion is suspended during the chaotic phase. Intruders heavier than the inner binary require an uncalibrated extrapolation, while encounters involving more than three black holes are simplified through forced mergers.

The computational benefit is substantial: measured subgrid integration took roughly 0.4–0.7 milliseconds per system per fine time step. In the cosmological run used for performance testing, its estimated share of total runtime was about 1.1%.

These are demonstrations, not population forecasts. Larger samples and improved calibration are needed before the model can reliably quantify merger and ejection rates. Its promise is to connect future gravitational-wave predictions with the evolving galaxies in which black holes actually live.