New calculations suggest that the merger of SMBH pairs into a single entity is facilitated by the previously underestimated behavior of dark matter particles. This discovery offers a potential solution to the "final parsec problem," which has puzzled astronomers for years.

The study, titled "Self-interacting dark matter solves the final parsec problem of supermassive black hole mergers," was published in Physical Review Letters this month.

In 2023, scientists detected a persistent "hum" of gravitational waves across the universe. They proposed that this signal came from the merging of millions of SMBH pairs, each billions of times more massive than the Sun. However, theoretical models indicated that these black holes stall at a distance of about a parsec (three light years) from each other, preventing their merger.

This "final parsec problem" not only challenged the idea that merging SMBHs were behind the gravitational wave background but also contradicted the theory that SMBHs grow through merging smaller black holes.

"We show that including the previously overlooked effect of dark matter can help supermassive black holes overcome this final parsec of separation and coalesce," said Gonzalo Alonso-Alvarez, a postdoctoral fellow at the University of Toronto and McGill University. "Our calculations explain how that can occur, in contrast to what was previously thought."

The study's co-authors include Professor James Cline from McGill University and the CERN Theoretical Physics Department, and Caitlyn Dewar, a physics master's student at McGill.

SMBHs are believed to reside at the centers of most galaxies. When galaxies collide, their SMBHs orbit each other and gradually spiral inward due to gravitational interactions with nearby stars. However, previous models suggested that as the SMBHs approach within a parsec, their interaction with the surrounding dark matter halo causes the dark matter particles to be ejected, halting the inward spiral.

Contrary to these models, Alonso-Alvarez and colleagues found that dark matter particles interact with each other, maintaining a high density that continues to affect the SMBHs' orbits, enabling them to merge.

"The possibility that dark matter particles interact with each other is an assumption that we made, an extra ingredient that not all dark matter models contain," said Alonso-Alvarez. "Our argument is that only models with that ingredient can solve the final parsec problem."

The gravitational waves produced by these massive mergers form a background hum of much longer wavelengths than those detected by LIGO in 2015. This hum has been observed by the Pulsar Timing Array, which measures tiny variations in signals from pulsars.

"A prediction of our proposal is that the spectrum of gravitational waves observed by pulsar timing arrays should be softened at low frequencies," noted Cline. "The current data already hint at this behavior, and new data may be able to confirm it in the next few years."

Besides providing insights into SMBH mergers and the gravitational wave background, this research also advances our understanding of dark matter.

"Our work is a new way to help us understand the particle nature of dark matter," added Alonso-Alvarez. "We found that the evolution of black hole orbits is very sensitive to the microphysics of dark matter, and that means we can use observations of supermassive black hole mergers to better understand these particles."

The team's models suggest that the interaction rate of dark matter particles affects the structure of galactic dark matter halos.

"We found that the final parsec problem can only be solved if dark matter particles interact at a rate that can alter the distribution of dark matter on galactic scales," said Alonso-Alvarez. "This was unexpected since the physical scales at which the processes occur are three or more orders of magnitude apart. That's exciting."

Research Report:Self-Interacting Dark Matter Solves the Final Parsec Problem of Supermassive Black Hole Mergers

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