In 2023, astrophysicists announced the discovery of a "hum" of gravitational waves permeating the universe. They believed this background signal came from the merger of millions of pairs of supermassive black holes (SMBH), each billions of times more massive than our Sun.

However, theoretical simulations have shown that as these massive celestial objects approach each other, their progress halts at a distance of approximately one parsec - about three light-years - preventing their merger. This "final parsec problem" not only contradicts the theory that SMBH mergers are the source of gravitational waves but also the theory that SMBH grow by merging with smaller black holes.

New research
Now, a team including Gonzalo Alonso-Álvarez has shown that pairs of SMBH can overcome the one-parsec barrier and merge into a single larger black hole. According to their new calculations, SMBH continue to approach each other due to previously overlooked interactions with particles within the vast cloud of dark matter surrounding them.

"We show that including the previously neglected effect of dark matter can help supermassive black holes overcome this final parsec separation and merge," says Alonso-Álvarez. "Our calculations explain how this can happen, contrary to previous beliefs."

The research is described in the paper "Self-interacting dark matter solves the final parsec problem of supermassive black hole mergers" published this month in the journal Physical Review Letters.

The co-authors of the paper include Alonso-Álvarez, a postdoctoral researcher in the Department of Physics at the Faculty of Arts and Sciences and the Department of Physics and Trottier Space Institute at McGill University; Professor James Cline from McGill University and CERN's Department of Theoretical Physics in Switzerland; and Caitlyn Dewar, a master's student in physics at McGill University.

SMBH and dark matter
SMBH are thought to lie at the centers of most galaxies, and when two galaxies collide, their SMBH enter into orbit around each other. As they orbit each other, the gravitational pull of nearby stars drags and slows them down. As a result, the SMBH spiral towards merging.

Previous merger models showed that when SMBH get to about one parsec apart, they begin to interact with the dark matter cloud or halo in which they reside. They indicated that the gravity of the spiraling SMBH ejects dark matter particles from the system, and the resulting dark matter scarcity means energy is no longer drawn from the pair, and their mutual orbit no longer shrinks.

Although these models dismissed the impact of dark matter on SMBH orbits, the new model from Alonso-Álvarez and his colleagues reveals that dark matter particles interact in a way that they do not scatter. The density of the dark matter halo remains high enough for interactions between the particles and the SMBH to continue degrading the SMBH orbits, creating a path to merging.

"The possibility that dark matter particles interact with each other is an assumption we made, an additional ingredient that not all dark matter models have," says Alonso-Álvarez. "Our argument is that only models with this ingredient can solve the final parsec problem."

Gravitational wave detection
The background hum caused by these colossal cosmic collisions consists of gravitational waves with much longer wavelengths than those first detected by astrophysicists in 2015 using the Laser Interferometer Gravitational-Wave Observatory (LIGO). Those gravitational waves were generated by the merger of two black holes, each about 30 times the mass of the Sun.

The background hum has been detected in recent years by scientists working on the Pulsar Timing Array. This network detects gravitational waves by measuring tiny variations in signals from pulsars, rapidly rotating neutron stars that emit powerful radio pulses.

"The prediction of our proposal is that the spectrum of gravitational waves detected by the pulsar timing array should be softened at low frequencies," says Cline. "Current data already hints at this behavior, and new data could confirm it in the next few years."

In addition to providing insight into SMBH mergers and the background signal of gravitational waves, the new result also offers a window into the nature of dark matter.

"Our work is a new way to better understand the particle nature of dark matter," says Alonso-Álvarez. "We found that the evolution of black hole orbits is very sensitive to the micro-physics of dark matter, meaning we can use observations of supermassive black hole mergers to better understand these particles."

For example, researchers found that interactions between the dark matter particles they modeled also explain the shapes of galactic dark matter halos.

"We found that the final parsec problem can only be solved if dark matter particles interact with each other at a rate that can change the distribution of dark matter on galactic scales," says Alonso-Álvarez. "This was unexpected because the physical scales at which the processes occur are three or more orders of magnitude different. It is exciting."

Moreover, the research suggests that further gravitational wave observations could reveal additional details about the nature of dark matter, potentially allowing scientists to distinguish between different dark matter models based on the behavior of supermassive black holes during mergers. This discovery could open new avenues of research in astrophysics and cosmic micro-physics, providing deeper insights into the fundamental ingredients of the universe.

Source: University of Toronto