New study uses self-interacting dark matter to solve the final parsec problem

In a new study, Canadian scientists have proposed a solution to the last parsec problem of supermassive black hole (SMBH) mergers using self-interacting dark matter.

As the two galaxies merge, gas and dust collide and stars form, but the stars themselves are too far away to collide. The SMBHs at the centers of the two galaxies also begin to merge.

but, Black Hole It will stall after one parsec (30.9 trillion kilometers) away. This problem is known in astronomy and astrophysics as the Last Parsec Problem.

the study, Published in Physical Review Letter (PRL)attempts to solve this problem and explain the gravitational wave spectrum observed in 2021 by the Pulsar Timing Array Collaboration.

Phys.org spoke with the study’s first author, Dr. Gonzalo Alonso-Alvarez, a postdoctoral researcher at the University of Toronto.

Speaking about the motivation for his team’s effort, he said: “When the Pulsar Timing Array Collaboration published evidence of a gravitational wave spectrum, what struck us most was that there was scope to test it. New particles Physical scenarios, specifically Dark matter Even within the standard astrophysical explanation of supermassive black hole mergers, there is no self-interaction.”

Why stop at one parsec?

When the SMBHs from two merging galaxies are one parsec apart, two opposing effects arise.

First, large objects like SMBHs cause ripples in space-time, leading to the formation of gravitational waves that travel through space-time. These gravitational waves carry energy away from their source. When two SMBHs merge, the gravitational waves carry energy away from the merged part, causing the black hole to spiral inward more rapidly.

The second force is called kinetic friction. When a massive object like a black hole passes through a medium (such as dust or stars), it leaves behind a trail of turbulent fluid called a wake. For example, when a ship moves through water, it leaves behind a trail of turbulent water behind it – that’s its wake.

Particles attracted to an SMBH by gravity can cause a drag force, or kinetic friction. This friction resists the motion of the massive object, forcing it to slow down. If two SMBHs merge, this can cause them to stop moving towards each other.

“Previous calculations suggest that this process stops when the black holes are about one parsec apart, a situation sometimes referred to as the Final Parsec Problem,” Dr Alvarez explained.

This is where kinetic friction comes into play: it can either hinder or help the two SMBHs from merging.

Self-interacting dark matter

Researchers have proposed that some form of dark matter could be a solution to this problem.

“In this paper, we show that taking into account the previously overlooked influence of dark matter can help black holes survive this final parsec separation and merger, emitting a gravitational wave signal that is consistent with what has been observed with the Pulsar Timing Array,” said Dr Alvarez.

In galaxies, dark matter resides primarily in the galactic halo, the region that surrounds the visible galaxy, but it also exists close to the galactic nucleus where SMBHs reside, so the properties of dark matter may play an important role in the merger of SMBHs.

Self-interacting dark matter (SIDM) is a hypothesized form of dark matter in which dark matter particles interact with each other through new, unknown forces.

In galaxies containing SIDMs, interactions between dark matter particles may affect the density (distribution) and velocity of dark matter, leading to a more efficient centralization of matter and energy in SMBHs, overcoming dynamical friction.

A delicate balance

To investigate the role of SIDM in SMBH mergers, the researchers performed detailed calculations of the dark matter density profile around the SMBH, for SIDM and cold dark matter (which has fewer interactions).

They also modeled the effects of dynamical friction on the SMBH orbit, calculated the energy transfer between the SMBH and dark matter, and performed simulations of gravitational wave spectra under different dark matter scenarios.

The researchers then compared these results with observational data from the Pulsar Timing Array.

The researchers found that the interaction cross section of the dark matter particles needs to be in an optimal range: the larger the cross section, the more frequent the interactions, leading to dark matter particles interacting and scattering, resulting in a flatter density profile near the SMBH.

This decrease in density reduces the kinetic friction required for SMBH coalescence.

“On the other hand, sufficiently frequent dark matter self-interactions are needed to prevent this profile from being dispersed by the motion of the black hole,” Dr. Alvarez explained.

The ideal range of cross sections would allow enough interactions to affect the motion of the SMBHs without dispersing the dark matter too much, thereby maintaining enough dynamical friction to aid the merging process.

The researchers found this value to be between 2.5 and 25 cm.²/g, which means that for every gram of dark matter, the effective area over which particles interact is between 2.5 and 25 square centimeters.

Rate-dependent interactions

The researchers also found that the speed of the SIDM particles must be optimal, and this speed is influenced by the mass of an unknown force carrier or mediator that drives the interaction between the SIDM particles.

If the intermediary is heavy, it Dark matter particles Significant interactions only occur when they are moving slowly relative to each other. Conversely, interactions can occur at higher speeds if the intermediary object is lighter.

“Interestingly, this velocity dependence is well supported theoretically: it is exactly what is found when the mass of the particle acting as the carrier of the dark matter self-interaction force is around 1 percent of the mass of the dark matter particle,” Dr. Alvarez said.

The researchers estimated this value to be between 300 and 600 km/s.

“These velocity-dependent self-interactions leave a signature in the gravitational wave spectrum because when the black holes are only a parsec apart, a significant fraction of their orbital energy is lost to dark matter friction rather than through the emission of gravitational waves, resulting in a relative suppression of the gravitational wave signal at some frequencies compared to others,” Dr Alvarez added.

Implications and future initiatives

The researchers’ SIDM particle model: Gravitational waves At lower frequencies, the signal becomes weaker or less intense. This prediction is consistent with what is observed in the actual data.

We also show that SIDM with velocity-dependent cross sections can solve the final parsec problem and survive the merger process.

Dr. Alvarez said of the impact of his research: “We found that the orbital evolution of black holes is highly sensitive to the microphysics of dark matter, which means that we can use the gravitational wave emission of SMBH binaries to constrain dark matter models. This provides a new window to investigate the nature of dark matter in the innermost regions of galaxies, which were previously inaccessible by observations.”

The team also refined the model, Numerical simulation To confirm the results found in this paper, these simulations will help improve our understanding of how the dark matter profile responds to the energy injected by merging black holes.

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