A new study uses dark matter that affects itself to solve the ultimate parsec problem

In a new study, scientists from Canada have proposed a solution to the finite parsec problem of merging supermassive black holes (SMBHs) using self-interacting dark matter.

When two galaxies merge, gas and dust collide to form stars. However, the stars themselves do not collide due to their vast distances. The SMBHs at the center of the two galaxies are also beginning to merge.

However, black holes stop merging when they are 1 parsec (or 30.9 trillion kilometers) apart. This problem is known as the finite parsec problem in astronomy and astrophysics.

The study, published in Physical Inspection Letters (PRLs)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, postdoc at the University of Toronto.

Speaking about the motivation behind the team’s work, he said: “What struck us most when the Pulsar Timing Array collaboration reported evidence for a gravitational wave spectrum is that there is scope for testing new scenarios in particle physics, specifically the self-interaction of dark matter, even within the standard astrophysical explanation of supermassive black hole mergers.”

Why stop at 1 parsec?

When the SMBHs of two merging galaxies are separated by 1 parsec, there are two opposing things at play.

First, large objects like the SMBH cause ripples in space-time, giving rise to gravitational waves that travel through space-time. These gravitational waves carry energy away from the source. When two SMBHs merge, gravitational waves carry energy away from the merger, causing the black holes to spiral inward faster.

The other is a frictional force called dynamic friction. When massive objects such as black holes travel through the medium (such as dust and stars), they have a wake of disturbed fluid called a wake. For example, when a ship moves through water, it leaves behind a turbulent water wake; this is his wake.

Particles attracted to the SMBH by gravity can cause a drag force, which is dynamic friction. This friction prevents the massive object from moving and makes it slow down. In the case of two SMBHs merging, this can cause them to stop moving towards each other.

“Previous calculations found that this process stops when the black holes are about 1 parsec apart, a situation sometimes referred to as the finite parsec problem,” explained Dr. Alvarez.

This is where dynamic friction comes into play. This can either oppose or assist the merger of the two SMBHs.

Self-interacting dark matter

Scientists suggest that the solution to this problem could be a form of dark matter.

“In this paper, we show that including the previously overlooked dark matter effect can help black holes overcome this last parsec of separation and merge, thus emitting a gravitational wave signal that matches the signal observed by Pulsar Timing Arrays,” said Dr. Alvarez. .

In a galaxy, dark matter is mostly present in the galactic halo, the region surrounding the visible galaxy. But it is also present near the galactic core where the SMBH is present. Therefore, the nature of dark matter could play a crucial role in SMBH coupling.

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

In galaxies containing SIDMs, interactions between dark matter particles can affect the density (distribution) and velocity of dark matter, leading to a more efficient flow of mass and energy towards the SMBH, which could potentially overcome dynamical friction.

A fine balance

To investigate the role of the SIDM in the SMBH coupling, the researchers performed detailed calculations of the dark matter density profiles around the SMBH for the SIDM and the cold (less interacting) dark matter.

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 in different dark matter scenarios.

They then compared these results with observational data from pulsar timing fields.

The researchers found that the interaction cross-section of dark matter particles must be in the optimal range. A larger cross-sectional area, implying more frequent interactions, causes dark matter particles to interact and scatter, flattening the density profile near the SMBH.

This reduction in density reduces the dynamic friction necessary for SMBH coupling.

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

The ideal cross-section range allows enough interactions to influence the motion of the SMBH without too much dark matter dissipation, thereby maintaining sufficient dynamical friction to aid the merger process.

The researchers found this value to be between 2.5 and 25 cm²/G. This means that for every gram of dark matter, the effective area over which the particles interact should be between 2.5 and 25 centimeters squared.

Rate-dependent interactions

The researchers also found that the speed of the SIDM particles must be optimal. This velocity is in turn affected by the unknown force carrier or mass of the mediator, which facilitates the interaction between the SIDM particles.

If the mediator is heavy, this could mean that dark matter particles interact significantly only when they are moving slowly relative to each other. Conversely, if light is the medium, interactions could occur at higher speeds.

“Interestingly, this velocity dependence is theoretically well motivated. It is exactly what one finds when the particle that acts as the force carrier for dark matter’s own interactions has a mass that is roughly 1 percent of the mass of a dark matter particle. ” Dr. Alvarez said.

Scientists estimated this value at 300 to 600 km/s.

“These velocity-dependent self-interactions leave an imprint on the gravitational wave spectrum, because when black holes are separated by a fraction of a parsec, a significant fraction of the orbital energy is lost through dark matter friction rather than gravitational wave emission.” , thereby relatively suppressing the gravitational wave signal at some frequencies compared to others,” added Dr. Alvarez.

Implications and future work

The SIDM particle research model predicted that gravitational waves would be weaker or less intense at low frequencies. This prediction matched what was observed in the actual data.

They also showed that SIDM with a rate-dependent cross-section can solve the finite parsec problem and survive the merging process.

When talking about the impact of their work, Dr. Alvarez said: “We found that the evolution of the black hole’s orbit is very sensitive to the microphysics of dark matter, which means we can use the gravitational wave emission of SMBH binaries to constrain the dark matter.” This offers a new window to investigate the nature of dark matter in the innermost regions of galaxies, previously inaccessible to observations.”

The team is also refining their model and developing numerical simulations to confirm the results found in this paper. These simulations will provide a better understanding of how dark matter profiles respond to the energy injected by black hole mergers.

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