Title: Self-Interacting Dark Matter Solves the Final Parsec Problem of Supermassive Black Hole Merger
Authors: Gonzalo Alonso-Álvarez, James M. Cline, and Caitlyn Dewar
First author institution: University of Toronto, Toronto, ON, Canada
Status: Published in Physics Review Letters [open access]
Last year, multiple pulsar timing array (PTA) experiments published evidence for a nanohertz-frequency stochastic gravitational wave background (GWB) – a hum of overlapping gravitational waves (GW) coming from all directions in the universe. The origin of the GWB is still to be determined. Is it from a ‘cosmological’ source, such as from cosmic strings or cosmological phase transitions, or is it from a population of supermassive black hole binaries (SMBHBs)?
SMBHBs are regarded as the most likely source because this explanation doesn’t require invoking unproven new physics. However, there are some issues with the current SMBHB model. A SMBHB is formed when two galaxies merge. The black holes at the centers of those galaxies fall towards the new, common center, where the pair interact gravitationally, forming a binary. As the black holes orbit around each other, they emit GWs, hence they lose angular momentum and begin to inspiral towards each other. The closer they become, the more energetic and higher the frequency of the GWs they emit, causing them to inspiral faster. Eventually, they should merge.
Observationally, this makes sense – we see single supermassive black holes at the centers of local galaxies such as M87. However, this model doesn’t quite work, because the GWs emitted are so weak that it’d take longer than the age of the universe for the SMBHBs to merge, which suggests that we should actually observe SMBHBs in the centers of local galaxies. The SMBHBs should ‘stall’ in the final parsec of separation, hence the ‘final parsec problem.’
There are a few solutions to this problem: interactions between the SMBHB and its gaseous and stellar environment would drive the inspiral faster, with stars available for interactions being replenished by a triaxially-shaped galactic halo. This is what PTA experiments are hoping to probe, but don’t have the sensitivity to measure yet. In the meantime, other explanations are also being theorised.
In today’s paper, the authors present a new solution, requiring a certain type of dark matter. The nature of dark matter is still enigmatic, however, we do have an idea of how it should behave and some of its properties. The leading model of the cosmos, ‘Lambda-CDM,’ requires a universe containing collisionless cold dark matter (CDM), which moves very slowly compared to the speed of light. Because dark matter interacts gravitationally, we’d expect it to accumulate around black holes, creating a ‘spike’ in density. When the SMBHB inspirals, it also interacts gravitationally with the surrounding dark matter spike, causing it to slow down. This dynamical friction accelerates the inspiral such that the SMBHB will merge over a faster timescale.
How could PTAs determine that dark matter is helping to drive the inspiral? If there were no interactions between the SMBHB and dark matter, we’d expect to observe a power-law-shaped GW spectrum (see the dashed, red line in Fig. 2). If there are interactions between SMBHB and dark matter, then the effect is stronger at larger separations, i.e. lower GW frequencies, because the GWs being emitted are weaker here. Because the inspiral is being accelerated, the SMBHB is emitting GW at the lower frequencies for less time, therefore the spectrum is expected to be weaker than the power-law at these frequencies. Hence, if we observe a low-frequency ‘turnover,’ it could suggest interactions with dark matter.
The authors investigate two types of theorised dark matter – CDM, as previously mentioned, and self-interacting dark matter (SIDM), which interacts strongly with itself – and if current PTA data supports their existence. Against raw data (see Figure 2), it appears that both CDM and SIDM fit the data. However, CDM has a problem. As the SMBHB interacts with the CDM by dynamical friction, it heats the CDM. This causes the CDM density spike to disperse, causing it to become less dense, and weakening the effect of dynamical friction on the SMBHB. Therefore, while the CDM model fits the data, it is not a physically viable solution.
In contrast, when dynamical friction heats the SIDM, the self-interactions between the dark matter replenish the density spike, allowing for further dynamical friction to drive the SMBHB inspiral. The timescale to merge for a circular SMBHB, where the primary black hole has a mass of 3×109 
To determine if SIDM is an important ingredient in the evolution of SMBHBs, more PTA data will be required. This will allow us to discriminate between the effects from dark matter with the effects from stars and circumbinary gas interacting with the SMBHBs. That data will be continuously published over the next decade from various PTA experiments, so hopefully, we’ll have our answer soon.
Edited by Kylee Carden
Featured image: NASA’s Goddard Space Flight Center/Scott Noble; simulation data, d’Ascoli et al. 2018
Discover more from astrobites
Subscribe to get the latest posts to your email.
Related posts:
How to Find Supermassive Black Hole Binaries in Pulsar Timing Array data without the Pulsars
Drop the Bass: Evidence for a Gravitational Wave Background from a Galaxy-sized Detector
Continued analysis on the continuous search for continuous waves (continued)
Counting supermassive black hole binaries with customers at a coffee shop
Since dark matter does not interact with normal matter via the electromagnetic force, one could argue that the Eddington limit does not apply, and that SMBH’s should be able to ingest massive amounts of dark matter through gravity alone. What would that do to influence the Final Parsec problem?
Huh, that’s a really interesting thought. I don’t know, but you’re correct that the Eddington limit won’t apply – at least for collisionless CDM. SIDM could be different, because there are interactions between SIDM particles (or whatever it is..?). mediated by a different force. Perhaps DM has a different Eddington limit that based on a different force that mediates between dark matter.
I talked to professors in my department and they say that yes, there isn’t an Eddington Limit for collisionless cold dark matter and the black hole *theoretically* could continue to accrete dark matter indefinitely
The problem is, dark matter is incredibly diffuse throughout the universe. Whatever amount of it there is, isn’t a lot. Also, because it doesn’t interact with itself or anything else (except through gravity), then whatever amount of dark matter is accreted by the black hole isn’t replenished. So, the black hole takes in the dark matter directly surrounding it, until there’s no more dark matter within its direct viscinity to continue to feed it. So regardless of if there’s an Eddington Limit or not, there’s just not enough dark matter to continue to feed the black hole
Therefore, it wouldn’t hae an affect on the Final Parsec Problem. Really, it just exacerbates it, unless you have something like self-interacting dark matter (SIDM) that can continue to replenish itself around the black hole and continue to interact with and accrete into it
Very well explained. Thank you.
Although its a bit unclear what the author meant by “as it interacts with the SMBHB, it’ll heat up and disperse….” Is that possible? For the CDM to be heated up and dispersed?
That’s a great question caused by my poor explaining! When we say “temperature,” we usually mean the average kinetic energy of particles. Hot dark matter have high average velocities, while CDM, being “cold,” have small average kinetic energies. As the SMBHBs interact gravitationally with the CDM, it increases the average kinetic energy of the CDM particles, increasing their “temperature.”
Got it. Thank you.