Friday, February 17, 2023

Observational Evidence for Cosmological Coupling of Black Holes and its Implications for an Astrophysical Source of Dark Energy

This series of papers are very interesting. The results are a two-part series published in ApJ

The Astrophysical Journal:

The assembly of stellar and supermassive black hole (SMBH) mass in elliptical galaxies since z ∼ 1 can help to diagnose the origins of locally observed correlations between SMBH mass and stellar mass.

Using a Bayesian analysis framework, we find evidence for translational offsets in both stellar mass and SMBH mass between the local sample and both higher-redshift samples.

We conclude that either there is a physical mechanism that preferentially grows SMBHs in elliptical galaxies at z ≲ 2, or that selection and measurement biases are both underestimated, and depend on redshift.

The Astrophysical Journal (via arXiv):

The Kerr black hole solution is, however, provisional as its behavior at infinity is incompatible with an expanding universe. Black hole models with realistic behavior at infinity predict that the gravitating mass of a black hole can increase with the expansion of the universe independently of accretion or mergers, in a manner that depends on the black hole’s interior solution. We test this prediction by considering the growth of supermassive black holes in elliptical galaxies over 0 < z ≲ 2.5. We find evidence for cosmologically coupled mass growth among these black holes, with zero cosmological coupling excluded at 99.98% confidence.

We thus propose that stellar remnant black holes are the astrophysical origin of dark energy, explaining the onset of accelerating expansion at z ∼ 0.7.

These results are astonishingly consistent with current theoretical prediction for this kind of empirical analysis. But reading the second paper, I'm left a little confused by the nature of the coupling, and whether or not a viable physical mechanism exists within our current understanding.

We show that k = 3 stellar remnant BHs produce the measured value of ΩΛ within a wide range of observationally viable cosmic star formation histories, stellar IMFs, and remnant accretion. They remain consistent with constraints on halo compact objects and they naturally explain the “coincidence problem,” because dark energy domination can only occur after cosmic dawn. Taken together, we propose that stellar remnant k = 3 BHs are the astrophysical origin for the late-time accelerating expansion of the universe.

But a team of 17 international researchers led by the University of Hawaii has discovered the first evidence for the origin point of dark energy: Black holes.

The idea that black holes are a source of dark energy isn't new. In fact, it's part of Einstein's theory of general relativity. But this is the first time astronomers have obtained observational evidence to support the theory. 

The Guardian

Instead of dark energy being smeared out across spacetime, as many physicists have assumed, the scientists suggest that it is created and remains inside black holes, which form in the crushing forces of collapsing stars.

“We propose that black holes are the source for dark energy,” said Duncan Farrah, an astronomer at the University of Hawaii. “This dark energy is produced when normal matter is compressed during the death and collapse of large stars.”

The claim was met with raised eyebrows from some independent experts, with one noting that while the idea deserved scrutiny, it was far too early to link black holes and dark energy. “There’s a number of counter-arguments and facts that need to be understood if this claim is going to live more than a few months,” said Vitor Cardoso, a professor of physics at the Niels Bohr Institute in Copenhagen.

Vitor is a brilliant guy--I'm very curious to hear more of his thoughts as the theory gets tested more in the academic community.

“The importance of this work is that it’s taken the theories about black holes with dark energy cores and linked them for the first time to tangible observations of the universe,” said Chris Pearson, a co-author on the study and Astronomy Group Leader at STFC RAL Space in Oxfordshire. “These black holes are expected to grow in mass as the universe expands.”

But far more work is needed before it will gain acceptance. Among many questions remaining is how black holes can pull everything nearby towards them while simultaneously driving the universe apart.

Feels like a critical question there. A lot of scientists seem to be skeptical specifically because there doesn't seem to be a fundamental mechanism proposed for the cosmic coupling.

Ethan Siegel (via BigThink):

Which is why it was an absolute shock to see the headline appear, just days ago, that “Black holes are the source of dark energy.” Even more surprisingly — at least, to me — was that when I went into the scientific paper itself, this was based not on a theoretical calculation, but rather on observational evidence, which was absolutely shocking to see. The overall claim is that black holes, and specifically, supermassive black holes, couple to the Universe’s expansion on the largest cosmic scales, and that the specific way that they must couple could potentially explain some or even all of the dark energy effects we observe.

How do you do this? The approach the authors take is as follows.

They look at multiple samples of elliptical galaxies from across cosmic time: nearby (modern) galaxies, galaxies from ~6.6 billion years ago, galaxies from ~7.2 billion years ago, and galaxies from ~9.6 billion years ago.

They assume that there’s a universal relationship between the mass of the central black hole and the mass of the stars within a galaxy, which can evolve over cosmic time but should be universal at any particular time.

Then, they use their model of “cosmological coupling,” assuming there exists a relationship between the mass of a black hole at any particular cosmic time (or, more accurately, redshift) and the mass of the black hole at the time it “becomes cosmically coupled” to the expansion rate, to determine whether (and, if so, how) the coupling parameter, k, has the same value across cosmic time...if k = 3, then the coupling is at the maximum allowable value, and the mass of the black hole increases as the cube of the redshift ratio, and the black hole acts like it causes dark energy.

They find k=3 to a 3-sigma confidence level, and rule out the "default" k=0 case with a 99.98% certainty. Ethan is unconvinced, however, as they fail to put forth a meaningful mechanism as to how black holes grow and evolve over cosmic time.

But I think the default assumption should be that these black holes are really just behaving as any other mass in the Universe behaves, and that this empirical approach of “We’re going to measure the masses of supermassive black holes and stars in elliptical galaxies and use that to infer the cosmological coupling” totally glosses over the big astrophysics question that should be investigated: how do these black holes grow and evolve over cosmic time? Until you know that answer, you’re attributing a measured effect to what might be entirely the wrong cause.

Sabine Hossenfelder (via Twitter):

Yes, I've seen the headlines saying that black holes may be dark energy.  I think that's extremely implausible. First of all, the statement is immediately contradictory because what we mean by "dark energy" is defined by having a particular equation of state. A collection of black holes does not have the right equation of state, so it can't be dark energy. 

Then they say, we ASSUME that this extra growth comes from a cosmological source. And then there's some bla-bla about pressure and energy conservation saying that therefore it needs to be a type of dark energy. I can't follow the argument.

This means the argument in the paper basically comes down to saying: We have two things that we don't understand (a) growth of supermassive black holes and (b) the origin of dark energy. We assume they're linked and if we assume they're linked the stat significance is high.

To say the hopefully obvious, assuming that two things are related doesn't show they're related. 

Her interview about physics as a religion under the guise of mathematics was a very fun read. I'll keep updating this post with qualified opinions I run across, and my own thoughts as I get a better look at the papers.

(Updates to original post below)

If true, the connection would link two of the most mind-bending concepts in physics—black holes and dark energy—and suggest that the source of the latter has been under theorists’ noses for decades. However, some leading theorists are deeply skeptical of the idea.

“What they are proposing makes no sense to me,” says Robert Wald, a theoretical physicist at the University of Chicago who specializes in Albert Einstein’s general theory of relativity, the standard understanding of gravity.

Wald is unpersuaded. He questions how an orb of pure dark energy could be stable. He also says the numbers don’t seem to add up: Dark energy is known to make up 70% of the mass-energy of the universe, whereas black holes are a mere fraction of the ordinary matter, which constitutes less than 5% of the universe. “I don't see how it is in any way conceivable that such objects could be relevant to the observed dark energy,” he says.

Bob Wald not being on board is a pretty bad sign. I learned (as did many other students) general relativity from his classic texts. He is pretty broadly considered a leading expert in the field.

Other theorists were more receptive to the radical claim—even if it ends up being wrong. “I’m personally excited about it,” says astrophysicist Niayesh Afshordi of the Perimeter Institute for Theoretical Physics.

Nevertheless, Afshordi is supportive of efforts to rethink fundamental assumptions about the universe. “Most new theoretical ideas are dismissed by skepticism,” he says. “But if we dismiss all the new ideas then there won’t be anything left.”

This is an excellent point. Even if this proposed idea it ends up being incorrect, it has raised an incredibly interesting question about a particular subset of black holes. The black holes examined in the Farrah et al. dataset were chosen to be black holes who would have relatively constant mass over the eons. But a clear non-constant relationship is found in their distribution function. Even if these black holes are not dark energy as the paper proposes, what causes this? The article summarizes this but doesn't actually ask this question:

To test this possibility, Farrah and his colleagues studied elliptical galaxies, which contain black holes with millions or billions of times the Sun’s mass in their centers. They focused on galaxies with little gas or dust floating around between their stars, which would provide a reservoir of material that the central black hole could feed on. Such black holes wouldn’t be expected to change much over the course of cosmic history.

Yet by analyzing the properties of ellipticals over roughly 9 billion years, the team saw that black holes in the early universe were much smaller relative to their host galaxy than those in the modern universe, indicating they had grown by a factor of seven to 10 times in mass, Farrah and colleagues reported this month in the Astrophysical Journal.

Assuming this isn't the result of dark energy as the study proposes, it's still a compelling mystery. To our understanding, these black holes shouldn't be growing, and yet they did--by an order of magnitude in some cases. 

Oxford Student:

This evidence may appear strong, but the physics community is not wholly convinced. Dr Chris Pearson, a co-author of the study, stated “If the theory holds, this is going to revolutionise the whole of cosmology.” Pearson is a researcher at the Rutherford Appleton Laboratory, located just outside of Oxford.  Other cosmologists are taking a more measured approach, waiting for “a lot more evidence” before fully committing to the idea. Theoretical physicists feel that this does not quite solve the mystery, with concerns about how the proposed “ball of dark energy” could remain stable (i.e not explode, collapse, or otherwise become something else). It is clear that there is more work to be done, but this could be the beginning of something very exciting.


At the risk of repeating the overused adage, “extraordinary claims require extraordinary evidence.” The ability to verify results repeatedly is one of the most important qualifiers for evidence to be considered sound. In other words, results must be demonstratable again and again and (preferably) using varying methods. The authors acknowledge this and hope that repeated observations will bear them out. But for the time being, the claim they’ve made remains extraordinary and (given the implications) demands further investigation.

PhysicsWorld (linked here):

The new theory hasn’t passed without controversy in physics circles, with many researchers unwilling to accept this cosmological coupling just yet.

“I can spot things that are troubling,” Universidad ECCI cosmologist Luz Ángela García tells Physics World. “Saying that their observation sets evidence for black holes being made out of dark energy seems like a long shot, in particular, because we cannot perform measurements ‘inside’ the black hole.”

García is also troubled by the fact that by linking dark energy to black holes, the team’s theory connects this force to the life cycle of stars, describing it as “very risky”. This is because when scientists consider the energy–matter content of the universe, black holes and thus dark energy in this model have already been accounted for in the 5% “ordinary matter” proportion of the energy–matter content of the universe.

Finally, García notes that the timeline of the universe leaves a gap of two billion years that the team’s theory struggles to fill.

“The peak of the number of black holes and quasars coincides with the peak of the star formation history approximately 10 billion years ago, and after that there’s a rapid decline in the number of these massive objects,” she explains. “On the other hand, the kickstart of the dark-energy domination occurs more or less eight billion years ago.”

This article has a quote from Dr. Farrah regarding the "controversy":

Farrah himself concurs that the mystery of dark energy is far from solved, acknowledging that while the two papers provide evidence of an astrophysical source for dark energy, their argument needs much more scrutiny.

“Dark energy remains a deeply mysterious phenomenon,” Farrah concludes. “I would say our papers raise the possibility of black holes as a source for dark energy and provide an ‘interesting hypothesis’, but at present, no more than that.”

I put "controversy" in quotes because while there is a lot of disagreement in the community about the validity of the theory, "controversy" has a very gross inappropriate drama-esque association with it. Fundamentally, nothing about the paper is inappropriate or "controversial" in this sense. Farrah and his team split the work into two distinct volumes; the first providing a solid report on an exciting data analysis, leaving 100% of the interpretation for the second volume. Do you notice how no one is casting much doubt on the first of the papers? It's because their actual data analysis is excellent; it's the interpretation scientists are disagreeing on. Farrah recognizes this himself in his quotes and interviews. Not only was it a smart thing to do (to avoid any "guilt by association" with the data analysis), it was also (in my opinion) a very responsible thing to do. The data are untainted by the interpretation, and the interpretation is not lent undue credibility by the solid data analysis.

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