We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxies.Stacy McGaugh, Federico Lelli, Jim Schombert, "The Radial Acceleration Relation in Rotationally Supported Galaxies" (September 19, 2016).
The dynamics of galaxies of almost every kind can be fully explained by the distribution of ordinary matter in those galaxies.
Specifically, the observed gravitational potential (gobs) is a function of the baryonic gravitational potential (gbar) of the form:
where g† is an acceleration scale physical constant with a value of g† = 1.20 ± 0.02 (random) ±0.24 (systematic)×10−10 m s−2. The random error is a 1σ value, while the systematic uncertainty represents the 20% normalization uncertainty in the mass-luminosity ratio Y. A discussion in the paper explains that much of the error involves uncertainty in accurately determining the ordinary matter mass of a galaxy and accurately measuring rotation speeds.
Stated slightly differently, the gravitational potential attributable to dark matter, gDM=gobs-gbar and this in turn is expressed by the formula:
As a result, one of two things must be true. Either General Relativity is not an accurate description of weak gravitational fields and need to be modified in some fashion to reflect this reality, or there is some mechanism by which the distribution of dark matter in a galaxy and the distribution of ordinary matter in a galaxy are rigidly intertwined. The paper expresses the idea in this way (emphasis added, citations omitted):
Possible interpretations for the radial acceleration relation fall into three broad categories.1. It represents the end product of galaxy formation.2. It represents new dark sector physics that leads to the observed coupling.3. It is the result of new dynamical laws rather than dark matter.None of these options are entirely satisfactory.
In the standard cosmological paradigm, galaxies form within dark matter halos. Simulations of this process do not naturally lead to realistic galaxies. Complicated accessory effects (“feedback”) must be invoked to remodel simulated galaxies into something more akin to observations. Whether such processes can satisfactorily explain the radial acceleration relation and its small scatter remains to be demonstrated.
Another possibility is new “dark sector” physics. The dark matter needs to respond to the distribution of baryons (or vice-versa) in order to give the observed relation. This is not trivial to achieve, but the observed phenomenology might emerge if dark matter behaves as a fluid or is subject to gravitational polarization.
Thirdly, the one-to-one correspondence between gbar and gobs suggests that the baryons are the source of the gravitational potential. In this case, one might alter the laws of dynamics rather than invoke dark matter. Indeed, our results were anticipated over three decades ago by MOND. Whether this is a situation in which it would be necessary to invent MOND if it did not already exist is worthy of contemplation.
In MOND, eq. 4 [ed. the first equation above] is related to the MOND interpolation function. However, we should be careful not to confuse data with theory. Equation 4 provides a convenient description of the data irrespective of MOND.
Regardless of its theoretical basis, the radial acceleration relation exists as an empirical relation. The acceleration scale g† is in the data. The observed coupling between gobs and gbar demands a satisfactory explanation. The radial acceleration relation appears to be a law of nature, a sort of Kepler’s law for rotating galaxies
Nothing axiomatic about dark matter theories explains why there is such a tight relationship between the distribution of ordinary matter and the distribution of dark matter in a galaxy, although a wide variety of dark matter theories approximately reproduce observed galactic behavior. But, this could simply reflect our ignorance of an emergent property of what is naively a pretty simple dark matter model.
In this paper McGaugh, a leading physicists advocating for a gravity modification solution to dark matter phenomena in other publications, doesn't resolve that question.
In particular, what his paper silently suggests is that if you want to test a dark matter model, you shouldn't just do simulations. You should be able to produce the simple and tight analytical relationship that McGaugh derives from observation from your reasoning about how dark matter halos form in your model in the presence of ordinary matter. If that isn't possible, your dark matter model is probably wrong.
It also silently makes the point that if this empirical formula can describe reality which a single parameter within the domain of applicability, that any correct dark matter theory ought to be able to either do the same, or get a much tighter fit to the data with each additional parameter (which is almost impossible at this time because the magnitude of the observational uncertainty about the data points in this study is large enough to account for essentially all of the uncertainty and scatter in the final result).
An article discussing the paper is here, and the main fault in the article is the assumption that this research is new or groundbreaking, when it really simply sums up conclusions that have been widely discussed ever since Dr. Milgrom published his first paper on the topic thirty-four years ago in 1982 in which the theory is dubbed MOND.
Since 1982, MOND has on more than one occasion accurately predicted the dynamics of new kinds of gravitational systems that had not previously been observed, while dark matter theories did not.
MOND in its original conceptual was not relativistic, it was a modification of Newtonian gravity which we have known is flawed for a century, even though it is used for many practical purposes in terrestrial, solar system, and galactic scale calculations.
Fortunately, new data will allow the discussion to continue on a genuine scientific footing. It also helps there there is no singular consensus on exactly how gravity should be modified or exactly what parameters the dark matter theory should have.
Consider for example, a point made by McGaugh in a 2010 conference presentation:
Consider for example, a point made by McGaugh in a 2010 conference presentation:
Scientists believe that all ordinary matter, the protons & neutrons that make up people, planets, stars and all that we can see, are a mere fraction -- some 17 percent -- of the total matter in the Universe. The protons and neutrons of ordinary matter are referred to as baryons in particle physics and cosmology.
The remaining 83 percent apparently is the mysterious "dark matter," the existence of which is inferred largely from its gravitational pull on visible matter. Dark matter, explains McGaugh "is presumed to be some new form of non-baryonic particle - the stuff scientists hope the Large Hadron Collider in CERN will create in high energy collisions between protons."
McGaugh and his colleagues posed the question of whether the "universal" ratio of baryonic matter to dark matter holds on the scales of individual structures like galaxies.
"One would expect galaxies and clusters of galaxies to be made of the same stuff as the universe as a whole, so if you make an accounting of the normal matter in each object, and its total mass, you ought to get the same 17 percent fraction," he says. "However, our work shows that individual objects have less ordinary matter, relative to dark matter, than you would expect from the cosmic mix; sometimes a lot less!"
Just how much less depends systematically on scale, according to the researchers. The smaller an object the further its ratio of ordinary matter to dark matter is from the cosmic mix. McGaugh says their work indicates that the largest bound structures, rich clusters of galaxies, have 14 percent of ordinary baryonic matter, close to expected 17 percent.
"As we looked at smaller objects - individual galaxies and satellite galaxies, the normal matter content gets steadily less," he says. "By the time we reach the smallest dwarf satellite galaxies, the content of normal matter is only ~1percent of what it should be. (Such galaxies' baryon content is ~0.2 percent instead of 17 percent). The variation of the baryon content is very systematic with scale. The smaller the galaxy, the smaller is its ratio of normal matter to dark matter. Put another way, the smallest galaxies are very dark matter dominated.In contrast, ellipical galaxies have far less dark matter relative to their ordinary matter content.