This guest post was written by Indranil Banik, a Humboldt postdoctoral research fellow at the University of Bonn. Indranil works on a variety of tests exploring whether gravity in the weak field regime follows the Milgromian rather than the Newtonian law, which seems very likely given current evidence, and also tests the related hypothesis of galaxies having their own dark matter halos. My work is accessible through ORCID (identifier 0000-0002-4123-7325).
Authors: Kyu-Hyun Chae, Federico Lelli, Harry Desmond, Stacy S. McGaugh, Pengfei Li, and James M. Schombert
First Author’s Institution: Sejong University, Seoul, Republic of Korea
Status: Accepted to ApJ, open access on arxiv
We’ve all heard the story of how an apple supposedly fell on Newton’s head and inspired him to write down ideas about gravity. Newton proposed that gravity is an invisible force that holds objects like the Earth and Moon in place. Little did he know, he was actually missing some pieces. Albert Einstein came along in the early 20th century and revolutionized the world with his idea that the force of gravity is actually the result of the curvature of an invisible fabric called spacetime, an idea we now call general relativity (GR). Though Newtonian gravity and GR rely on totally different principles, there is little noticeable difference in the case of relatively low speeds (i.e speeds much slower than the speed of light) and relatively weak gravity (i.e when you are not near a black hole).
Standard Newtonian gravity obeys the superposition principle, which says that the total gravitational field from a system of masses is equal to the sum of the gravitational fields from the individual masses. In systems such as the Solar System and the outer edges of galaxies, because the speeds are small and the gravity is relatively weak, Newtonian gravity, and hence the the superposition principle, is obeyed. Importantly, GR is the only relativistic theory of gravity (i.e. covering objects moving at any velocity) that obeys the Strong Equivalence Principle exactly in all domains of gravity. This principle states that in any freely falling local inertial frame (experiencing only gravitational forces), all physics is unaffected by the external field, including internal dynamics under self-gravity. Take our Milky Way galaxy, which feels gravity from other galaxies like Andromeda. The Strong Equivalence Principle says that if we measure the acceleration of the Solar System relative to the Milky Way, the external gravitational fields from other galaxies should not influence the measurement.
This has never been directly tested. In a more complicated gravity theory, a constant background gravitational field on an experiment might affect its results beyond just moving the system as a whole. This is more complicated than assuming the superposition principle holds (as in GR), but since our description of gravity is far from complete and not compatible with quantum mechanics, perhaps superposition is just a useful approximation.
This is where galaxies come in: their typical rotation periods are roughly a billion years, allowing small differences in the gravity to accumulate to big differences in the velocity. We can use the measured rotational velocity v at distance r to deduce the orbital acceleration v2/r, even if this is so low it cannot be directly measured. Each galaxy also accelerates as a whole due to the external gravitational fields from surrounding structures like other galaxies.
This study shows that galaxies experiencing a stronger external field do in fact have weaker self-gravity (rotate slower) than similar galaxies in weaker external field environments, building on a similar previous work. As the external field is relatively more important further from the galaxy, its rotation curve shape (a plot of a galaxy’s rotation speed against distance from its center) is also different — it declines in the outskirts with a strong external field (Figure 1), but remains flat with a weak external field (Figure 2). Observation of just this represents a statistically significant, robust detection of the external field effect in the internal dynamics of rotating disc galaxies. The results of the new study are more comprehensive and robust than any previous attempt. There were individual detections based on comparing well-measured galaxies experiencing very strong and weak external fields from their environment, as well as statistical detections from more than 100 disc galaxies feeling a more typical external field.
The results indicate that GR (and Newtonian gravity) break down when the gravity g is weaker than a0, a new fundamental acceleration constant of nature. All the experimental successes of GR – including Solar System tests, black holes, and gravitational waves – are in the strong gravity domain (g > a0), so the new results for the weak gravity domain are fully consistent with previous results. Galaxy rotation curves are one of the few probes of the weak gravity domain.
In this regime, there is much other evidence for GR breaking down. The gravity g inferred from rotation curves often greatly exceeds the expectation gN based on applying Newtonian gravity to the visible mass. This could be due to halos of cold dark matter surrounding galaxies, but then galaxies with different star formation rates, merger histories etc. might have different amounts of visible and dark matter. However, there is an extremely tight correlation between the observed and predicted gravity in galaxies with widely different properties spanning many orders of magnitude in parameters like luminosity. Galaxy rotation curves can thus be predicted from their visible mass alone, which according to Occam’s Razor is a strong hint that only visible mass is present. If so, gravity must be non-Newtonian, with Modified Newtonian Dynamics (MOND) being the leading alternative. Its basic idea is that in the strong gravity regime, the actual and Newtonian-predicted gravity are the same to recover Solar System results. But if gN is much weaker than a0, then g = √(a0*gN). The square root causes the rotation curve of an isolated galaxy to be flat at a large distance, unlike the Keplerian 1/√r decline observed in the Solar System. Importantly, it implies that gravity is non-linear in the mass distribution ‒ if a mass causes gravity x, then doubling the mass would only strengthen the gravity to 1.41x. Applying MOND to more complicated systems requires solving an equation for the gravitational field.
If a galaxy’s internal gravity is very weak, we might expect MOND effects to cause g >> gN. This is often the case, but only if the galaxy is isolated. If there is a massive galaxy nearby that creates a strong gravitational field >> a0, then the internal dynamics of the first galaxy become Newtonian (g = gN). There is of course a continuum between these extremes, with a stronger external field weakening the self-gravity. The current study found just such a correlation, confirming the MOND prediction.
MOND can also be applied to relativistic phenomena like gravitational waves. In the relativistic MOND theory of Skordis & Zlosnik 2019, these waves should travel at the speed of light, as observed. Other evidence for MOND is discussed here.
This study supports previous works that we must reconsider the assumption of galaxies obeying GR and having their own halos of cold dark matter, which were only invented to preserve this >100 year old non-quantum theory built solely on evidence gathered within the Solar System. Our gravitational theories need to be revised, causing significant changes to the overall cosmological paradigm. For strong evidence of this from large scale structure and discussion of a possible alternative paradigm, check out this article.
Featured image credit: M. A. Garlick/Wikipedia Creative Commons
Edited by: Haley Wahl