세종대학교

Breakdown of the Newton-Einstein Standard Gravity in Wide Binary Stars: A Revolution in Astrophysics and Cosmology

Prof. Kyu-Hyun Chae

at Department of Physics and Astronomy

1. Introduction and Newton’s universal law of gravitation

The observed universe consists of a hierarchy of gravitating systems. Earth maintains itself under its self-gravity, while the Moon orbits around Earth under their mutual gravity. Planets and other solar system bodies orbit around the Sun under the dominant influence of the Sun’s gravity. The Sun and hundreds of billions of fellow stars travel along their own orbits under the influence of the aggregate gravity of all constituents of the Milky Way galaxy. The Milky Way and other uncountable galaxies reside in the expanse of the universe. Some galaxies interact gravitationally one another in a group or cluster. The expansion dynamics of the universe itself is governed by gravity.

The nature of gravity began to reveal itself through the empirical mathematical rules of the planetary motions in the solar system, as uncovered by Johannes Kepler between 1609-1619, drawing from the database established by Tyco Brahe through his lifetime’s work. Kepler’s laws led to the discovery of Newton’s universal law of gravitation. This law has the elegance of simplicity: it dictates that any two masses exert an attractive force upon each other that is inversely proportional to the square of the distance between them. Newton’s gravity appeared to explain all gravitational dynamics on Earth as initially studied by Galileo Galilei and in the solar system as revealed by Kepler's laws, perhaps even in the entire universe since galaxies and the expansion of the universe were not known in Newton’s time.

2. The gravitational anomaly in strong gravity: The advent of Einstein’s general relativity

During the nineteenth century, Urbain Le Verrier and other astronomers studied the motions of planets. In 1859, Le Verrier noticed that the precession of Mercury’s orbit around the Sun could not be fully explained by the Newtonian gravity of the Sun and perturbations exerted by the known planets. This gravitational anomaly (the apparent anomaly in Uranus’s orbit was explained by the discovery of Neptune) was real and meant the breakdown of Newton’s gravity in relatively strong gravity.

The gravitational anomaly eventually led to Einstein’s groundbreaking theory of gravity, general relativity, which is consistent with Einstein’s new theory of mechanics and spacetime, special relativity. General relativity was completed in 1915 and has been the standard theory of gravity ever since. General relativity has the virtue of being consistent with Newton’s law of gravity when the gravitational acceleration is weak, i.e. in the non-relativistic limit when the speed is much lower than the speed of light. Thus, as far as non-relativistic gravitational dynamics is concerned in the universe, Newton’s and Einstein’s theories provide equivalent descriptions. This Newton-Einstein standard gravity in the non-relativistic regime was anticipated to depict the dynamics of planetary motions, stellar systems, galaxies, and galaxy clusters, while general relativity was further expected to describe the spacetime structure and dynamics of the universe and relativistic phenomena such as black holes and gravitational waves.

3. Gravitational anomaly in weak gravity: Dark matter or MOND?

In 1933, Fritz Zwicky noticed that the Coma cluster of galaxies could not be explained by the Newton-Einstein standard gravity because galaxies had excessively fast orbital motions. He was the first to postulate "dunkle Materie", the German word for dark matter, to explain the anomalous gravitational force in the galaxy cluster, assuming that standard gravity holds in those systems. 

In the 1970s, astronomers including Vera Rubin and Albert Bosma started to observe galactic rotation curves to large radii from galactic centers. These curves revealed the most distinct and idiosyncratic gravitational anomaly at weak gravity or low acceleration (Figure 1). When gravitational acceleration is stronger than about 1 nm (nanometer) per second squared, there is no tangible gravitational anomaly. The gravitational anomaly starts to appear at about 1 nm per second squared and grows with radius to result in nearly flat rotation curves. 

Figure 1. Observed rotation curve of the Andromeda galaxy (M31) shows a clear gravitational anomaly in the outer part of the galaxy. The observed rotation curve is nearly flat, while the Newton-predicted curve declines in the outer part. (Image available online) 

Gravity weaker than 1 nm per second squared is well outside the gravity range of the inner solar system where standard gravity has been verified. However, with the extrapolation that standard gravity holds in weak gravity, dark matter halos surrounding visible galaxies were introduced. The introduction of dark matter halos soon gained popularity among scientists, primarily because it can save the theories of the two greatest luminaries. Except for the low-acceleration anomaly, Einstein’s general relativity has been successfully verified by the solar system tests, the detection of gravitational waves, and the observations of neutron stars and black holes. Standard cosmology based on general relativity has been developed assuming dark matter and has successfully explained the cosmic microwave background (CMB) temperature anisotropies and the large-scale structure of the universe revealed by the observed distribution of galaxies. Also, the amount of dark matter in the universe appears to be compatible with dark matter halos embedding galaxies and galaxy clusters. 

However, standard cosmology has recently faced serious problems, such as the incompatibility between the locally measured Hubble constant and that predicted by general relativity based on the CMB data observed by the Planck satellite. Additionally, the James Webb Space Telescope has revealed galaxies that appear to be excessively massive at early epochs, posing further dilemmas for the current cosmological model.

Dark matter means unobservable or invisible matter that cannot be observed through electromagnetic emission or absorption. For example, dark nebulae, which consists of massive amounts of dust particles that absorb light and thus appear dark, are not dark matter but ordinary baryons. There is no shortage of theoretical candidate particles for dark matter. Historically, weakly interacting massive particles (WIMPs) were the favored candidates but have been largely excluded by now through worldwide direct detection experiments. Supersymmetric particles (SUSYs) were also considered promising, but were largely excluded by the CERN experiments following the discovery of the Higgs particle. Of course, there remain a host of theoretical candidates such as axions, mini black holes, ultra-light bosons, etc., and the hunt for dark matter is ongoing.

While dark matter has been a favored solution to the gravitational anomaly for many scientists, it is important to realize the fact that the Newton-Einstein standard gravity has never been experimentally verified in the low-acceleration limit. Sometimes, some scientists argue for dark matter through astronomical observations such as gravitational lensing. However, the logic is bound to be circular because dark matter is inferred based on the assumption of standard gravity, and standard gravity would be valid in the low-acceleration limit if dark matter were detected in the right quantity.

Indeed, not all scientists agree with the dark matter solution. Already in 1983, Mordehai Milgrom suggested that the characteristic rotation curves of galaxies imply the breakdown of Newtonian gravitational dynamics (and thus general relativity as well) in the low-acceleration phenomena. Milgrom’s new paradigm termed modified Newtonian dynamics (MOND), posits that standard gravity breaks down near or weaker than an acceleration constant , that is, at about 0.1 nm per second squared. Thus, Milgrom introduced a new constant into gravitational theories. MOND gravity requires the external field effect that the internal dynamics of a gravitating system falling freely is affected by the gravitational field of the surrounding system, even if it is constant. In this sense, MOND gravity follows Mach’s principle that gravitational dynamics is affected by the surrounding universe.

MOND can explain the observed rotation curves of galaxies without invoking dark matter. MOND’s predictions of Kepler-like laws in galactic kinematics, such as the baryonic Tully-Fisher relation and the radial acceleration relation, have been observed. Moreover, external field effects in the outer parts of galactic rotation curves have been recently detected. However, these observations are challenged by dark matter supporters because dark matter halos can mimic MOND’s predictions to some degree, although future accurate high-precision observations should eventually distinguish between MOND and dark matter halos.

4. Wide binary stars: Natural laboratories to directly test gravity at low acceleration

In using galaxies to distinguish between dark matter and MOND, it is required to deal with the overlapping predictions of the two paradigms because the outer parts of galaxies occupy immense space. In 2012, Xavier Hernandez and his collaborators suggested wide binaries to test gravity at low acceleration. Wide binaries are long-period, gravitationally bound pairs orbiting each other under their mutual gravitational force. For typical binaries with total mass of about 1 solar mass the mutual gravity reaches weak acceleration of Milgrom’s constant when the separation (or the orbit size) is several kilo astronomical units (kau). The dark matter contained within the relatively small space bounded by the orbit, as predicted by standard gravity, is completely negligible, and so gravity can be directly tested without the need for distinguishing the effects of dark matter and MOND.

The European Space Agency’s Gaia space telescope has been tracking motions of stars with the goal of constructing 3D map of 2 billion objects (mostly stars) in the Milky Way. Gaia has been releasing data since 2016. The latest release is data release 3 (DR3). Over the span from 2023 to 2024, Sejong University professor Kyu-Hyun Chae has developed algorithms to test gravity with wide binaries by considering three gravity-sensitive parameters, namely the observed 2D velocity projected on the plane-of-the-sky, the 2D velocity normalized by the Newtonian circular velocity, and a kinematic acceleration statistically reconstructed by Monte Carlo de-projection of the observed 2D velocity and the 2D separation to the 3D real space.

Gaia data for binaries have varying qualities. Also, some binary systems may include unobserved additional stars that orbit in close proximity to one or both of the primary stars. Those with hidden additional components are called multiple-star or hierarchical systems. Chae considered a range of binary samples, spanning from a small sample of pure binaries with the highest data qualities to a sample 10 times larger, which included hierarchical systems and had relaxed data quality criteria. For samples including hierarchical systems, Chae calibrated the occurrence rate of hierarchical systems using binaries with separation less than 1 kau that are known to satisfy standard gravity. This procedure can work because all binaries were selected with the same criteria regardless of the separation, and resolved hierarchical systems have already been removed. The probability of having unresolved hidden companions must then be independent of the separation because their photometric, astrometric, and kinematic properties are statistically the same by the selection.

5. Results

Figure 2 shows gravity test results for a sample of 2463 pure binaries selected with stringent data quality requirements. At acceleration higher than about 1 nm per second squared or separation smaller than about 2 kau, the observed acceleration or velocity agrees with the Newtonian prediction. This is a remarkable result because there was no adjustment whatsoever to any observed quantities. Newtonian dynamics is naturally borne out by the observed quantities down to acceleration scales of nm per second squared. 

However, at 1 nm per second squared or 2 kau, the observed acceleration/velocity starts to deviate from the Newtonian prediction, and for separation larger than about 5 kau, the velocity and acceleration are boosted respectively by about 20% and 40-50%. Because those binaries with larger separations satisfy the same data qualities, these boosts represent real gravitational anomalies. What is truly remarkable is that the degree and characteristic of the anomalous behavior agrees with the generic prediction of MOND gravity under the external field effect of the Milky Way, as represented by the AQUAL model due to Jacob Bekenstein and Milgrom. This result is independently confirmed by a concurrent independent analysis, by Xavier Hernandez and his collaborators, of an independently selected sample of wide binaries.

Figure 2. Gravity test results for 2463 pure binaries statistically free of hidden additional components are shown. Three gravity-sensitive parameters, i.e., a Monte Carlo reconstructed kinematic acceleration, the observed plane-of-the-sky projected relative velocity, and that velocity normalized by the Newtonian circular velocity, are shown from left to right. In all three cases, the observed values are compared with the corresponding Newtonian predictions. The gravitational anomaly at low acceleration or larger separation is clearly revealed.

Figure 3 shows the acceleration anomalies for two general samples including hierarchical (higher-order multiple) systems. The calibrated values of the fraction of hierarchical systems are indicated. In concurrence with the anomaly in the pure binary sample, the observed gravity starts to deviate from the Newtonian prediction at about 1 nm per second squared, and the degree and trend of the anomaly agrees well with the prediction of MOND gravity.

Figure 3. Gravity test results with the Monte Carlo reconstructed kinematic acceleration for two general wide binary samples including hierarchical (multiple-star) systems. The fraction of unresolved hierarchical systems was calibrated at a high acceleration in the Newtonian regime. These results corroborate with those for the pure binary sample, but the statistical significances are much higher thanks to the much larger sample sizes. 

Figure 4 shows the observed normalized velocities as a function of normalized separation where a value of 1 corresponds to Milgrom’s acceleration in the acceleration scale, for the two general samples. At sufficiently small values of the normalized separation, the observed normalized velocities agree well with the Newtonian predictions. However, the normalized velocity gradually increases with the normalized separation up to about 1 and then flattens for both samples agreeing with the MOND gravity prediction. 

Figure 4. Similar to Figure 3 but with the normalized velocity. The Newtonian prediction is clearly ruled out, while the Milgromian AQUAL prediction agrees well with the Gaia data.

6. Implications: Revolution in astrophysics and cosmology

Dark matter competes with MOND in explaining the gravitational anomalies in galaxies and galaxy clusters thanks to the apparent compatibility of the cosmic dark matter density. Such a competition does not work for the observed gravitational anomaly in wide binaries. The gravitational anomaly plainly means that standard gravity breaks down at low acceleration, independent of the dark matter concept even if it existed.

It is striking that the wide binary gravitational anomaly is observed at the same acceleration as in galactic rotation curves. Since dark matter, which is invoked for the anomaly in galactic rotation curves, cannot explain the anomaly in wide binaries, the dark matter paradigm itself appears to be ad-hoc. Thus, the ongoing failure to detect or identify dark matter particles, despite intense worldwide campaigns, may be considered consequence of this discrepancy.

MOND gravity models, such as AQUAL and QUMOND, not only necessitate the gravitational anomalies in galaxies and wide binaries but also predict correctly the enormous quantitative differences between the galactic and wide binary anomalies arising from the differences in the external field effect. These results prove the basic tenet of MOND that standard gravity breaks down through Milgrom’s acceleration constant. They also strongly indicate that MOND is realized through a non-standard (or modified) gravity.

The impact of MOND on astrophysics and cosmology is no less than that of general relativity. While general relativity broadened human understanding of gravity and spacetime to relativistic phenomena such as black holes and gravitational waves, it is reduced to Newtonian gravity in such nonrelativistic phenomena as planetary systems, stellar systems, galaxies, and galaxy clusters. Whenever these nonrelativistic phenomena reach the MOND regime set by Milgrom’s constant, they become Milgromian, lose the linearity and superposition principle, and suffer from the external field effect. As seen in wide binaries, Milgromian phenomena are expected to be widespread, encompassing stellar systems, galaxies, and even the universe itself. 

Thus, gravitational dynamics appears to be Machian from the strongest gravity to the weakest gravity. The Machian nature of gravity in the strong gravity regime is represented by Einstein’s nonlinear theory of general relativity, whereas in the weak gravity regime, it is represented by Milgrom’s theory. Only in the sweet spot of ``normal gravity’,’ such as in the inner solar system, Newtonian theory remains unaffected by the Machian nature, along with linearity and gravitational dynamics.

7. Future work and prospects

The current evidence for Milgromian gravity is derived from the Gaia DR3 database. Gaia is expected to release DR4 in early 2026. Gaia DR4 will provide full astrometric, photometric, and radial-velocity catalogues, and thus significantly improve statistics of wide binary gravity tests. Through precise measurements of radial velocities with specific instruments for targeted wide binaries, one can measure the 3D velocities that provide more direct tests of gravity than the plane-of-the-sky 2D velocities. Through the relatively new technology of speckle photometry, one can search for the unresolved hidden components to remove the uncertainties associated with them.

The evidence for Milgromian gravity is already strong, and thus theoretical developments in the MOND paradigm are in order. MOND cosmology needs to be developed following the pioneering works of Robert Sanders. Such a study needs to be done in line with theoretical developments of relativistic theories beyond Einstein’s theory with the correct MOND phenomenology. The search for the underlying fundamental theory will go on to explain simultaneously general relativity in the relativistic regime and MOND in the low acceleration limit. The fundamental theory will also have to include a successful description of quantum physics of gravity.

Reference

1. F. Zwicky 1933 Helvetica Physica Acta (in German) 6 110–127 "Die Rotverschiebung von extragalaktischen Nebeln" [The red shift of extragalactic nebulae]

2. V. Rubin, W. K. Jr. Ford 1970 Astrophysical Journal 159 379 "Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions"

3. A. Bosma 1978 Ph.D. thesis “The Distribution and Kinematics of Neutral Hydrogen in Spiral Galaxies of Various Morphological Types” (Rijksuniversiteit Groningen)

4. M. Milgrom 1983 Astrophysical Journal 270 365 "A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis”

5. S. S. McGaugh, J. M. Schombert, G. D. Bothun, and W. J. G. de Blok 2000 Astrophysical Journal 533 L99 “The Baryonic Tully-Fisher Relation”

6. Stacy S. McGaugh, Federico Lelli, and James M. Schombert 2016 Phys. Rev. Lett. 117, 201101 “Radial Acceleration Relation in Rotationally Supported Galaxies”

7. Kyu-Hyun Chae, Federico Lelli, Harry Desmond, Stacy S. McGaugh, Pengfei Li, and James M. Schombert 2020 Astrophysical Journal 904 51 “Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies”

8. Kyu-Hyun Chae 2022 Astrophysical Journal 941 55 “Distinguishing Dark Matter, Modified Gravity, and Modified Inertia with the Inner and Outer Parts of Galactic Rotation Curves”

9. X. Hernandez, M. A. Jiménez, C. Allen 2012 The European Physical Journal C 72 1884 “Wide binaries as a critical test of classical gravity”

10. Kyu-Hyun Chae 2023 Astrophysical Journal 952 128 “Breakdown of the Newton–Einstein Standard Gravity at Low Acceleration in Internal Dynamics of Wide Binary Stars”

11. Kyu-Hyun Chae 2024 Astrophysical Journal 960 114 “Robust Evidence for the Breakdown of Standard Gravity at Low Acceleration from Statistically Pure Binaries Free of Hidden Companions”

12. Kyu-Hyun Chae 2024 Astrophysical Journal (submitted; preprint arXiv:2402.05720) "Measurements of the Low-Acceleration Gravitational Anomaly from the Normalized Velocity Profile of Gaia Wide Binary Stars and Statistical Testing of Newtonian and Milgromian Theories“

13. X.Hernandez, V. Verteletskyi, L. Nasser, A. Aguayo-Ortiz 2024 Monthly Notices of the Royal Astronomical Society 528 4720 "Statistical analysis of the gravitational anomaly in Gaia wide binaries"

14. J. Bekenstein, M. Milgrom 1984 Astrophysical Journal 286 7 "Does the missing mass problem signal the breakdown of Newtonian gravity?”

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16. R. H. Sanders 1998 Monthly Notices of the Royal Astronomical Society 296 1009 "Cosmology with modified Newtonian dynamics (MOND)”