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Wide binary stars with separation greater than about 2000 astronomical units are interesting natural laboratories that allow a direct probe of gravity at low acceleration weaker than about 1 nanometer per second squared. Astrophysicist Kyu-Hyun Chae at Sejong University (Seoul, South Korea) has developed a new method of measuring gravity with all three components of the velocities (3D velocities) of stars, as a major improvement over existing statistical methods relying on sky-projected 2D velocities.

The new method based on the Bayes theorem derives directly the probability distribution of a gravity parameter (a parameter that measures the extent to which the data departs from standard gravitational dynamics) through the Markov Chain Monte Carlo simulation of the relative 3D velocity between the stars in a binary. The work is in The Astrophysical Journal.

Regarding the significance of the new method, Chae says, "The existing methods to infer gravity have the limitation that only the sky-projected velocities are used. Moreover, they have some limitations in accounting for the uncertainties of various factors, including stellar masses, to derive the probability distribution of a gravity parameter.

"The new method overcomes all these limitations. It is a sort of revolutionary and ultimate method for wide binaries whose motions can only be 'snapshot-observed' (that is, observed only at a specific phase of the orbital motion: because of the very long orbital periods of these binaries, a direct consequence of the low accelerations involved, one can only measure the positions and velocities of the stars at one moment, which is far less informative than having, ideally, data on a full orbit or at least a segment of it).

"However, the new method requires accurate and precise values of the third velocity component, that is, the line-of-sight (radial) velocity. In other words, only wide binaries with precisely measured radial velocities can be used."

On the significance of the methodology, Xavier Hernandez, who initiated wide binary gravity tests in 2012, says, "The latest paper by Dr. Chae on wide binaries presents a fully rigorous Bayesian approach which will surely become the standard in the field. Further, this latest paper also presents a proof of concept in going from 2-dimensional projected velocities to full 3D relative velocities between the two components of a wide binary. The level of accuracy reached from making full use of all available information is impressive."

For the first application of the new method, Chae used about 300 wide binaries with relatively precise radial velocities selected from the European Space Agency's Gaia data release 3. Although the first results are limited by the fact that Gaia's reported radial velocities are not as precise as the sky-projected velocities, the derived probability distributions of gravity agree well with the recent results published by Chae and independently by Hernandez's group as well.

For wide binaries whose stars orbit each other with an internal acceleration greater than about 10 nanometers per second squared, the inferred gravity is precisely Newtonian, but for an internal acceleration lower than about 1 nanometer per second squared (or separation greater than about 2000 au), the inferred gravity is about 40% to 50% stronger than Newton.

The significance of the deviation is 4.2δ meaning that standard gravity is outside the 99.997% probability range. What is striking is that the deviation agrees with the generic prediction of modified gravity theories under the theoretical framework called modified Newtonian dynamics (MOND, sometimes referred to as Milgromian dynamics), introduced about 40 years ago by Mordehai (Moti) Milgrom.

On the first results based on the new method, Chae says, "It is encouraging that a direct inference of the probability distribution of gravity can be obtained for wide binaries that are bound by extremely weak internal gravity. This methodology may play a decisive role in the coming years in measuring gravity at low acceleration. It is nice that the first results agree well with the results for the past 2 years obtained by Hernandez's group and myself with the existing methods."

Pavel Kroupa, professor at the University of Bonn in Germany, says, "This is an impressive study of gravitation using very wide binaries as probes taken to a new level of accuracy and clarity by Prof. Dr. Chae. This work greatly advances this topic, and the data, which will be improving over time, are already showing an increasingly significant deviation from Newtonian gravitation with an impressive consistency with the expectations from Milgromian gravitation. This has a major fundamentally important impact on theoretical physics and cosmology."

Milgrom expresses his thoughts on the general significance of the wide binary results: "This new result by Prof. Chae strengthens in important ways earlier findings by him and others. They demonstrate a departure from the predictions of Newtonian dynamics in low-acceleration binary stars in our galaxy.

"Such a departure from standard dynamics would be existing in itself. But it is even more exciting because it enters and appears in the same way as the departure from Newtonian dynamics appears in galaxies. It appears in the analysis only at or below a certain acceleration scale that is found to agree with the fundamental acceleration of MOND, and the magnitude of the anomaly they find is also consistent with the generic predictions of existing MOND theories.

"In galaxies, the observed (and MOND-predicted) anomaly is much larger, and is established very robustly, but much of the community support the view that it is due to the presence of dark matter; so, to them the galactic anomalies do not bespeak a conflict with standard dynamics. But, an anomaly as found by Prof. Chae, while more modest, cannot be accounted for by dark matter, and thus would indeed necessarily spell a breakdown of standard dynamics."

Chae and his collaborators, including Dongwook Lim and Young-Wook Lee at Yonsei University (Seoul, South Korea) and Byeong-Cheol Lee at Korea Astronomy and Space Science Institute (Daejeon, South Korea) are now obtaining precise radial velocities from their new measurements using observation facilities such as GEMINI North Observatory (with the instrument MAROON-X) and Las Cumbres Observatory, and from archival data outside Gaia as well.

Hernandez and his collaborators are carrying out the speckle photometry of target wide binaries to identify any systems with a hidden third star.

Hernandez comments on this point: "This methodology requires using pure binaries that are free of any hidden companion stars. This highlights the relevance of upcoming results from dedicated ground-based follow-up studies which will unambiguously rule out dubious systems containing hidden third components and hence permit to reach the full potential of the new method."

When all these observation results are combined, decisive results on the low-acceleration anomaly are expected.

On the near future prospect, Chae says, "With new data on radial velocities, most of which have already been obtained, and results from speckle photometric observations, the Bayesian inference is expected to measure gravity sufficiently precisely, not only to distinguish between Newton and MOND well above 5δ, but also to narrow theoretical possibilities of gravitational dynamics. I expect exciting opportunities for theoretical physics with new results in the coming years."