The missing gravity in galaxies requires dark matter or a modification of gravity or inertia. The statistical relation may distinguish these theoretical possibilities of fundamental importance between the observed centripetal acceleration of particles in orbital motion and the expected Newtonian acceleration from the observed distribution of baryons in galaxies.

We have conducted several searches, but no dark matter particles have been found. As a result, a few astronomers choose an alternative, such as the Modified Newtonian Dynamics (MoND) or Modified Gravity Model. And a recent galaxy rotation study appears to confirm them.

The galactic rotation supports the idea of MoND. MoND makes several salient predictions about galactic kinematics. Theoretically, MOND can be realized by modified gravity.

All the stars within a galaxy rotate at about the same speed. Instead of declining, the rotation curve is practically flat. According to the dark matter explanation, galaxies are encircled by an invisible halo of matter, but in 1983 Mordehai Milgrom contended that our gravitational model must be wrong.

The gravitational pull between stars is primarily Newtonian at interstellar distances. For this reason, Milgrom suggested changing Newton’s Universal Law of Gravity instead of general relativity. He claimed that gravity has a slight residual pull regardless of distance, as opposed to the force of attraction being a pure inverse square relation. Even though this remnant only makes up about 10 trillionths of gee, it is enough to explain galaxy rotation curves.

Of course, even a little modification to Newton’s theory of gravity necessitates changing Einstein’s equations. Consequently, MoND has been generalized in several ways, including AQUAL, which stands for A Quadradic Lagrangian. AQUAL and the conventional LCDM model can account for the galactic rotation curves observed, but there are some slight differences.

This is where a recent study comes in. The rotational velocities of stars in their inner vs. outer orbits are one difference between AQUAL and LCDM. The matter distribution in LCDM should control both; hence the curve should be spherical. Because of the dynamics of the theory, AQUAL predicts a small kink in the curve. Although statistically, there should be a slight difference between the inner and outer velocity distributions, it is too faint to detect in a single galaxy.

This work considers 152 galaxies with good-quality RCs selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. Recently tested MOND-modified gravity theories (AQUAL and QUMOND) with the outer part of rotation curves (RCs). They find that AQUAL is preferred over QUMOND because the AQUAL-required external field strength is well consistent with the value expected from cosmic environments, while the QUMOND-required value is a little higher than the expected value.

It is then interesting to ask whether AQUAL can correctly predict the observed inner part of RCs. Unlike the outer RCs, numerically predicted properties of the inner RCs under AQUAL (also QUMOND) are so complex that a single model curve cannot describe them on an acceleration plane. As scientists demonstrated for various configurations, AQUAL and QUMOND unambiguously predict that the inner part RCs deviate, though by a small amount, from the algebraic MOND relation even when the inner part is in a supercritical acceleration regime.

For the first time, dark matter, modified gravity, and modified inertia are tested and distinguished by considering the inner and outer parts of galactic rotation curves together and separately.

Authors noted,Â *“The result is exciting, but it doesn’t conclusively overturn dark matter. The AQUAL model has issues, such as its disagreement with observed gravitational lensing by galaxies. But it is a win for the underdog theory, which has some astronomers cheering “Vive le MoND!”*

**Journal Reference:**

- Chae, Kyu-Hyun. “Distinguishing Dark Matter, Modified Gravity, and Modified Inertia with the Inner and Outer Parts of Galactic Rotation Curves.” The Astrophysical Journal 941.1 (2022): 55. arXiv:2207.11069v4