The missing gravity in galaxies requires dark matter or an adjustment of gravity or inertia. The statistical relationship can distinguish these theoretical possibilities of fundamental importance between the observed centripetal acceleration of particles in orbital motion and the expected Newtonian acceleration of the observed distribution of baryons in galaxies.

We’ve done several searches, but no dark matter particles have been found. As a result, some astronomers opt for an alternative, such as the Modified Newtonian Dynamics (MoND) or Modified Gravity Model. And a recent study of the rotation of galaxies seems to confirm this.

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

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

The attraction between stars is mainly 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, unlike the pull which is a pure inverse square relationship. Although this remnant is only about 10 trillionths of gee, it is enough to explain the rotational curves of galaxies.

Of course, even a small change in Newton’s theory of gravity requires a change in 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 explain the observed galactic rotation curves, but there are some minor differences.

This is where a recent study comes into play. The rotational speeds of stars in their inner versus outer orbits are one difference between AQUAL and LCDM. The matter distribution in LCDM should control both; hence the curve must be spherical. Due to the dynamics of the theory, AQUAL predicts a small kink in the curve. While 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 gravitational theories (AQUAL and QUMOND) with the outer part of rotational curves (RCs). They find that AQUAL is preferable to QUMOND because the external field strength required by AQUAL matches well with the expected value of cosmic environments, while the value required by QUMOND is slightly 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, the 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 have shown for various configurations, AQUAL and QUMOND unequivocally predict that the inner part RCs deviate, albeit to a small degree, 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, *“The result is exciting, but it doesn’t definitively change dark matter. The AQUAL model has issues, such as disagreement with observed gravitational lensing by galaxies. But it’s a win for the underdog theory, leading some astronomers to shout “Vive le MoND!”*

**Magazine reference:**

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