Testing of MOND with Local Group Timing

The timing of the Local Group is used to test Modified Newtonian Dynamics (MOND). The result shows that the masses predicted by MOND are well below the baryonic contents of the Milky Way and Andromeda galaxies.

💡 Research Summary

The paper investigates whether Modified Newtonian Dynamics (MOND) can account for the dynamics of the Local Group, specifically the mutual approach of the Milky Way and Andromeda galaxies. The authors begin by reproducing the classic “timing argument” within the Newtonian framework. Treating the two galaxies as point masses separated by roughly 770 kpc and moving toward each other at a relative velocity of about –110 km s⁻¹, they integrate the equations of motion from the epoch of the Big Bang to the present. This Newtonian calculation requires a total mass of roughly 5 × 10¹² M☉ to reproduce the observed separation and velocity, a value that exceeds the combined baryonic mass of the Milky Way and Andromeda (≈1 × 10¹² M☉) by a factor of five. The excess is traditionally interpreted as evidence for a substantial dark‑matter component in the Local Group.

Next, the authors apply the MOND prescription. In MOND, when the characteristic acceleration falls below the empirical constant a₀ ≈ 1.2 × 10⁻¹⁰ m s⁻², the effective gravitational force transitions from the Newtonian form F = GMm/r² to the deep‑MOND regime F ≈ √(GMa₀) m/r. Because the inter‑galactic acceleration at the ∼770 kpc scale is far below a₀, the deep‑MOND limit is appropriate. Using the same initial conditions as in the Newtonian case, the authors solve the modified equations of motion and find that only about 2 × 10¹¹ M☉ of mass is needed to reproduce the present‑day separation and velocity. This MOND‑derived mass is dramatically lower—by a factor of roughly 2–3—than the observed baryonic mass of the two galaxies combined (≈5 × 10¹¹ M☉). In other words, MOND predicts that the Milky Way and Andromeda could have reached their current state with far less matter than is actually present in stars and gas.

The paper then scrutinizes the implications of this discrepancy. First, it confirms that the acceleration in the Local Group is indeed in the deep‑MOND regime, validating the use of the √(GMa₀) force law for this system. Second, it argues that the timing argument’s initial conditions—namely the assumption of a common origin at the Big Bang with a Hubble‑type expansion—are equally applicable in both Newtonian and MOND frameworks, making the comparison fair. Third, the authors emphasize that the MOND prediction of a total mass well below the measured baryonic content suggests that MOND cannot, on its own, explain the large‑scale dynamics of the Local Group without invoking additional unseen mass. This conclusion challenges the notion that MOND can fully replace dark matter across all astrophysical scales.

Potential counter‑arguments are addressed. The contribution of smaller satellite galaxies within the Local Group, which were neglected in the point‑mass model, could modestly increase the effective MOND mass, but not enough to close the gap. Adjusting the value of a₀ to a higher number would improve the MOND fit for the Local Group but would then conflict with the successful fits of galaxy rotation curves that originally motivated MOND. The authors also explore whether uncertainties in the measured relative velocity or distance could reconcile the results; however, even generous error margins leave a substantial mismatch.

In conclusion, the timing argument for the Local Group provides a stringent, independent test of MOND that complements the well‑known successes of MOND in fitting galaxy rotation curves. While MOND reproduces the internal dynamics of individual galaxies without dark matter, the present analysis shows that on the scale of the Milky Way–Andromeda system it dramatically underestimates the required mass. Therefore, MOND either requires an additional, non‑baryonic component in the Local Group or must be supplemented by further modifications to the theory. The study underscores that any viable alternative to dark matter must simultaneously satisfy constraints from both galactic‑scale phenomena and the dynamics of galaxy groups and clusters.