The Local Group as a test system for Modified Newtonian Dynamics

TL;DR

This study tests Modified Newtonian Dynamics (MOND) using the Local Group as a natural laboratory, modeling galaxy interactions and including the Cosmological Constant to compare mass predictions with observations.

Contribution

It extends previous models by incorporating the Cosmological Constant into the two-body MOND analysis of the Local Group, providing new mass estimates and dynamical insights.

Findings

MOND predicts a total mass of approximately 0.447 trillion solar masses for the Local Group.

The ratio of baryonic to total mass in MOND aligns with dark matter ratios in other galaxies.

The model suggests a past encounter between M31 and the Milky Way.

Abstract

The Local Group (LG) is {an appropriate} test system for Modified Newtonian Dynamics, since the acceleration of M31 galaxy is fully in the deep MOND regime $a \ll a_0$. We model the LG as a two body problem of $M31$ and the Milky Way (MW) galaxies. {Extending previous studies, we also include the Cosmological Constant.} The assumption that in the big bang the galaxies emerged from the same place and approach to the measured distance and velocity today (the Timing Argument), predicts the total mass for the LG: $(0.447 \pm 0.005)\cdot 10^{12} M_{\odot}$. The corresponding motion of the LG predicts a past encounter. The ratio between the baryonic mass that MOND considers to the mass that Newtonian case predicted, which includes dark matter is $10.74 \pm 0.82$. This ratio agrees with the ratio between the dark matter and baryonic matter in other galaxies.