Distant star clusters of the Milky Way in MOND

TL;DR

This study tests modified Newtonian dynamics (MOND) against classical gravity by measuring velocity dispersions in six distant Milky Way globular clusters, finding that MOND predicts higher dispersions which can be distinguished with 30-80 star velocity measurements.

Contribution

It applies a MOND-specific N-body simulation to predict velocity dispersions in outer halo clusters, proposing a practical observational test to differentiate between MOND and Newtonian gravity.

Findings

Newtonian predicts lower velocity dispersions

MOND predicts higher velocity dispersions

30-80 star velocity measurements needed for distinction

Abstract

We determine the mean velocity dispersion of six Galactic outer halo globular clusters, AM 1, Eridanus, Pal 3, Pal 4, Pal 15, and Arp 2 in the weak acceleration regime to test classical vs. modified Newtonian dynamics (MOND). Owing to the non-linearity of MOND's Poisson equation, beyond tidal effects, the internal dynamics of clusters is affected by the external field in which they are immersed. For the studied clusters, particle accelerations are much lower than the critical acceleration a_0 of MOND, but the motion of stars is neither dominated by internal accelerations (a_i >> a_e) nor external accelerations (a_e >> a_i). We use the N-body code N-MODY in our analysis, which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti, Londrillo, and Nipoti (2006) to derive the line-of-sight velocity dispersion by adding the external field effect. We show that Newtonian dynamics predicts a low-velocity dispersion for each cluster, while in modified Newtonian dynamics the velocity dispersion is much higher. We calculate the minimum number of measured stars necessary to distinguish between Newtonian gravity and MOND with the Kolmogorov-Smirnov test. We also show that for most clusters it is necessary to measure the velocities of between 30 to 80 stars to distinguish between both cases. Therefore the observational measurement of the line-of-sight velocity dispersion of these clusters will provide a test for MOND.