Testing fundamental physics with distant star clusters: theoretical models for pressure-supported stellar systems

TL;DR

This paper uses numerical simulations and analytic formulas within MOND to model velocity dispersions in star clusters, aiming to distinguish between Newtonian and MONDian gravity through observations.

Contribution

It provides the first analytic formulas for velocity dispersion in the intermediate MOND regime and applies these to globular cluster Pal 14 for testing gravity theories.

Findings

Reproduces previous estimates in deep MOND regime

Derives new analytic formulas for intermediate regime

Applies models to globular cluster Pal 14

Abstract

We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in MOND, using the N-body code N-MODY, which is a particle-mesh based code with a numerical MOND potential solver developed by Ciotti, Londrillo and Nipoti (2006). We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of $10^4 M_\odot$ to $10^9 M_\odot$ and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND regime ($a_i, a_e \ll a_0$), where the motion of stars is either dominated by internal accelerations ($a_i \gg a_e$) or constant external accelerations ($a_e \gg a_i$). In addition, we derive for the first time analytic formulae for the line-of-sight velocity dispersion in the intermediate regime ($a_i \sim a_e \sim a_0$). This allows for a much improved comparison of MOND with observed velocity dispersions of stellar systems. We finally derive the velocity dispersion of the globular cluster Pal 14 as one of the outer Milky Way halo globular clusters that have recently been proposed as a differentiator between Newtonian and MONDian dynamics.