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

We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in modified Newtonian dynamics (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 & Nipoti. We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of 10(4) to 10(9)M(circle dot) 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) << a(0)), where the motion of stars is either dominated by internal accelerations (a(i) >> a(e)) or constant external accelerations (a(e) >> 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) similar to a(e) similar to 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.