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.Comment: A&A, accepted, LaTeX, 8 pages, 4 figure
