Direct $N$-body simulations of globular clusters - II. Palomar 4

We use direct $N$-body calculations to study the evolution of the unusually extended outer halo globular cluster Palomar 4 (Pal~4) over its entire lifetime in order to reproduce its observed mass, half-light radius, velocity dispersion and mass function slope at different radii. We find that models evolving on circular orbits, and starting from a non-mass segregated, canonical initial mass function (IMF) can reproduce neither Pal 4s overall mass function slope nor the observed amount of mass segregation. Including either primordial mass segregation or initially flattened IMFs does not reproduce the observed amount of mass segregation and mass function flattening simultaneously. Unresolved binaries cannot reconcile this discrepancy either. We find that only models with both a flattened IMF and primordial segregation are able to fit the observations. The initial (i.e. after gas expulsion) mass and half-mass radius of Pal~4 in this case are about 57000 M${odot}$ and 10 pc, respectively. This configuration is more extended than most globular clusters we observe, showing that the conditions under which Pal~4 formed must have been significantly different from that of the majority of globular clusters. We discuss possible scenarios for such an unusual configuration of Pal~4 in its early years.

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 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.