ROLLIN': Rotating globular cluster simulations. I. The kinematic evolution of realistic direct N-body models

Abstract

Internal rotation has emerged as a fundamental feature of globular clusters (GCs), yet its origin and long-term evolution remain poorly understood. We explore the evolution of rotating GCs over a Hubble time under the combined influence of two-body relaxation, tidal field, and stellar evolution. We introduce the ROLLIN' simulations, a suite of 25 N-body models characterized by a realistic number of stars from 250k to 1.5M, ran with the direct N-body code NBODY6++GPU and evolved for 14 Gyr. With present-day masses of 5 x 10^4 - 5x10^5 M_sun, the models cover the parameter space of low-density MW GCs. Our analysis reveals that rapidly rotating GCs experience earlier and more pronounced core collapse, efficiently segregating massive objects and remnants in their centers within the first few 100 Myr. In the long-term, internal rotation declines and a correlation emerges between rotation and GC mass, in agreement with observations. The primary driver of this evolution is mass loss, capturing both internal (stellar evolution, evaporation) and external processes (tidal stripping). The velocity anisotropy also evolves in response to mass loss: GCs initially near isotropy develop radial anisotropy, peaking around 40% mass loss, before progressing toward isotropy or tangentiality. The GC orbital history also plays a role, as retrograde rotators retain rotation more effectively than prograde rotators. Finally, we quantify the long-term changes of GCs after 12 Gyr: (1) The surface density decreases by up to 2 orders of magnitude. (2) The half-mass radius increases by a factor of 3-5. (3) The rotation decreases by a factor >5 for GCs that have lost >50% of their mass. The ROLLIN' simulations demonstrate that angular momentum is crucial to understand the origin, evolution, and survival of GCs. These models provide a benchmark for interpreting GC observations in the local and high-z Universe.