ROLLIN’: Rotating globular cluster simulations

I. The kinematic evolution of realistic direct N-body models

¹ Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
² School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Kings Buildings, Edinburgh EH9 3FD, UK
³ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁴ Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
⁵ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
⁶ Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Università di Padova, Stradella S. Nicola 3, 36100 Vicenza, Italy
⁷ Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, 35122, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 30 October 2025
Accepted: 5 February 2026

Abstract

Context. Internal rotation has recently emerged as a fundamental dynamical feature of globular clusters (GCs). Its presence can serve as a direct fossil record of GC formation and of their subsequent evolution within a galactic context, yet its origin and long-term evolution remain poorly understood.

Aims. In this paper, we systematically explore the evolution of rotating GCs over a Hubble time under the combined influence of two-body relaxation, external tidal field, and stellar evolution. Our goal is to establish a theoretical framework to interpret the growing wealth of 3D kinematic data and unveil primordial properties of GCs.

Methods. We introduce the ROLLIN’ simulations, a suite of 25 large N-body simulations of rotating GCs characterized by having a realistic number of stars from 250k to 1.5M and ran with the direct N-body code NBODY6++GPU. The simulations are evolved for 14 Gyr and are initialized with a wide range of rotation strengths, densities, and tidal fields. With present-day masses of 5 × 10⁴–5 × 10⁵ M_⊙, the models cover the typical parameter space of low-density Milky Way GCs.

Results. Our analysis highlights the pivotal role of rotation in shaping the early evolution of GCs. Rapidly rotating GCs experience earlier and more pronounced core collapse, efficiently segregating massive objects—including stellar remnants—in their centers within the first few hundred million years. In the long-term, internal rotation steadily declines, and after 12 Gyr, a correlation emerges between rotation strength and total GC mass, in agreement with recent 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: Clusters initially near isotropy develop radial anisotropy, peaking around 40% mass loss, before progressing toward isotropy or tangential anisotropy at higher mass losses. Additionally, the GC orbital history plays a key role, as retrograde rotators retain angular momentum more effectively than prograde rotators, and their rotation profiles differ significantly already well within the Jacobi radius. Finally, our simulations enabled us to quantify the long-term structural changes of GCs after 12 Gyr: (i) The surface density decreases by up to two orders of magnitude. (ii) The half-mass radius increases by a factor of three to five. (iii) The rotation strength decreases by a factor greater than five for clusters that have lost more than 50% of their initial mass.

Conclusions. The ROLLIN’ simulations demonstrate that angular momentum, along with initial cluster density and mass, is one of the crucial aspects to understand the origin, evolution, and survival of GCs. These simulations therefore provide a valuable benchmark for interpreting GC observations both in the local and high-redshift Universe.