New parameters for star-cluster dynamics: Observational results

¹ Dipartimento di Fisica e Astronomia, Università degli Studi di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
² INAF, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
³ Dept. of Astronomy, Indiana University, Bloomington, IN 47401, USA

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

Received: 13 November 2025
Accepted: 26 January 2026

Abstract

We recently used a large set of Monte Carlo simulations of globular clusters (GCs) to define new, fully empirical parameters (named A₅₁, P₅₁, and S_2.5) able to trace the internal dynamical evolution of dense stellar systems. These parameters are specifically designed to quantify the steepness of the cumulative radial distribution of stars in the innermost region of the host system, which tends to progressively increase with dynamical aging due to core contraction. Following the original definitions, here we measure A₅₁ and P₅₅ in a sample of 40 Galactic GCs homogeneously surveyed through HST photometric observations. In agreement with the predictions of our simulations, the largest values of A₅₅ and P₅₅ are found for the most dynamically evolved GCs - i.e., those previously classified as post-core-collapse systems based on the shape of their density profile - and those characterized by the shortest central relaxation times. Moreover, the new dynamical parameters here measured strongly correlate with A⁺_rh, another fully empirical, independent parameter that traces the dynamical age of star clusters through the level of central segregation of blue straggler stars.