STRAWBERRY: Finding haloes in the gravitational potential

¹ Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4 20018 Donostia-San Sebastián Gipuzkoa, Spain
² Institute for Astronomy, University of Vienna Türkenschanzstraße 17 Vienna 1180, Austria
³ IKERBASQUE, Basque Foundation for Science E-48013 Bilbao, Spain

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

Received: 13 August 2025
Accepted: 17 January 2026

Abstract

We present a novel algorithm that discriminates between bound and unbound particles by consideration of the gravitational potential from an accelerated reference frame, also referred to as the ‘boosted potential’. Particles are considered to be bound if their energy does not exceed the escape energy of a potential well, given by the closest saddle point that connects to a deeper potential minimum. This approach has core benefits over previous approaches, since it does not require any ad hoc thresholds (such as overdensity criteria), while it does include the gravitational effect of all particles in the binding criterion (improving over widely used self-potential binding checks) and it only operates with instantaneous information (making it simpler than approaches based on dynamical histories). We show that particles typically become bound between their first peri- and apo-centeric passage and that bound and unbound populations show very distinct characteristics through their distribution in phase space, as well as in their density profiles, virial ratios, and redshift evolution. Our findings suggest that it is possible to understand haloes as two-component systems, with one component being bound, virialised, of a finite extent, and evolving slowly in quasi-equilibrium and the other component being unbound, un-virialised, and evolving rapidly.