Nemesis: A multi-scale, multi-physics algorithm for astrophysics

Leiden Observatory, University of Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands

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Received: 11 November 2025
Accepted: 10 March 2026

Abstract

Context. Astronomical environments are governed by a complex interplay of physical processes, including gravitational dynamics, radiative transfer, stellar evolution, chemistry, and hydrodynamics. These processes span a vast range of spatial scales, from short-range interactions where intra-particle distances are vital, to cosmological scales. Both of these characteristics make astrophysics a multi-scale, multi-physics discipline. This complexity introduces complications to numerical methods where round-off errors and a wide range of temporal timescales on which processes act can influence the reliability of results and the efficiency of algorithms.

Aims. In this work, we present an updated version of the multi-scale, multi-physics algorithm, Nemesis, which makes use of the Astrophysical Multipurpose Software Environment (AMUSE). We formally introduce and validate the algorithm.

Methods. We ran a suite of simulations to assess its performance in simulating star clusters containing planetary systems, its ability to capture the von Zeipel–Lidov–Kozai effect, and its computational scalability.

Results. The Nemesis code yields indistinguishable results on both the global and local scales when compared with the direct N-body code Ph4. We find the same result when analysing its ability to capture the von Zeipel–Lidov–Kozai effect. When we analyse its computational performance, the wall-clock time scales roughly as t_sim ∝ 1/ δt_nem, where δt_nem represents the time synchronisation between the global and local scales. When we vary the number of planetary systems, the wall-clock time remains unchanged as long as the number of available cores exceeds the number of systems. Beyond this, we find that, at worst, the computational time increases linearly with the number of excess systems.

Conclusions. The method introduced here can be used in numerous domains of astronomy, thanks to its flexibility and modularity, from simulating protoplanetary discs in star clusters to binary black holes in the galactic centre.