Searching for a signature of turnaround in galaxy clusters with convolutional neural networks

¹ Department of Physics and Institute for Computational and Theoretical Physics, University of Crete, 70013 Heraklio, Greece
² Institute of Astrophysics, Foundation for Research and Technology – Hellas, Vassilika Vouton, 70013 Heraklio, Greece
³ Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (PI), Italy

^⋆ Corresponding authors: nikolaos.triantafyllou@sns.it; gkorkidis@physics.uoc.gr

Received: 17 December 2024
Accepted: 13 August 2025

Abstract

Context. Galaxy clusters are important cosmological probes that have helped to establish the Λ cold dark matter paradigm as the standard model of cosmology. However, recent tensions between different types of high-accuracy data highlight the need for novel probes of the cosmological parameters. Such a probe is the turnaround density: the mass density on the scale where galaxies around a cluster join the Hubble flow. To measure the turnaround density, one must locate the distance from the cluster center where turnaround occurs. Earlier work has shown that a turnaround radius can be readily identified in simulations by analyzing the 3D dark matter velocity field. However, measurements using realistic data face challenges due to projection effects.

Aims. This study aims to assess the feasibility of measuring the turnaround radius using machine learning techniques applied to simulated idealized observations of galaxy clusters.

Methods. We employed N-body simulations across various cosmologies to generate galaxy cluster projections. Utilizing convolutional neural networks, we assessed the predictability of the turnaround radius based on galaxy line-of-sight velocity, number density, and mass profiles.

Results. We find a strong correlation between the turnaround radius and the central mass of a galaxy cluster, rendering the mass distribution outside the virial radius of little relevance to the model’s predictive power. The velocity dispersion among galaxies also contributes valuable information concerning the turnaround radius. Importantly, the accuracy of a line-of-sight velocity model remains robust even when the data within the R₂₀₀ of the central overdensity are absent.

Conclusions. Single-cluster turnaround radius inference from projected observables seems to be highly challenging. Future progress is likely to require statistical approaches, especially stacking, to exploit cosmological information encoded at turnaround scales.