Predicting halo formation time using machine learning

¹ Departamento de Fisíca Teórica, M-8, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
² Centro de Investigación Avanzada en Física Fundamental (CIAFF), Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
³ School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK
⁴ INAF, Osservatorio Astronomico di Trieste, via Tiepolo 11, 34143 Trieste, Italy
⁵ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
⁶ Department of Physics; University of Michigan, 450 Church St, Ann Arbor, MI 48109, USA
⁷ Tsung-Dao Lee Institute & Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁸ Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai 200240, PR China
⁹ Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, PR China

^★ Corresponding author.

Received: 26 November 2024
Accepted: 19 June 2025

Abstract

Context. The formation time of dark-matter halos quantifies their mass assembly history and, as such, directly impacts the structural and dynamical properties of the galaxies within them, and even influences galaxy evolution. Despite its importance, halo formation time is not directly observable, necessitating the use of indirect observational proxies-often based on star formation history or galaxy spatial distributions. Recent advancements in machine learning allow for a more comprehensive analysis of galaxy and halo properties, making it possible to develop models for more accurate prediction of halo formation times.

Aims. This study aims to investigate a machine learning-based approach to predict halo formation time-defined as the epoch when a halo accretes half of its current mass-using both halo and baryonic properties derived from cosmological simulations. By incorporating properties associated with the brightest cluster galaxy located at the cluster center, its associated intracluster light component, and satellite galaxies, we aim to surpass these analytical predictions, improve prediction accuracy, and identify key properties that can provide the best proxy for the halo assembly history.

Methods. Using The Three Hundred cosmological hydrodynamical simulations, we trained random forest and convolutional neural network (CNN) models. The random forest models were trained using a range of dark matter halo and baryonic properties, including halo mass, concentration, stellar and gas masses, and properties of the brightest cluster galaxy and intracluster light within different radial apertures, while CNNs were trained on two-dimensional radial property maps generated by binning particles as a function of radius. Based on these results, we also constructed simple linear models that incrementally incorporate observationally accessible features to optimize the prediction of halo formation time for minimal bias and scatter.

Results. Our RF models demonstrated median biases between 4% and 9% with relative error standard deviations of around 20% in the prediction of the halo formation time. The CNN models trained on two-dimensional property maps, further reduced the median bias to .4%, though with a higher scatter than the random forest models. With our simple linear models, one can easily predict the halo formation time with only a limited number of observables and with the bias and scatter compatible with random forest results. Lastly, we also show that the traditional relations between halo formation time and halo mass or concentration are well preserved with our predicted values.