Exploring the Dependence of Gas Cooling and Heating Functions on the Incident Radiation Field with Machine Learning

Aug 5, 2026

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Gas cooling and heating functions are fundamental to modeling galaxy formation, yet computing them exactly for arbitrary incident radiation fields is computationally demanding. The study investigates how machine learning can approximate these functions using a generalized radiation field while reducing reliance on costly photoionization calculations. XGBoost models predict cooling and heating functions computed with Cloudy at fixed metallicity, using selected photoionization rates as input features. PCA and SHAP guide feature importance and subset selection.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages16

Reading Time40 min

AccessFree to download

Abstract

Introduction

Galaxy formation and the role of cooling/heating

Cooling-heating functions and radiative equilibrium

Photoionization codes and Cloudy background

arXiv :2310 .09328v2 [ astro-ph .CO] 18 Jan 2024 Exploring the Dependence of Gas Cooling and Heating Functions on the Incident Radiation Field with Machine Learning David Robinson , 1 ★ Camille Avestruz , 1,2 Nickolay Y. Gnedin 3,4,5 1 Department of Physics; University of Michigan, Ann Arbor, MI 48109, USA 2 Leinweber Center for Theoretical Physics; University of Michigan, Ann Arbor, MI 48109, USA 3 Theoretical Physics Division; Fermi National Accelerator Laboratory; Batavia, IL 60510, USA 4 Kavli Institute for Cosmological Physics; The University of Chicago; Chicago, IL 60637, USA 5 Department of Astronomy & Astrophysics; The University of Chicago; Chicago, IL 60637, USA Accepted XXX. Received YYY; in original form ZZZ ABSTRACT Gas cooling and heating functions play a crucial role in galaxy formation. But, it is computationally expensive to exactly compute these functions in the presence of an incident radiation field. These computations can be greatly sped up by using interpolation tables of pre-computed values, at the expense of making significant and sometimes even unjustified approximations. Here, we explore the capacity of machine learning to approximate cooling and heating functions with a generalized radiation field. Specifically, we use the machine learning algorithm XGBoost to predict cooling and heating functions calculated with the photoionization code Cloudy at fixed metallicity, using different combinations of photoionization rates as features. We perform a constrained quadratic fit in metallicity to enable a fair comparison with traditional interpolation methods at arbitrary metallicity. We consider the relative importance of various photoionization rates through both a principal component analysis (PCA) and calculation of SHapley Additive exPlanation (SHAP) values for our XGBoost models. We use feature importance information to select different subsets of rates to use in model training. Our XGBoost models outperform a traditional interpolation approach at each fixed metallicity, regardless of feature selection. At arbitrary metallicity, we are able to reduce the frequency of the largest cooling and heating function errors compared to an interpolation table. We find that the primary bottleneck to increasing accuracy lies in accurately capturing the metallicity dependence. This study demonstrates the potential of machine learning methods such as XGBoost to capture the non-linear behavior of cooling and heating functions. Key words: galaxies: formation—methods: numerical—cosmology: miscellaneous 1 INTRODUCTION Galaxy formation involves many interacting processes, of which the primary one is the gravitational collapse of baryonic gas into the potential wells of dark matter halos after the decoupling of baryons and photons. Since baryonic gas can provide thermal pressure support, the rate at which the gas can dissipate energy (via cooling) is a critical factor in determining the density and temperature at which the gravitational collapse stops (Rees & Ostriker 1977) . Cooling and heating functions are a traditional way of describing how the internal energy of the gas changes due to radiative processes (e.g. Cox & Tucker 1969; Sutherland & Dopita 1993; Lykins et al. 2013; Wanget al. 2014), and determine the thermal evolution of gas (e.g. Dalgarno & McCray 1972; Gnat & Sternberg 2007) . Coupled with other relevant processes, cooling and heating functions help determine the overall evolution of the gas (e.g. Martínez-Serrano et al. 2008; Richings et al. 2014; Galligan et al. 2019; Romero et al. 2021) . Hence, cooling and heating functions are important to theoretical modeling of galaxy formation (see the review of Benson 2010) . For example, the comparison between the gas cooling time and the gravitational ★ E-mail: [dbrobins@umich.edu](dbrobins@umich.edu) freefall time introduces characteristic scales where the two are equal (e.g. Rees & Ostriker 1977; Silk 1977; White & Frenk 1991; Kauff

FAQs

Why are cooling and heating functions important in galaxy formation?

They describe how gas internal energy changes due to radiative processes and determine the gas’s thermal evolution, affecting where gravitational collapse and accretion proceed.

What machine learning method is used to approximate the cooling and heating functions?

The study uses XGBoost to predict cooling and heating functions calculated with the Cloudy photoionization code.

How do the authors evaluate which photoionization rates matter most?

They use PCA and SHAP value analysis for the XGBoost models to assess relative importance and to choose subsets of rates for training.

Aug 5, 2026

Upload by Ivy