Classifying binary black holes from Population III stars with the Einstein Telescope: A machine-learning approach

¹ Gran Sasso Science Institute (GSSI), 67100 L’Aquila, Italy
² INFN, Laboratori Nazionali del Gran Sasso, 67100 Assergi, Italy
³ Département de Physique Théorique, Université de Genève, 24 quai Ernest Ansermet, 1211 Genève, Switzerland
⁴ Gravitational Wave Science Center (GWSC), Université de Genève, 1211 Genève, Switzerland
⁵ Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli studi di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
⁶ INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
⁷ Institut für Theoretische Astrophysik, ZAH, Universität Heidelberg, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
⁸ Dipartimento di Fisica “G. Occhialini”, Università degli studi di Milano-Bicocca, piazza della Scienza 3, 20126 Milano, Italy
⁹ INFN, Sezione di Milano-Bicocca, piazza della Scienza 3, 20126 Milano, Italy
¹⁰ School of Physics and Astronomy & Institute for Gravitational Wave Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
¹¹ Département de Physique, Université de Montréal, 1375 Avenue Thérèse-Lavoie-Roux, Montréal, Canada
¹² Mila – Quebec Artificial Intelligence Institute, 6666 Rue Saint-Urbain, Montréal, Canada
¹³ Ciela – Montréal Institute for Astrophysical Data Analysis and Machine Learning, Montréal, Canada

Received: 15 April 2024
Accepted: 21 August 2024

Abstract

Third-generation (3G) gravitational-wave detectors such as the Einstein Telescope (ET) will observe binary black hole (BBH) mergers at redshifts up to z ∼ 100. However, an unequivocal determination of the origin of high-redshift sources will remain uncertain because of the low signal-to-noise ratio (S/N) and poor estimate of their luminosity distance. This study proposes a machine-learning approach to infer the origins of high-redshift BBHs. We specifically differentiate those arising from Population III (Pop. III) stars, which probably are the first progenitors of star-born BBH mergers in the Universe, and those originated from Population I-II (Pop. I–II) stars. We considered a wide range of models that encompass the current uncertainties on Pop. III BBH mergers. We then estimated the parameter errors of the detected sources with ET using the Fisher information-matrix formalism, followed by a classification using XGBOOST, which is a machine-learning algorithm based on decision trees. For a set of mock observed BBHs, we provide the probability that they belong to the Pop. III class while considering the parameter errors of each source. In our fiducial model, we accurately identify ≳10% of the detected BBHs that originate from Pop. III stars with a precision > 90%. Our study demonstrates that machine-learning enables us to achieve some pivotal aspects of the ET science case by exploring the origin of individual high-redshift GW observations. We set the basis for further studies, which will integrate additional simulated populations and account for further uncertainties in the population modeling.