Machine learning classification of black holes in the mass--spin diagram

TL;DR

This paper introduces a mass--spin diagram for black hole classification, combining evolutionary models with machine learning techniques to analyze black hole populations and their formation pathways.

Contribution

It presents a novel mass--spin diagram framework and applies advanced machine learning methods, including deep autoencoders, for classifying black hole populations based on their mass and spin data.

Findings

Unsupervised clustering nearly recovers known black hole population boundaries.

Deep learning enhances clustering of overlapping subclasses in mass--spin space.

Supervised random forests accurately classify populations depending on dataset complexity.

Abstract

We present the mass--spin diagram for classifying black holes and studying their formation pathways providing an analogue to the Hertzsprung-Russell diagram. This allows for black hole evolutionary tracks as a function of redshift, combining formation, accretion, and merger histories for the variety of black hole populations. A realistic black hole continuum constructed from initial mass and spin functions and approximate redshift evolution reveals possible black hole main sequences, such as sustained coherent accretion through cosmic time or hierarchical merger trees. In the stellar-mass regime, we use a binary population synthesis software to compare three spin prescriptions for tidal evolution of Wolf-Rayet progenitors, showing how the mass--spin diagram exposes interesting modeling differences. We then classify black hole populations by applying supervised and unsupervised machine learning clustering methods to mass--spin datasets. While bare unsupervised clustering can nearly recover canonical population boundaries (stellar-mass, intermediate-mass, and supermassive), a more sophisticated approach utilizing deep learning via variational autoencoders for latent space representation learning aids in clustering of realistic datasets with subclasses that highly overlap in mass--spin space. We find that a supervised random forest can accurately recover the correct clusters from the learned latent space representation depending on the complexity of the underlying dataset, semi-supervised methods show potential for further development, and the performance of unsupervised classifiers is a great challenge. Our findings motivate future machine learning applications and demonstrate that the mass--spin diagram can be used to connect gravitational-wave and electromagnetic observations with theoretical models.