A geometric physics-informed machine learning inference for the neutron star maximum mass and the inverse problem

TL;DR

This paper introduces a physics-informed machine learning approach using a Transformer model to infer the maximum mass and internal properties of neutron stars from astrophysical observations, addressing uncertainties in dense matter physics.

Contribution

It develops a novel geometric and physics-informed machine learning framework that predicts neutron star maximum mass and internal sound speed profiles from observational data.

Findings

Maximum neutron star mass predicted as 2.477 solar masses.

Minimum radius for 1.4 solar mass neutron star is about 11.5 km.

Massive stars favor a stiff equation of state at low density.

Abstract

The existence of a distinct mass boundary between the heaviest neutron stars and the lightest black holes remains in question. It is an artefact of our ignorance of the properties of matter at supra-nuclear densities, which exist in the cores of neutron stars. The study addresses these problems with a physics-informed machine learning approach, guided by astrophysical observations. The Transformer model is trained on an agnostically generated ensemble of equations of state. Two geometric parameters are defined on the mass-radius sequence of a neutron star--the front bending and the back bending. The transformer provides a two-step solution: first, the model predicts the maximum mass and radius using the bending parameters. Second, it predicts the square of the sound speed profile, completing the inverse mapping. The prediction is that massive neutron stars form when the sound speed peaks at low density, leading to strong back-bending and an early phase transition to quark matter. Massive stars favour a stiff equation of state at low density, and the density of matter at the star's core is sufficiently small. The maximum mass for a neutron star predicted by the astrophysical constrained transformer model is $2.477$ solar masses, and a minimum radius of about $11.498$ km for a neutron star of $1.4$ solar masses.