Mapping mass and radius of compact objects to neutron star equation of state or boson star scalar potential

Project Description Various astronomical observations provide mass and radius information about compact stellar objects that are generally thought to be neutron stars. This mass-versus-radius curve reveals information about the equation of state of the dense matter constituting the neutron star. An alternative explanation for some of these objects is that they are actually boson stars -- hypothetical compact objects made up of exotic matter. For boson stars, the mass-radius curve would reveal information about their scalar potential, the analog of a neutron star's equation of state. An important question is to what extent neutron stars and boson stars can be observationally distinguished based on their mass-versus-radius curves, or conversely to what extent these two types of object can produce the same mass-versus-radius curves.

Inferring the properties of a neutron star or boson star from its mass-versus-radius curve is the inverse of the usual "forward" approach of solving the stellar structure equations with the equation of state / scalar potential to compute this curve. By parameterizing a wide class of equations of state and scalar potentials, we plan to train neural networks to predict these properties from a given mass-versus-radius curve. The question of distinguishability can then be investigated directly by studying the resulting networks and their predictions.

We will first generate thousands of examples of mass-versus-radius curves corresponding to a range of neutron-star equations of state and boson-star scalar potentials by solving the Tolman-Oppenheimer-Volkoff (TOV) equations, a system of ODEs that describe the structure of these stars. We will rely on two open-source TOV solver packages for this step, though we also plan investigate a fast, GPU-enabled TOV solver written by a current graduate student at Princeton. We will then train and test neural networks that, given a mass-versus-radius curve, will predict the underlying equation of state or scalar potential that gave rise to it. The infrastructure developed in the course of this project will support future exploration of the primary scientific questions of neutron/boson star distinguishability.

A previous student worked briefly on this problem and produced an initial implementation that handles a severely limited range of mass-versus-radius curves and runs on a single processor. For this project, we will need to scale both production of mass-versus-radius curves and neural network training/inference to HPC platforms. We anticipate using PyTorch for the machine-learning aspects of the project.