Universal relations for rapidly rotating neutron stars using supervised machine-learning techniques

As some of the most compact stellar objects in the Universe, neutron stars are unique cosmic laboratories. The study of neutron stars provides an ideal theoretical test bed for investigating both physics at supranuclear densities as well as fundamental physics. Their global astrophysical properties however depend strongly on the star's internal structure, which is currently unknown due to uncertainties in the equation of state. In recent years, a lot of work has revealed the existence of universal relations between stellar quantities that are insensitive to the equation of state. At the same time, the field of multimessenger astronomy has been uniquely expanded with the advent of gravitational wave astronomy, which has recently been making strides towards incorporating machine learning techniques. In this paper, we develop universal relations for rapidly rotating neutron stars, by using supervised machine learning methods, thus proposing a new way of discovering and validating such relations. The analysis is performed for tabulated hadronic, hyperonic, and hybrid equation of state ensembles that obey the multimessenger constraints and cover a wide range of stiffnesses. The relations discussed could provide an accurate tool to constrain the equation of state of nuclear matter when measurements of the relevant observables become available.