Universal relations for neutron stars refer to parameter connections between macroscopic stellar quantities that exhibit a remarkable insensitivity to the underlying stellar core microphysics, which is parametrized through the equation of state (EoS). These relations hold across a wide variety of nuclear matter EoS models, despite the significant uncertainties in the microphysical description of dense matter. They serve as powerful tools to probe neutron star structure and dynamics without requiring detailed knowledge of the internal EoS. The field has gained increasing importance in the era of multimessenger astronomy, where observations from electromagnetic and gravitational wave signals offer complementary constraints on neutron star structure. In this context, machine learning techniques have recently emerged as a robust and flexible framework for discovering, refining, and validating these relations. These computational tools allow for high-accuracy regression and feature selection across large ensembles of EoS models, enabling data-driven insights into the global behavior of their properties. Above all, Universal relations have the potential to inform future observational missions—such as NICER or advanced gravitational wave detectors—by linking measurable astrophysical observables to otherwise inaccessible internal properties, thereby providing a means to break degeneracies and constrain the physics of ultra-dense matter.
Key Features
- This work proposes new universal relations regarding the surface of a rotating neutron star, employing machine-learning techniques for regression. More specifically, we developed highly accurate universal relations for a neutron star’s eccentricity, the star’s ratio of the polar to the equatorial radius, and the effective gravitational acceleration at both the pole and the equator. Furthermore, we propose an accurate theoretical formula for (dlogR(μ)/dθ)max. Our regression methodology enables accurate estimations of the star’s surface R(μ), its corresponding logarithmic derivative dlogR(μ)/dθ, and its effective acceleration due to gravity g(μ) with accuracy better than 1 %. The analysis is performed for an extended sample of rotating configurations constructed using a large ensemble of 70 tabulated hadronic, hyperonic, and hybrid EoS models that obey the current multimessenger constraints and cover a wide range of stiffnesses. Above all, the suggested relations could provide an accurate framework for the star’s surface estimation using data acquired with the NICER X-ray telescope or future missions.
Link: 🔗 GitHub Repository