Core States of Neutron Stars from Anatomizing their Scaled Structure Equations

Abstract

Given an Equation of State (EOS) for neutron star (NS) matter, there is a unique mass-radius sequence characterized by a maximum mass $M_{\mathrm{NS}}^{\max }$ at radius $R_{\max }$. We first show analytically that the $M_{\mathrm{NS}}^{\max }$ and $R_{\max }$ scale linearly with two different combinations of NS central pressure $P_{\mathrm{c}}$ and energy density ${\epsilon }_{\mathrm{c}}$ by dissecting perturbatively the dimensionless Tolman-Oppenheimer-Volkoff (TOV) equations governing NS internal variables. The scaling relations are then verified via 87 widely used and rather diverse phenomenological as well as 17 microscopic NS EOSs with/without considering hadron-quark phase transitions and hyperons by solving numerically the original TOV equations. The EOS of densest NS matter allowed before it collapses into a black hole (BH) is then obtained. Using the universal $M_{\mathrm{NS}}^{\max }$ and $R_{\max }$ scalings and NICER (Neutron Star Interior Composition Explorer) and XMM-Newton mass-radius observational data for PSR J0740+6620, a very narrow constraining band on the NS central EOS is extracted directly from the data for the first time without using any specific input EOS model.

APJ in press

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• Mass and radius of the most massive neutron star: The probe of the equation of state and perturbative QCD
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• Bayesian Inference of Hybrid Star Properties from Future High-Precision Measurements of Their Radii
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• Is The Trace Anomaly at its Minimum Value at Neutron Star Centers?