2023ApJ...952..147C

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 the NS central pressure P_c and energy density ε_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 the densest NS matter allowed before it collapses into a black hole is then obtained. Using the universal ${M}_{\mathrm{NS}}^{\max }$ and R_max scalings and 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.