Novel Scalings of Neutron Star Properties from Analyzing Dimensionless Tolman--Oppenheimer--Volkoff Equations

The TOV equations govern the radial evolution of pressure and energy density in static neutron stars (NSs) in hydrodynamical equilibrium. Using the reduced pressure and energy density with respect to the NS central energy density, the original TOV equations can be recast into dimensionless forms. While the traditionally used integral approach for solving the original TOV equations require an input nuclear Equation of State (EOS), the dimensionless TOV equations can be anatomized by using the reduced pressure and energy density as polynomials of the reduced radial coordinate without using any input nuclear EOS. Interesting and novel perspectives about NS core EOS can be extracted directly from NS observables using this new approach based on Intrinsic and Perturbative Analyses of the Dimensionless (IPAD) TOV equations (IPAD-TOV). In this review, we first discuss the length and energy density scales of NSs as well as the dimensionless TOV equations for scaled variables and their perturbative solutions near NS cores. We then review several new insights into NS physics gained from using the IPAD-TOV. We also demonstrate that the strong-field gravity plays a fundamental role in extruding a peak in the density/radius profile of the speed of sound squared (SSS) in massive NS cores independent of the nuclear EOS. Finally, some future perspectives of NS research using the IPAD-TOV are outlined.