Central speed of sound, the trace anomaly, and observables of neutron stars from a perturbative analysis of scaled Tolman-Oppenheimer-Volkoff equations

The central speed of sound (SS) measures the stiffness of the equation of state (EOS) of superdense neutron star (NS) matter. Its variations with density and radial coordinate in NSs in conventional analyses often suffer from uncertainties of the specific nuclear EOS used. Using the central SS and NS mass/radius scaling obtained from solving perturbatively the scaled Tolman-Oppenheimer-Volkoff (TOV) equations, we study the variations of SS, trace anomaly and several closely related properties of NSs in an EOS-model-independent manner. We find that the SS increases with the reduced central pressure P_{^ c}≡P_c/ϵ_c (scaled by the central energy density ϵ_c), and the conformal bound for SS tends to break down for NSs with masses higher than about 1.9 M_⊙. The ratio P /ϵ is upper bounded as P /ϵ ≲0.374 around the centers of stable NSs. We demonstrate that it is an intrinsic property of strong field gravity and is more relevant than the perturbative QCD bound on it. While a sharp phase transition at high densities characterized by a sudden vanishing of SS in cores of massive NSs are basically excluded, the probability for a continuous crossover signaled by a peaked radial profile of SS is found to be enhanced as P_^c decreases, implying it likely happens near the centers of massive NSs. Moreover, a new and more stringent causality boundary as R_max/km ≳4.73 M_NS^max/M_⊙+1.14 for the NS mass-radius curve is found to be excellently consistent with observational data on NS masses and radii. Furthermore, new constraints on the ultimate energy density and pressure allowed in NSs before collapsing into black holes are obtained and compared with earlier predictions in the literature.