Strong gravity extruding peaks in speed of sound profiles of massive neutron stars

The speed of sound squared (SSS) s² in massive neutron stars (NSs) characterizes not only the stiffness of supradense neutron-rich matter within but also equivalently properties of the curved geometry due to the strong-field gravity and matter-geometry coupling. A peaked density or radius profile of s² has been predicted for massive NSs using various NS equation of state (EOS) models. However, the nature, cause, location and size of the peak in s² profiles are still very EOS model dependent. In this work, we investigate systematically s² profiles in massive NSs in a new approach that is independent of the nuclear EOS model and without any presumption about the NS structure and/or composition. In terms of the small quantities (reduced radius, the energy density and pressure scaled by their central values), we perform double-element perturbative expansions in solving perturbatively the scaled Tolman-Oppenheimer-Volkoff (TOV) equations and analyzing s² profiles from the Newtonian limit to the general relativistic (GR) case. The GR term in the TOV equations plays a twofold role: it compresses NS matter and modifies the pressure/energy density ratio from small values in Newtonian stars showing no s² peak to large ones for massive NSs possessing a peak in their s² profiles, and eventually takes away the peak in extremely compact/massive NSs approaching the causality limit. In particular, the peaked behavior in s² is expected to emerge near the center of massive NSs like PSR J⁢0740+6620, while a sharp phase transition is unlikely to occur there. Furthermore, these features revealed from our analyses are universal as they are intrinsic properties of the GR stellar structure equations independent of the still very uncertain EOS of supradense neutron-rich matter in NSs.. Authors: Cai, Bao-Jun [Shadow Creator Inc., Shanghai (China); East Texas A&M University (formerly known as Texas A&M University-Commerce)] (ORCID:0000000281501020); Li, Bao-An [Texas A&M University-Commerce, TX (United States)] (ORCID:0000000179974817). DOE Contract: SC0009971; SC0013702. Subjects: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS; Nuclear equation of state; general relativity; neutron stars; nuclear astrophysics; nuclear matter in neutron stars