The Role of the Core in Setting Massive Neutron-Star Radii

Recent observations by the Neutron Star Interior Composition Explorer (NICER) indicate that the massive pulsar PSR J0740+6620 (2.08,M) has a radius comparable to those inferred for stars near 1.4,M, as shown by PSR J0030+0451 and updated analyses. Such near-vertical mass-radius behavior is difficult to obtain unless the high-density equation of state (EOS) stiffens strongly. We show that, for massive pulsars, the leading radial scale can be set by a relativistic, high-sound-velocity core beginning near twice the nuclear saturation scale, while the outer low-density layer, comprising the true crust and outer core, supplies only a subdominant correction. The key evidence comes from radius decomposition: replacing the low-density branch below the matching point with unified EOS models spanning a factor of two in transition pressure changes the 2.08,M core radius by only about160 m, about half the variation of the total radius. This convergence is genuinely a high-mass phenomenon: at 1.4,M the core radius remains more branch-sensitive, varying by about 0.5 km. Fixed-fraction comparisons confirm that core dominance emerges systematically as the star grows more massive, where the traditional separation between ``radius physics'' and ``maximum-mass physics'' breaks down. We establish this picture by combining analytical Tolman VII profiles and thin-crust matching, numerical Tolman-Oppenheimer-Volkoff integration with a piecewise EOS, and direct-grid Bayesian inference using NICER and GW170817 constraints under causal and mass-support filters. Data modestly constrain the transition stiffness but leave the quadratic stiffening governed mainly by causality. A comparison with a constant-sound-speed core remains inconclusive: both descriptions produce comparable core-dominated radii, leaving a degeneracy that sub-kilometre radius measurements can break.