Upper Limit of Sound Speed in Nuclear Matter: A Harmonious Interplay of Transport Calculation and Perturbative Quantum Chromodynamic Constraint

Abstract

Very recently, it has been shown that there is an upper bound on the squared sound speed of nuclear matter from the transport, which reads $c_{\rm s}^2 \leq 0.781$. In this work, we demonstrate that this upper bound is corroborated by the reconstructed equation of state (EOS; modeled with a nonparametric method) for ultradense matter. The reconstruction integrates multimessenger observation for neutron stars, in particular, the latest radius measurements for PSR J0437-4715 ($11.36^{+0.95}_{-0.63}$ km), PSR J0030+0451 ($11.71^{+0.88}_{-0.83}$ km, in the ST+PDT model), and PSR J0740+6620 ($12.49^{+1.28}_{-0.88}$ km) by NICER have been adopted. The result shows in all cases, the $c_{\rm s}^2 \leq 0.781$ upper limit for EOS will naturally yield the properties of matter near the center of the massive neutron star consistent with the causality-driven constraint from pQCD, where, in practice, the density in implementing the pQCD likelihood ($n_{\rm L}$) is applied at $10n_s$ (where $n_s$ is the nuclear saturation density). We also note that there is a strong correlation for the maximum $c_s^2$ with $n_{\rm L}$, and $c_{\rm s}^2 \leq 0.781$ is somehow violated when $n_{\rm L} = n_{\rm c,TOV}$. The result indicates that a higher $n_{\rm L}$, even considering the uncertainties from statistics, is more natural. Moreover, the remarkable agreement between the outcomes derived from these two distinct and independent constraints (i.e., the transport calculation and pQCD boundary) lends strong support to their validity. In addition, the latest joint constraint for $R_{1.4}$, $R_{2.0}$, $R_{1.4}-R_{2.0}$, and $M_{\rm TOV}$ are $11.94_{-0.68}^{+0.77}$ km, $11.99_{-0.67}^{+0.88}$ km, $-0.1_{-0.27}^{+0.42}$ km, and $2.24_{-0.10}^{+0.13}M_\odot$ (at $90\%$ credible level), respectively.