Which Neutron Stars Reach the Stiffening Regime? Multimessenger Constraints on Core Sound Speed and Stellar-Mass Thresholds

Abstract

We present a concise multimessenger inference of the neutron-star core sound-speed profile using GW170817 and three \textit{NICER} mass--radius posteriors (PSR J0030$+$0451, PSR J0740$+$6620, and PSR J0437$-$4715). The main result is not only a preference for intermediate-density stiffening within smooth equation-of-state families, but a translation of that inference into the stellar masses that access the relevant density regime. In the baseline smooth peaked family, the posterior probability that $c_s^2>1/3$ at $3.5n_{\mathrm{sat}}$ is $85.4\%$, while equal-prior averaging over peaked, monotonic, piecewise, and transition-capable families gives a more conservative $79.0\%$. Posterior-resampled exact Tolman--Oppenheimer--Volkoff solutions show that the onset density of the inferred stiffening is typically reached near $1.6M_{\odot }$, whereas the peak region is accessed only near $2.1M_{\odot }$. A J0740-like $2.07M_{\odot }$ pulsar reaches the onset in $91\%$ of posterior draws but the peak in only $46\%$, showing that current data mainly constrain whether massive stars have entered the stiffening regime rather than traversed its full peak.