On the Sound Speed in Neutron Stars

Determining the sound speed cs in compact stars is an important open question with numerous implications on the behavior of matter at large densities and hence on gravitational-wave emission from neutron stars. To this scope, we construct more than 107 equations of state (EOSs) with continuous sound speed and build more than 108 nonrotating stellar models consistent not only with nuclear theory and perturbative QCD, but also with astronomical observations. In this way, we find that EOSs with subconformal sound speeds, i.e., with ${c}_{s}^{2}\lt 1/3$ within the stars, are possible in principle but very unlikely in practice, being only 0.03% of our sample. Hence, it is natural to expect that ${c}_{s}^{2}\gt 1/3$ somewhere in the stellar interior. Using our large sample, we obtain estimates at 95% credibility of neutron-star radii for representative stars with 1.4 and 2.0 solar masses, ${R}_{1.4}={12.42}_{-0.99}^{+0.52}\,\mathrm{km}$, ${R}_{2.0}={12.12}_{-1.23}^{+1.11}\,\mathrm{km}$, and for the binary tidal deformability of the GW170817 event, ${\tilde{{\rm{\Lambda }}}}_{1.186}={485}_{-211}^{+225}$. Interestingly, our lower bounds on the radii are in very good agreement with the prediction derived from very different arguments, namely, the threshold mass. Finally, we provide simple analytic expressions to determine the minimum and maximum values of $\tilde{{\rm{\Lambda }}}$ as a function of the chirp mass.