A general, scale-independent description of the sound speed in neutron stars

Using more than a million randomly generated equations of state that satisfy theoretical and observational constraints we construct a novel, scale-independent description of the sound speed in neutron stars where the latter is expressed in a unit-cube spanning the normalised radius, $r/R$, and the mass normalized to the maximum one, $M/M_{\mathrm{T}\mathrm{O}\mathrm{V}}$. From this generic representation, a number of interesting and surprising results can be deduced. In particular, we find that light (heavy) stars have stiff (soft) cores and soft (stiff) outer layers, respectively, or that the maximum of the sound speed is located at the center of light stars but moves to the outer layers for stars with $M/M_{\mathrm{T}\mathrm{O}\mathrm{V}}\gtrsim 0.7$, reaching a constant value of $c_s^2=1/2$ as $M\to M_{\mathrm{T}\mathrm{O}\mathrm{V}}$. We also show that the sound speed decreases below the conformal limit $c_s^2=1/3$ at the center of stars with $M=M_{\mathrm{T}\mathrm{O}\mathrm{V}}$. Finally, we construct an analytic expression that accurately describes the radial dependence of the sound speed as a function of the neutron-star mass, thus providing an estimate of the maximum sound speed expected in a neutron star.