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A considerable effort has been dedicated recently to the construction of generic equations of state (EOSs) for matter in neutron stars. The advantage of these approaches is that they can provide model-independent information on the interior structure and global properties of neutron stars. Making use of more than 106 generic EOSs, we assess the validity of quasi-universal relations of neutron-star properties for a broad range of rotation rates, from slow rotation up to the mass-shedding limit. In this way, we are able to determine with unprecedented accuracy the quasi-universal maximum-mass ratio between rotating and nonrotating stars and reveal the existence of a new relation for the surface oblateness, i.e., the ratio between the polar and equatorial proper radii. We discuss the impact that our findings have on the imminent detection of new binary neutron-star mergers and how they can be used to set new and more stringent limits on the maximum mass of nonrotating neutron stars, as well as to improve the modeling of the X-ray emission from the surface of rotating 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 cs 1 3 2 < 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 cs 1 3 2 > 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, R1.4 12.42 km 0.99 0.52 = - + , R2.0 12.12 km 1.23 1.11 = - + , and for the binary tidal deformability of the GW170817 event, 1.186 485 211 225 L = - ˜ + . 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 L˜ as a function of the chirp mass.
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 normalized radius, r/R, and the mass normalized to the maximum one, M/MTOV. 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, 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/MTOV ≳ 0.7, reaching a constant value of cs = 1 2 2 as M → MTOV. We also show that the sound speed decreases below the conformal limit cs = 1 3 2 at the center of stars with M = MTOV. 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.