On the Sound Speed in Neutron Stars

Abstract

Determining the sound speed c s 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 < 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 > 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 km , R 2.0 = 12.12 − 1.23 + 1.11 km , and for the binary tidal deformability of the GW170817 event, Λ ˜ 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 Λ ˜ as a function of the chirp mass.

Quark formation and phenomenology in binary neutron-star mergers using V-QCD

“…Finally, shown with a black dashed line is a theoretical lower bound for the radii as computed from considerations on the threshold mass by Koeppel et al [27]. We note that we have checked that our EOSs respect the upper bound on the binary tidal deformability Λ < 720 (low-spin priors) obtained from GW171817 and are well within the bounds recently proposed on general parameterization of the sound speed in neutron stars [60] (see Table 1).…”

Thoughts about the utility of perturbative QCD in the cores of neutron stars – contribution to a roundtable discussion on neutron stars and QCD

“…In addition giving direction to model building, the perturbative-QCD constraint affects the model-agnostic inference of equation of state. This is implicitly visible already in the interpolation studies that have incorporated the QCD constraint by interpolating the thermodynamic potential [3,10,[14][15][16][17][18][19]. As discussed before, these studies consistently give differing results compared to the studies without QCD.…”

“…This softening is seen again and again in subsequent works. It is seen in works by myself and my collaborators as well as other groups that have imposed the perturbative-QCD input to their inference setups [3,[14][15][16][17][18][19]. The obvious criticism to the findings of the early works was that the interpolation over two orders of magnitude was performed with only two-or three-segment interpolation functions, it was performed only with single basis function and the ensembles where only rather small, and so on.…”

“…It is important to note that the constraints are not novel, in the sense many interpolation studies, starting from [10] and including many others [3,[14][15][16][17][18][19], have included the QCD constraint by interpolating the thermodynamic potential, not the reduced equation of state. The novelty of this work is two-fold.…”

“…As discussed before, these studies consistently give differing results compared to the studies without QCD. But in these studies, the questions about the generality of interpolation functions, number of segments and other details convolute the conclusion (even if several works have seen approximate convergence as a number of interpolation segments, nicely documented, e.g., in [16]). A doubt always remains to what extent is the constraint arising from limitations of the interpolation and to what extent they are a robust prediction of QCD.…”