On the Sound Speed in Neutron Stars

Abstract

Determining the sound speed cs in compact stars is an important open question with numerous implications on the behaviour of matter at large densities and hence on gravitational-wave emission from neutron stars. To this scope, we construct more than 10 7 equations of state (EOSs) with continuous sound speed and build more than 10 8 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 sub-conformal sound speeds, i.e., with c 2 s < 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 2 s > 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, R1.4 = 12.42 +0.52 −0.99 km, R2.0 = 12.12 +1.11 −1.23 km, and for the binary tidal deformability of the GW170817 event, Λ1.186 = 485 +225 −211 . 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 [61] (see Table I).…”

Speed of sound in dense strong-interaction matter

“…It is also interesting to speculate whether it is possible to use constraints on the speed of sound from nuclear physics and observations to constrain the properties of color-superconducting matter. To be more specific, constraints on the speed of sound from observations provide estimates for lower bounds of the crossing density [17][18][19]. Since our present study suggests that this density can be related to the size of the gap, constraints on the crossing density allow to draw conclusions on the size of the gap in dense strong-interaction matter, see Fig.…”

“…Still, on a qualitative level, the density dependence of the speed of sound in neutron-star matter may also be constrained by mechanisms which are similar to the ones discussed in the present work. Indeed, with respect to the maximum in the speed of sound, constraints from neutron-star masses also strongly support the existence of a maximum in the speed of sound in neutron-rich matter [13][14][15][16][17][18][19]. In particular, the existence of a maximum in the speed of sound and a local minimum in the speed of sound at high densities has already been discussed in an analysis of constraints from astrophysical observations in Ref.…”

“…In recent studies based on the functional renormalization group (fRG) approach, it has then been found that the presence of a color-superconducting gap in the excitation spectrum of the quarks gives rise to a maximum in the speed of sound [23,47,48]. Notably, in accordance with constraints from nuclear physics and observations [13][14][15][16][17][18][19], this maximum exceeds the asymptotic value associated with the non-interacting quark gas, for both isospin-symmetric matter and neutron-star matter.…”

“…The impressive progress made in the observation of neutron-star mergers via gravitational-wave signals [1,2] together with the advances made in direct measurements of the radius and the mass of heavy neutron stars [3][4][5][6][7][8][9][10][11][12] challenges our understanding of the properties of dense strong-interaction matter. For example, constraints from neutron-star masses suggest the existence of a maximum in the speed of sound in dense matter which exceeds the asymptotic value of a non-interacting quarks gas [13][14][15][16][17][18][19], preferably at densities n/n 0 10 (where n 0 is the nuclear saturation density).…”