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Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EOS) at densities and temperatures realized inside neutron stars and their mergers is a long-standing open problem. The holographic V-QCD framework provides a model for the EOS of dense and hot QCD, which describes the deconfinement phase transition between a dense baryonic and a quark matter phase. We use this model in fully general relativistic hydrodynamic (GRHD) simulations to study the formation of quark matter and the emitted gravitational wave signal of binary systems that are similar to the first ever observed neutron star merger event GW170817.
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.
We have investigated the systematic differences introduced when performing a Bayesian-inference analysis of the equation of state of neutron stars employing either variable- or constant-likelihood functions. The former have the advantage that it retains the full information on the distributions of the measurements, making an exhaustive usage of the data. The latter, on the other hand, have the advantage of a much simpler implementation and reduced computational costs. In both approaches, the EOSs have identical priors and have been built using the sound-speed parameterization method so as to satisfy the constraints from X-ray and gravitationalwaves observations, as well as those from Chiral Effective Theory and perturbative QCD. In all cases, the two approaches lead to very similar results and the 90%-confidence levels are essentially overlapping. Some differences do appear, but in regions where the probability density is extremely small and are mostly due to the sharp cutoff set on the binary tidal deformability Λ˜ ≤ 720 employed in the constant-likelihood analysis. Our analysis has also produced two additional results. First, a clear inverse correlation between the normalized central number density of a maximally massive star, nc,TOV/ns, and the radius of a maximally massive star, RTOV. Second, and most importantly, it has confirmed the relation between the chirp mass Mchirp and the binary tidal deformability Λ˜. The importance of this result is that it relates a quantity that is measured very accurately, Mchirp, with a quantity that contains important information on the micro-physics, Λ˜. Hence, once Mchirp is measured in future detections, our relation has the potential of setting tight constraints on Λ˜.
Using full 3+1 dimensional general-relativistic hydrodynamic simulations of equal- and unequal-mass neutron-star binaries with properties that are consistent with those inferred from the inspiral of GW170817, we perform a detailed study of the quark-formation processes that could take place after merger. We use three equations of state consistent with current pulsar observations derived from a novel finite-temperature framework based on V-QCD, a non-perturbative gauge/gravity model for Quantum Chromodynamics. In this way, we identify three different post-merger stages at which mixed baryonic and quark matter, as well as pure quark matter, are generated. A phase transition triggered collapse already ≲10ms after the merger reveals that the softest version of our equations of state is actually inconsistent with the expected second-long post-merger lifetime of GW170817. Our results underline the impact that multi-messenger observations of binary neutron-star mergers can have in constraining the equation of state of nuclear matter, especially in its most extreme regimes.
Using full 3+1 dimensional general-relativistic hydrodynamic simulations of equal- and unequal-mass neutron-star binaries with properties that are consistent with those inferred from the inspiral of GW170817, we perform a detailed study of the quark-formation processes that could take place after merger. We use three equations of state consistent with current pulsar observations derived from a novel finite-temperature framework based on V-QCD, a non-perturbative gauge/gravity model for Quantum Chromodynamics. In this way, we identify three different post-merger stages at which mixed baryonic and quark matter, as well as pure quark matter, are generated. A phase transition triggered collapse already ≲ 10 ms after the merger reveals that the softest version of our equations of state is actually inconsistent with the expected second-long post-merger lifetime of GW170817. Our results underline the impact that gravitational wave observations of binary neutron-star mergers can have in constraining the equation of state of nuclear matter, especially in its most extreme regimes.