Merging binaries of neutron stars are not only strong sources of gravitational waves, but also have the potential of revealing states of matter at densities and temperatures not accessible in laboratories. A crucial and longstanding question in this context is whether quarks are deconfined as a result of the dramatic increase in density and temperature following the merger. We present the first fully general-relativistic simulations of merging neutron stars including quarks at finite temperatures that can be switched off consistently in the equation of state. Within our approach, we can determine clearly what signatures a quark-hadron phase transition would leave in the gravitational-wave signal. We show that if after the merger the conditions are met for a phase transition to take place at several times nuclear saturation density, they would lead to a post-merger signal considerably different from the one expected from the inspiral, that can only probe the hadronic part of the equations of state, and to an anticipated collapse of the merged object. We also show that the phase transition leads to a very hot and dense quark core that, when it collapses to a black hole, produces a ringdown signal different from the hadronic one. Finally, in analogy with what is done in heavy-ion collisions, we use the evolution of the temperature and density in the merger remnant to illustrate the properties of the phase transition in a QCD phase diagram. PACS numbers: 04.25.Dm, 04.25.dk, 04.30.Db, 04.40.Dg, 95.30.Lz, 95.30.Sf, 97.60.Jd 97.60.Lf 26.60Kp 26.60Dd arXiv:1807.03684v2 [astro-ph.HE]

A hadronic chiral SU(3) model is applied to neutron and protoYneutron stars, taking into account trapped neutrinos, finite temperature, and entropy. The transition to the chirally restored phase is studied, and global properties of the stars such as minimum and maximum masses and radii are calculated for different cases. In addition, the effects of rotation on neutron star masses are included, and the conservation of baryon number and angular momentum determines the maximum frequencies of rotation during the cooling.

We extend the hadronic SU(3) non-linear sigma model to include quark degrees of freedom. The choice of potential for the deconfinement order parameter as a function of temperature and chemical potential allows us to construct a realistic phase diagram from the analysis of the order parameters of the system. These parameters are the chiral condensate, for the chiral symmetry restoration, and the scalar field Φ (as an effective field related to the Polyakov loop) for the deconfinement to quark matter. Besides reproducing lattice QCD results, for zero and low chemical potential, we are in agreement with neutron star observations for zero temperature. PACS numbers:The models used to describe neutron stars can generally be divided into two classes. The first class includes approaches in which the constituent particles are hadrons [1][2][3]. Some of them incorporate certain symmetries from QCD, like chiral symmetry, but they do not include deconfinement. Examples of these are hadronic sigma models [4][5][6][7]. The second class includes quark star models, which usually do not directly incorporate hadronic degrees of freedom in the model formulation. Examples of these are bag-model studies [8] as well as quark-NJL model and quark sigma-models [9].Using these approaches hybrid neutron stars, which consist of a hadronic and a quark phase, are normally described by adopting two different models with separate equations of state for hadronic and quark matter (see e.g. [10]). They are connected at the chemical potential in which the pressure of the quark EOS exceeds the hadronic one, signalling the phase transition to quark matter. Within our approach we employ a single model for the hadronic and for the quark phase.The extension of the hadronic SU(3) non-linear sigma model to quark degrees of freedom is constructed in a spirit similar to the PNJL model [11], in the sense that it is a non-linear sigma model that introduces a scalar field which suppress the quark degrees of freedom at low densities/temperatures. In QCD this scalar field was named Polyakov loop and is defined via Φ = 1 3 Tr[exp (i dτ A 4 )], where A 4 = iA 0 is the temporal component of the SU(3) gauge field. In our case, this scalar field is also called Φ, in analogy to the PNJL approach with an effective potential for the field, as discussed below, that drives the phase transition in the field Φ representing a phenomenological description of the transition from the confined to the deconfined phase.The Lagrangian density of the non-linear sigma model * Electronic address: dexheimer@th.physik.uni-frankfurt.de † Electronic address: schramm@th.physik.uni-frankfurt.de in mean field approximation reads:where besides the kinetic energy term for hadrons, quarks, and leptons (included to insure charge neutrality) the terms:represent the interactions between baryons (and quarks) and vector and scalar mesons, the self interactions of scalar and vector mesons and an explicit chiral symmetry breaking term, responsible for producing the masses of the pseudo-scalar mesons....

We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulae appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations, Ω = −P and P ⊥ = P − M B, with M = −∂Ω/∂B being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.