Hadron-quark Mixed Phase Research Articles

Neutrino emissivity in the quark-hadron mixed phase of neutron stars

Numerous theoretical studies using various equation of state models have shown that quark matter may exist at the extreme densities in the cores of high-mass neutron stars. It has also been shown that a phase transition from hadronic matter to quark matter would result in an extended mixed phase region that would segregate phases by net charge to minimize the total energy of the phase, leading to the formation of a crystalline lattice. The existence of quark matter in the core of a neutron star may have significant consequences for its thermal evolution, which for thousands of years is facilitated primarily by neutrino emission. In this work we investigate the effect a crystalline quark-hadron mixed phase can have on the neutrino emissivity from the core. To this end we calculate the equation of state using the relativistic mean-field approximation to model hadronic matter and a nonlocal extension of the three-flavor Nambu-Jona-Lasinio model for quark matter. Next we determine the extent of the quark-hadron mixed phase and its crystalline structure using the Glendenning construction, allowing for the formation of spherical blob, rod, and slab rare phase geometries. Finally we calculate the neutrino emissivity due to electron-lattice interactions utilizing the formalism developed for the analogous process in neutron star crusts. We find that the contribution to the neutrino emissivity due to the presence of a crystalline quark-hadron mixed phase is substantial compared to other mechanisms at fairly low temperatures ($\lesssim 10^9$ K) and quark fractions ($\lesssim 30\%$), and that contributions due to lattice vibrations are insignificant compared to static-lattice contributions.

Entanglement interaction and the phase diagram of strongly interacting matter

The entanglement interactions between the Polyakov loop and chiral condensate have been recently studied in the entangled Polyakov-loop Nambu--Jona-Lasinio model (EPNJL). The calculation shows that such an interaction plays an important role in the pseudocritical temperatures of deconfinement and chiral symmetry restoration. As a further study, here we construct a hadron-quark two-equation-of-state (two-EoS) model, based on the Walecka-quantum hadrodynamics and the EPNJL pictures, in order to study the equilibrium transition between hadronic and quark matter in heavy-ion collisions at finite densities and temperatures. We can explore the phase diagram of strongly interacting matter and the transition boundaries from nuclear to quark matter. We discuss the influence of the entanglement interaction on the critical point of the expected first-order phase transition in the two-EoS model. In particular, for charge asymmetric matter, we analyze the local asymmetry of the $u$, $d$ quarks as a function of quark concentration in the hadron-quark mixed phase during the phase transition. We finally propose some related observables that are possibly measurable in heavy-ion collision experiments.

Massive hybrid stars with a first-order phase transition

We develop our previous study of the transition to deconfined quark phase in neutron stars, including the interaction in the quark equation of state to the leading order in the perturbative expansion within the confinement density-dependent mass model. Using the Gibbs conditions the hadron-quark mixed phase is constructed matching the latter with the hadron equation of state derived from the microscopic Brueckner-Hartree-Fock approximation. The influence of quark interaction parameters on threshold properties and phase diagram of dense neutron star matter are discussed in detail. We find that the leading-order quark interaction expands the density range of the mixed phase, pushing forward the disappearance of the hadron phase. Moreover, since the equation of state could turn out to be stiffer, a high-mass hybrid star is possible with mixed-phase core with typical parameter sets.

Appearance of a quark matter phase in hybrid stars

The appearance of quark matter in the core of hybrid stars is a fundamental issue in such compact stars. The central density of these stars is sufficiently high such that nuclear matter undergoes a further change into other exotic phases that consist of hyperons and quarks. However, the equation of state (EOS) for the high-density matter is still not clear and several recent observations have indicated the limitations of the EOSs; theoretical studies should try to elucidate the EOSs. It is believed that the inner regions of the stars should consist of a mixed hadron-quark phase. We study the mixed hadron-quark phase, taking into account finite-size effects, and find that that the mixed phase should be restricted to a narrower region. Therefore, a quark matter phase should appear in the central region.

Novel non-equilibrium phase transition caused by non-linear hadronic-quark phase structure

We consider how the occurrence of first-order phase transitions in non-constant pressure differs from those at constant pressure. The former has shown the non-linear phase structure of mixed matter, which implies a particle number dependence of the binding energies of the two species. If the mixed matter is mixed hadron–quark phase, nucleon outgoing from hadronic phase and ingoing to quark phase probably reduces the system to a non-equilibrium state, in other words, there exists the imbalance of the two phases when deconfinement takes place. This novel non-equilibrium process is very analogous to the nuclear reactions that nuclei emit neutrons and absorb them under appropriate conditions. We present self-consistent thermodynamics in description for the processes and identify the microphysics responsible for the processes. The microphysics is an inevitable consequence of non-linear phase structure instead of the effect of an additional dissipation force. When applying our findings to the neutron star containing mixed hadron–quark matter, it is found that the newly discovered energy release might strongly change the thermal evolution behavior of the star.

Shear oscillations in the hadron–quark mixed phase

Inside neutron stars, the hadron-quark mixed phase is expected during the first order phase transition from the hadron phase to the quark phase. The geometrical structure of the mixed phase strongly depends on the surface tension at the hadron-quark interface. We evaluate the shear modulus which is one of the specific properties of the hadron-quark mixed phase. As an application, we study shear oscillations due to the hadron-quark mixed phase in neutron stars. We find that the frequencies of shear oscillations depend strongly on the surface tension; with a fixed stellar mass, the fundamental frequencies are almost proportional to the surface tension. Thus, one can estimate the value of surface tension via the observation of stellar oscillations with the help of the information on the stellar mass.

Maximum mass of a hybrid star having a mixed-phase region based on constraints set by the pulsar PSR J1614-2230

Recent observation of pulsar PSR J1614-2230 with a mass of about two solar masses poses a severe constraint on the equations of state (EOSs) of matter describing stars under extreme conditions. Neutron stars (NSs) can reach the mass limit set by PSR J1614-2230, but stars having hyperons or quark stars (QSs) having boson condensates, with softer EOSs, can barely reach such limit and are ruled out. QSs with pure strange matter cannot attain such high mass unless the effect of strong coupling constants or color superconductivity are considered. In this work I calculate the upper mass limit for a hybrid star (HS) having a quark-hadron mixed phase. The hadronic matter (having hyperons) EOS is described by relativistic mean field theory and the quark matter EOS is modeled according to the Massachusetts Institute of Technology bag model. The intermediate mixed phase is constructed using the Glendenning prescription. A HS with a mixed phase cannot reach the mass limit set by PSR J1614-2230 unless one assumes a density-dependent bag constant. However, for such case the mixed-phase region is small. The maximum mass of a mixed hybrid star obtained with such a mixed-phase region is $2.01{M}_{\ensuremath{\bigodot}}$. A stiffer hadronic EOS can raise the maximum mass of a mixed HS to $2.1$ ${M}_{\ensuremath{\bigodot}}$.

Transport properties of a quark-hadron Coulomb lattice in the cores of neutron stars

Already more that 40 years ago, it has been suggested that because of the enormous mass densities in the cores of neutron stars, the hadrons in the centers of neutron stars may undergo a phase transition to deconfined quark matter. In this picture, neutron stars could contain cores made of pure (up, down, strange) quark matter which are surrounded by a mixed phase of quarks and hadrons. More than that, because of the competition between the Coulomb and the surface energies associated with the positively charged regions of nuclear matter and negatively charged regions of quark matter, the mixed phase may develop geometrical structures, similarly to what is expected of the sub-nuclear liquid-gas phase transition. In this paper we restrict ourselves to considering the formation of rare phase blobs in the mixed quark-hadron phase. The influence of rare phase blobs on the thermal and transport properties of neutron star matter is investigated. The total specific heat, $c_V$, thermal conductivity, $\kappa$, and electron-blob Bremsstrahlung neutrino emissivities, $\epsilon_{\nu,\text{BR}}$, of quark-hybrid matter are computed and the results are compared with the associated thermal and transport properties of standard neutron star matter. Our results show that the contribution of rare phase blobs to the specific heat is negligibly small. This is different for the neutrino emissivity from electron-blob Bremsstrahlung scattering, which turns out to be of the same order of magnitude as the total contributions from other Bremsstrahlung processes for temperatures below about $10^8$ K.

Amorphous state in the mixed phase of hadron-quark phase transition in protoneutron stars

We study the hadron-quark mixed phase in protoneutron stars, where neutrinos are trapped and lepton number becomes a conserved quantity besides the baryon number and electric charge. Considering protoneutron-star matter as a ternary system, the Gibbs conditions are applied together with the Coulomb interaction. We find that there no crystalline (``pasta'') structure appears in the regime of high lepton-number fraction; the size of pasta becomes very large and the geometrical structure becomes mechanically unstable due to the charge screening effect. Consequently the whole system is separated into two bulk regions like an amorphous state, where the surface effect is safely neglected. There, the local charge neutrality is approximately attained, so that the equation of state is effectively reduced to the one for a binary system. Hence, we conclude that there is no possibility for the density discontinuity to appear in protoneutron-star matter, which is a specific feature in a pure system. These features are important when considering astrophysical phenomena such as supernova explosions or radiation of the gravitational wave from protoneutron stars.

Shear modulus of the hadron-quark mixed phase

Robust arguments predict that a hadron-quark mixed phase may exist in the cores of some "neutron" stars. Such a phase forms a crystalline lattice with a shear modulus higher than that of the crust due to the high density and charge separation, even allowing for the effects of charge screening. This may lead to strong continuous gravitational-wave emission from rapidly rotating neutron stars and gravitational-wave bursts associated with magnetar flares and pulsar glitches. We present the first detailed calculation of the shear modulus of the mixed phase. We describe the quark phase using the bag model plus first-order quantum chromodynamics corrections and the hadronic phase using relativistic mean-field models with parameters allowed by the most massive pulsar. Most of the calculation involves treating the "pasta phases" of the lattice via dimensional continuation, and we give a general method for computing dimensionally continued lattice sums including the Debye model of charge screening. We compute all the shear components of the elastic modulus tensor and angle average them to obtain the effective (scalar) shear modulus for the case where the mixed phase is a polycrystal. We include the contributions from changing the cell size, which are necessary for the stability of the lower-dimensional portions of the lattice. Stability also requires a minimum surface tension, generally tens of MeV/fm^2 depending on the equation of state. We find that the shear modulus can be a few times 10^33 erg/cm^3, two orders of magnitude higher than the first estimate, over a significant fraction of the maximum mass stable star for certain parameter choices.

ENERGY RELEASE ASSOCIATED WITH QUARK PHASE TRANSITION IN NEUTRON STARS: COMPARATIVE ANALYSIS OF MAXWELL AND GLENDENNING SCENARIOS

We study the compact stars internal structure and observable characteristics alterations due to the quark deconfinement phase transition. To proceed with, we investigate the properties of isospin- asymmetric nuclear matter in the improved relativistic mean-field (RMF) theory, including a scalar-isovector δ-meson effective field. In order to describe the quark phase, we use the improved version of the MIT bag model, in which the interactions between u, d and s quarks inside the bag are taken into account in the one-gluon exchange approximation. We compute the amount of energy released by the corequake for both cases of deconfinement phase transition scenarios, corresponding to the Maxwellian type ordinary first-order phase transition and the phase transition with formation of a mixed quark-hadron phase (Glendenning scenario).

Pasta Structures of Quark-Hadron Phase Transition in Proto-Neutron Stars

We study the quark-hadron mixed phase in proto-neutron stars with the finite-size effects. In the calculations of pasta structures appeared in the mixed phase, the Gibbs conditions require the pressure balance and chemical equilibrium between two phases besides the thermal equilibrium. We find that the region of the mixed phase is limited due to thermal instability. Moreover, we study the effects of neutrinos to the pasta structures. As a result, we find that the existence of neutrinos make the pasta structures unstable, too. These characteristic features of the hadron-quark mixed phase should be important for the middle stage of the evolutions of proto-neutron stars.

Region of a hadron-quark mixed phase in hybrid stars

Hadron--quark mixed phase is expected in a wide region of the inner structure of hybrid stars. However, we show that the hadron--quark mixed phase should be restricted to a narrower region to because of the charge screening effect. The narrow region of the mixed phase seems to explain physical phenomena of neutron stars such as the strong magnetic field and glitch phenomena, and it would give a new cooling curve for the neutron star.

Symmetry energy effects on the mixed hadron-quark phase at high baryon density

The phase transition of hadronic to quark matter at high baryon and isospin density is analyzed. Relativistic mean-field models are used to describe hadronic matter, and the MIT bag model is adopted for quark matter. The boundaries of the mixed phase and the related critical points for symmetric and asymmetric matter are obtained. Due to the different symmetry term in the two phases, isospin effects appear to be rather significant. With increasing isospin asymmetry the binodal transition line of the ($T,{\ensuremath{\rho}}_{B}$) diagram is lowered to a region accessible through heavy-ion collisions in the energy range of the new planned facilities (e.g., the FAIR/NICA projects). Some observable effects are suggested, in particular an isospin distillation mechanism with a more isospin asymmetric quark phase, to be seen in charged meson yield ratios, and an onset of quark number scaling of the meson-baryon elliptic flows. The presented isospin effects on the mixed phase appear to be robust with respect to even large variations of the poorly known symmetry term at high baryon density in the hadron phase. The dependence of the results on a suitable treatment of isospin contributions in effective QCD Lagrangian approaches, at the level of explicit isovector parts and/or quark condensates, is discussed.

Signatures of hadron-quark mixed phase in gravitational waves

We calculate stellar oscillations including the hadron-quark mixed phase considering the finite size effects. We find that it is possible to distinguish whether the density discontinuity exists or not in the stars, even if one will observe the gravitational waves of the fundamental mode. Additionally, the normalized eigenfrequencies of pressure modes depend strongly on the stellar mass and on the adopted equation of state. Especially, in spite of the fact that the radius of the neutron star with $1.4M_\odot$, which is standard mass, is almost independent from the equation of state with quark matter, the frequencies of pressure modes depend on the adopted equation of state. Thus, via observing the many kinds of gravitational waves, it will be possible to make a restriction on the equation of state.

Quark–hadron mixed phases in protoneutron stars

We consider the possible formation of the quark–hadron mixed phase in protoneutron stars. We discuss two cases. The first one, corresponding to a vanishingly small value of the surface tension of quark matter, is the well-known mixed phase in which the global electric charge neutrality condition is imposed. In turn, this produces a non-constant pressure mixed phase. In the second case, corresponding to very large values of the surface tension, the charge neutrality condition holds only locally. However, the existence in protoneutron star matter of an additional globally conserved charge, the lepton number, allows for a new type of non-constant pressure mixed phase. We discuss the properties of the new mixed phase and the possible effects of its formation during the evolution of protoneutron stars.

Quark-Hadron Mixed Phase

The concept of a mixed quark-hadron phase is considered. Dynamics of heavy-ion collisins in a large energy range is outlined. Various possible probes of the mixed phase manifestation as well as modern status of experimental signals are discussed.

Hot hadron-quark mixed phase including hyperons

We study the hadron-quark phase transition with the finite-size effects at finite temperature. For the hadron phase, we adopt a realistic equation of state in the framework of the Brueckner-Hartree-Fock theory including hyperons. The properties of the mixed phase are clarified by considering the finite-size effects under the Gibbs conditions. We find that the equation of state becomes softer than that at zero temperature for some density region. We also find that the equation of state gets closer to that given by the Maxwell construction. Moreover, the number of hyperons is suppressed by the presence of quarks. These are characteristic features of the hadron-quark mixed phase, and should be important for many astrophysical phenomena such as mergers of binary neutron stars.

Dynamic migration of rotating neutron stars due to a phase transition instability

Using numerical simulations based on solving the general relativistic hydrodynamic equations, we study the dynamics of a phase transition in the dense core of isolated rotating neutron stars, triggered by the back bending instability reached via angular momentum loss. In particular, we investigate the dynamics of a migration from an unstable configuration into a stable one, which leads to a mini-collapse of the neutron star and excites sizeable pulsations in its bulk until it acquires a new stable equilibrium state. We consider equations of state with softening at high densities, a simple analytic one with a mixed hadron-quark phase in an intermediate pressure interval and pure quark matter at very high densities, and a microphysical one that has a first-order phase transition, originating from kaon condensation. Although the marginally stable initial models are rigidly rotating, we observe that during the collapse (albeit little) differential rotation is created. We analyze the emission of gravitational radiation, which in some models is amplified by mode resonance effects, and assess its prospective detectability by interferometric detectors. We expect that the most favorable conditions for dynamic migration exist in very young magnetars. We find that the damping of the post-migration pulsations strongly depends on the character of the equation of state softening. The damping of pulsations in the models with the microphysical equation of state is caused by dissipation associated with matter flowing through the density jump at the edge of the dense core. If at work, this mechanism dominates over all other types of dissipation, like bulk viscosity in the exotic-phase core, gravitational radiation damping, or numerical viscosity.

Lepton effects on the protoneutron stars with the hadron-quark mixed phase in the Nambu–Jona-Lasinio model

We study the structures of hybrid stars with leptons at finite temperature under beta equilibrium. For the quark phase, we use the three flavor Nambu--Jona-Lasinio (NJL) model. For the hadron phase, we adopt the nuclear equation of state (EOS) by Shen et al.. This EOS is in the framework of the relativistic mean field theory including the tree body effects. For the hadron-quark phase transition, we impose the bulk Gibbs construction or the Maxwell construction to take into account uncertainties by finite-size effects. We find that the pure quark phase does not appear in stable star cores in all cases. With the phase transition, the maximum masses increase $\ensuremath{\sim}10%$ for high lepton fraction. On the contrary, without the transition, they decrease $\ensuremath{\sim}10%$. We also find that, in the NJL model, the lepton fraction is more important for structures of unstable stars than the temperature. This result is important for many astrophysical phenomena such as the core collapse of massive stars.