We extend the hadronic SU(3) non-linear sigma model to include quark degrees of freedom. The choice of potential for the Polyakov loop 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 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.
We discuss a three-flavor Nambu--Jona-Lasinio (NJL) type quantum field theoretical approach to the quark matter equation of state (EoS) with scalar diquark condensate, isoscalar vector mean field and Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction. While often the diquark and vector meson couplings are considered as free parameters, we will fix them here to their values according to the Fierz transformation of a one-gluon exchange interaction. In order to estimate the effect of a possible change in the vacuum pressure of the gluon sector at finite baryon density we exploit a recent mo…
We describe an extension of the hadronic SU(3) non-linear sigma model to include quarks. As a result, we obtain an effective model which interpolates between hadronic and quark degrees of freedom. The new parameters and the potential for the Polyakov loop (used as the order parameter for deconfinement) are calibrated in order to fit lattice QCD data and reproduce the QCD phase diagram. Finally, the equation of state provided by the model, combined with gravity through the inclusion of general relativity, is used to make predictions for neutron stars.
The hadron-quark phase transition in the core of massive neutron stars is studied with a newly constructed two-phase model. For nuclear matter, a nonlinear Walecka type model with general nucleon-meson and meson-meson couplings, recently calibrated by Steiner, Hemper and Fischer, is taken. For quark matter, a modified Polyakov-Nambu--Jona-Lasinio (mPNJL) model, which gives consistent results with lattice QCD data, is used. Most importantly, we introduce an isoscalar-vector interaction in the description of quark matter, and we study its influence on the hadron-quark phase transition in the int…
We study the cooling of hybrid stars coupling with spin-down. Due to the spin-down of hybrid stars, the interior density continuously increases, different neutrino reactions may be triggered(from the modified Urca process to the quark and nucleon direct Urca process) at different stages of evolution. We calculate the rate of neutrino emissivity of different reactions and simulate the cooling curves of the rotational hybrid stars. The results show the cooling curves of hybrid stars clearly depend on magnetic field if the direct urca reactions occur during the spin-down. Comparing the results of…
We study the so called hybrid stars, which are hadronic stars that contain a core of deconfined quarks. For this purpose, we make use of an extended version of the SU(3) chiral model. Within this approach, the degrees of freedom change naturally from hadrons (baryon octet) to quarks (u, d, s) as the temperature and/or density increases. At zero temperature we are still able to reproduce massive stars, even with the inclusion of hyperons.
We aim to study the possibility of a hadron-quark phase transition in the interior of neutron stars, taking into account different schematic evolutionary stages at finite temperature. We also discuss the strange quark matter stability in the quark matter phase. Furthermore, we aim to analyze the astrophysical properties of hot and cold hybrid stars, considering the constraint on maximum mass given by the pulsars J1614-2230 and J0348+0432. We have developed a computational code to construct semi-analytical hybrid equations of state at fixed entropy per baryon and to obtain different families of…
We study the behavior of hybrid stars using an extended hadronic and quark SU(3) non-linear sigma model. The degrees of freedom change naturally, in this model, from hadrons to quarks as the density/temperature increases. At zero temperature, we reproduce massive neutron stars containing a core of hybrid matter of 2 km for the non-rotating case and 1.18 km and 0.87 km, in the equatorial and polar directions respectively, for stars rotating at the Kepler frequency (physical cases lie in between). The cooling of such stars is also analyzed.
We model the cooling of hybrid neutron stars combining a microscopic nuclear equation of state in the Brueckner-Hartree-Fock approach with different quark models. We then analyze the neutron star cooling curves predicted by the different models and single out the preferred ones. We find that the possibility of neutron p-wave pairing can be excluded in our scenario.
It is shown that the unusual thermodynamic properties of matter within the region of two-phase coexistence in hybrid stars result in a change of the standard condition for beginning of convection. In particular, the thermal flux transported by convection may be directed towards the stellar center. We discuss favorable circumstances leading to such an effect of "inverse convection" and its possible influence on the thermal evolution of hybrid stars.
We discuss constraints for the equation of state of hybrid star matter which can be obtained from heavy-ion collisions at FAIR and NICA. Particular emphasis is on the planned NICA facility at JINR Dubna which shall provide fixed-target and collider experiments just in the relevant energy ranges.
We study the effects of strangeness on the quark sector of a hybrid star equation of state. Since the model we use to describe quarks is the same as the one we use to describe hadrons, we can also study the effects of strangeness on the chiral symmetry restoration and deconfinement phase transitions (first order or crossover). Finally, we analyze combined effects of hyperons and quarks on global properties of hybrid stars, like mass, radius and cooling profiles. It is found that a large amount of strangeness in the core is related to the generation of twin-star solutions, which can have the sa…
In this contribution, we describe new chemically-equilibrated charge-neutral hybrid equations of state for neutron stars. They present a first-order phase transition to quark matter and differentiate by the particle population considered and how these particles interact. While some equations of state contain just nucleons and up, down-quarks, others also contain hyperons, Delta baryons, and strange quarks. The hybrid equations of state, together with corresponding hadronic ones, are available on the CompOSE repository and can be used for different astrophysical applications.
We explore the possibility of obtaining heavy hybrid stars within the framework of the two flavor Nambu--Jona-Lasinio model with 8-quark interactions in the scalar and in the vector channel. The main impact of the 8-quark scalar channel is to reduce the onset of quark matter, while the 8-quark vector channel acts to stiff the equation of state at high densities. Within the parameter space where the 4-quark vector channel is small, and the 8-quark vector channel sizeable, stable stars with $2 M_\odot$ and above are found to hold quark matter in their cores.
Using a nonlocal extension of the SU(3) Nambu-Jona Lasinio model, which reproduces several of the key features of Quantum Chromodynamics, we show that mixed phases of deconfined quarks and confined hadrons (quark-hybrid matter) may exist in the cores of neutron stars as massive as around 2.1 M_Sun. The radii of these objects are found to be in the canonical range of $\sim 12-13$ km. According to our study, the transition to pure quark matter does not occur in stable neutron stars, but is shifted to neutron stars which are unstable against radial oscillations. The implications of our study for …
In this work we study the effects of strong magnetic fields on hybrid stars by using a full general-relativity approach, solving the coupled Maxwell-Einstein equation in a self-consistent way. The magnetic field is assumed to be axi-symmetric and poloidal. We take into consideration the anisotropy of the energy-momentum tensor due to the magnetic field, magnetic field effects on equation of state, the interaction between matter and the magnetic field (magnetization), and the anomalous magnetic moment of the hadrons. The equation of state used is an extended hadronic and quark SU(3) non-linear …
We have carried out a statistic survey on the pulsating variable stars with multiple identities. These stars were identified to exhibit two types of pulsation or multiple light variability types in the literature, and are usually called hybrid pulsators. We extracted the hybrid information based on the Simbad database. Actually, all the variables with multiple identities are retrieved. The survey covers various pulsating stars across the Hertzsprung-Russell diagram. We aim at giving a clue in selecting interesting targets for further observation. Hybrid pulsators are excellent targets for aste…
An analytical study that explains the existence of a very small region on the mass radius diagram of hybrid stars where all of the lines representing the sequences of models with different constant values of the bag constant B intersect is presented. This circumstance is shown to be a consequence of the linear dependence of pressure on energy density in the quark cores of hybrid stars.
In this work we present a study of magnetars composed of hadronic and quark matter, under the influence of strong magnetic fields. We present our results for hadronic matter taking into account the effects that the inclusion of anomalous magnetic moment corrections may cause on the equations of state (EOS). Particle abundances are also presented and discussed. Additionally, the case of hybrid stars under the influence of strong magnetic fields is considered. We study the structure of hybrid stars based on the Maxwell condition (without a mixed phase), where the hadron phase is described by the…
It is understood that strong magnetic fields affect the structure of neutron stars. Nevertheless, many calculations for magnetized neutron stars are still being performed using symmetric solutions of Einstein's equations. In this conference proceeding, we review why this is not the correct procedure and we also discuss the effects of magnetic fields on the stellar population and temperature profiles.
We describe two aspects of the physics of hybrid stars that have a sharp interface between a core of quark matter and a mantle of nuclear matter. Firstly, we analyze the mass-radius relation. We describe a generic "Constant Speed of Sound" (CSS) parameterization of the quark matter equation of state (EoS), in which the speed of sound is independent of density. In terms of the three parameters of the CSS EoS we obtain the phase diagram of possible forms of the hybrid star mass-radius relation, and we show how observational constraints on the maximum mass and typical radius of neutron stars can …
We study the hadron-quark phase transition in the interior of neutron stars. For the hadronic sector, we use a microscopic equation of state involving nucleons and hyperons derived within the Brueckner-Hartree-Fock many-body theory with realistic two-body and three-body forces. For the description of quark matter, we employ the Dyson-Schwinger approach and compare with the MIT bag model. We calculate the structure of neutron star interiors comprising both phases and find that with the Dyson-Schwinger model, the hadron-quark phase transition takes place only when hyperons are excluded, and that…
We apply an extended version of the SU(3) parity model, containing quark degrees of freedom, to study neutron stars. The model successfully reproduces the main thermodynamic features of QCD which allows us to describe the composition of dense matter. Chiral symmetry restoration is realized inside the star and the chiral partners of the baryons appear, their masses becoming degenerate. Furthermore, quark degrees of freedom appear in a transition to a deconfined state. Performing an investigation of the macroscopic properties of neutron stars, we show that observational constraints, like mass an…
We present results on the second-faintest pulsating subdwarf B (sdB) star known, RAT J0455+1305, derived from photometric data obtained in 2009. It shows both short and long periods oscillations, theoretically assigned as pressure and gravity modes. We identify six short-period frequencies (with one being a combination) and six long-period frequencies. This star is the fourth hybrid sdB star discovered so far which makes it of special interest as each type of mode probes a different part of the star. This star is similar to the sdB hybrid pulsator Balloon 090100001 in that it exhibits short-pe…
We construct stellar models of hadron stars and hybrid stars and calculate the frequencies of their lowest radial mode of vibration. Chandrasekhar's equation for radial oscillations is generalized for stars with internal electric fields and earlier versions of that generalization are simplified. For the hybrid stars a Gibbs construction is employed. It is found that the softening of the equation of state associated with the presence of deconfined quarks reduces the oscillation frequency. We show that a slight charge inbalance should lead to increased maximum mass, decreased central density and…
We perform a comparison between two radiative transfer algorithms commonly employed in hydrodynamical calculations of star formation: grey flux limited diffusion and the hybrid scheme, in addition we compare these algorithms to results from the Monte-Carlo radiative transfer code MOCASSIN. In disc like density structures the hybrid scheme performs significantly better than the FLD method in the optically thin regions, with comparable results in optically thick regions. In the case of a forming high mass star we find the FLD method significantly underestimates the radiation pressure by a factor…
We study the consequences of quark matter nucleation in cold hadronic matter employing three relativistic-mean-field (RMF) models to describe the hadronic phase and the Nambu-Jona-Lasinio (NJL) model for the quark one. We explore the effect of a vector interaction in the NJL Lagrangian and of a phenomenological bag constant on neutron stars metastability. We delineate the region of parameters of the quark phase that allow for the formation of stable hybrid stars with mass compatible with the almost $2 \ M_\odot$ pulsars PSR J1614-2230 ($1.97 \pm 0.04 M_\odot$) and PSR J0348+0432 ($2.01 \pm 0.0…
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.
A noticeable fraction of subdwarf B stars shows either short-period (p-mode) or long-period (g-mode) luminosity variations, with two objects so far known to exhibit hybrid behaviour, i.e. showing both types of modes at the same time. The pulsating subdwarf B star V391 Pegasi (or HS2201+2610), which is close to the two known hybrid pulsators in the log g - Teff plane, has recently been discovered to host a planetary companion. In order to learn more about the planetary companion and its possible influence on the evolution of its host star (subdwarf B star formation is still not well understood)…
We discuss the properties of neutron stars and their modifications due to the occurrence of hyperons and quarks in the core of the star. More specifically, we consider the general problem of exotic particles inside compact stars in light of the observed two-solar mass pulsar. In addition, we investigate neutron star cooling and a possible explanation of the recently measured cooling curve of the neutron star in the supernova remnant Cas A.
Hybrid $δ$ Scuti-$γ$ Doradus pulsating stars show acoustic ($p$) oscillation modes typical of $δ$ Scuti variable stars, and gravity ($g$) pulsation modes characteristic of $γ$ Doradus variable stars simultaneously excited. Observations from space missions like MOST, CoRoT, and \emph{Kepler} have revealed a large number of hybrid $δ$ Scuti-$γ$ Doradus pulsators, thus paving the way for a exciting new channel for asteroseismic studies. We perform a detailed asteroseismological modeling of five hybrid $δ$ Scuti-$γ$ Doradus stars. We employ a grid-based modeling approach to sound the internal stru…
We present calculations for a magnetised hybrid wind model for Asymptotic Giant Branch (AGB) stars. The model incorporates a canonical Weber-Davis (WD) stellar wind with dust grains in the envelope of an AGB star. The resulting hybrid picture preserves traits of both types of winds. It is seen that this combination requires that the dust-parameter ($Γ_{d}$) be less than unity in order to achieve an outflow. The emergence of critical points in the wind changes the nature of the dust-driven outflow, simultaneously, the presence of a dust condensation radius changes the morphology of the magnetoh…
We study the mass-radius curve of hybrid stars, assuming a single first-order phase transition between nuclear and quark matter, with a sharp interface between the quark matter core and nuclear matter mantle. We use a generic parameterization of the quark matter equation of state, which has a constant, i.e. density-independent, speed of sound ("CSS"). We argue that this parameterization provides a framework for comparison and empirical testing of models of quark matter. We obtain the phase diagram of possible forms of the hybrid star mass-radius relation, where the control parameters are the t…
Delta Sct - gamma Dor hybrids pulsate simultaneously in p- and g-modes, which carry information on the structure of the envelope as well as to the core. Hence they are key objects for investigating A and F type stars with asteroseismic techniques. An important requirement for seismic modeling are small errors in temperature, gravity and chemical composition. Furthermore, we want to investigate the existence of an abundance indicator typical for hybrids, something that is well established for the roAp stars. Previous to the present investigation, the abundance pattern of only one hybrid and ano…
We study the principal core g-mode oscillation in hybrid stars containing quark matter and find that they have an unusually large frequency range ($\approx$ 200 - 600 Hz) compared to ordinary neutron stars or self-bound quark stars of the same mass. Theoretical arguments and numerical calculations that trace this effect to the difference in the behaviour of the equilibrium and adiabatic sound speeds in the mixed phase of quarks and nucleons are provided. We propose that the sensitivity of core g-mode oscillations to non-nucleonic matter in neutron stars could be due to the presence of a mixed …
