Maximum Mass Of Hybrid Stars Research Articles

Constraining free parameters of a color superconducting nonlocal Nambu–Jona-Lasinio model using Bayesian analysis of neutron stars mass and radius measurements

We provide a systematic study of hybrid neutron star equations of state (EOS) consisting of a relativistic density functional for the hadronic phase and a covariant nonlocal Nambu--Jona-Lasinio (nlNJL) model to describe the color superconducting quark matter phase. Changing the values of the two free parameters, the dimensionless vector and diquark coupling strengths ${\ensuremath{\eta}}_{V}$ and ${\ensuremath{\eta}}_{D}$ results in a set of EOS with varying stiffness and deconfinement onset. The favorable parameters are obtained from a systematic Bayesian analysis for which the multimessenger constraint on the neutron star radius at $14{M}_{\ensuremath{\bigodot}}$ and the combined mass-radius constraint for PSR $\mathrm{J}0740+6620$ from NICER experiment are used as the constraints. Additionally, the transition from hadronic matter to deconfined quark matter is constrained to occur above nuclear saturation density. Hybrid stars modeled with these favorable parameters are compatible with the NICER results for the radius of the highest known mass neutron star, PSR $\mathrm{J}0740+6620$. Three new observations interesting for neutron star phenomenology are reported: (i) we show that the constant sound speed (CSS) EOS provides an excellent fit to that of the nlNJL model which implies the squared speed of sound at high densities to be about 0.5 for the optimized parameters; (ii) we give a simple functional form for the mapping between the parameter spaces of these two models valid for the whole range of relevant chemical potentials and (iii) we observe that the special point property of hybrid EOS based on CSS quark matter generalizes to a set of lines consisting of special points when two EOS parameters are varied instead of one. A lower limit for the maximum mass of hybrid stars as a function of the vector coupling strength is obtained.

Locating the special point of hybrid neutron stars

The special point is a feature unique to models of hybrid neutron stars. It represents a location on their mass–radius sequences that is insensitive to the phase transition density. We consider hybrid neutron stars with a core of deconfined quark matter that obeys a constant–sound–speed (CSS) equation of state model and provide a fit formula for the coordinates of the special point as functions of the squared sound speed (cs2) and pressure scale (A) parameters. Using the special point mass as a proxy for the maximum mass of the hybrid stars we derive limits for the CSS model parameters based on the recent NICER constraint on mass and radius of pulsar PSR J0740+6620, 0.36 < Cs min2 < 0.43 and 80 < A[MeV/fm3] < 160. The upper limit for the maximum mass of hybrid stars depends on the upper limit for cs2 so that choosing cs,max2 = 0.6 results in Mmax < 2.7 M⊙, within the mass range of GW190814.

Maximum mass of hybrid star formed via shock-induced phase transition in cold neutron stars

ABSTRACT This paper studies the maximum mass limit of the hybrid star formed after the shock-induced phase transition of a cold neutron star. By employing hadronic and quark equation of state that satisfies the current mass bound, we use combustion adiabat conditions to find such a limit. The combustion adiabat condition results in a local or a global maximum pressure at an intermediate density range. The maximum pressure corresponds to a local or global maximum mass for the phase transformed hybrid star. The phase transition is usually exothermic if we have a local maximum mass. The criteria for exothermic or endothermic phase transition depend on whether the quark pressure/energy ratios to nuclear pressure/energy are smaller or greater than 1. We find that exothermic phase transition in a cold neutron star usually results in hybrid stars whose mass is smaller than a parent neutron star. The phase transition is endothermic for a global maximum pressure; thereby, one gets a global maximum mass. Hybrid stars much massive than phase transformed local maximum mass can be formed, provided there is some external energy source during the phase transition process. However, for some cases, even massive hybrid stars can form with exothermic phase transition for equations of state having global maximum pressure.

Systematic study on the quark-hadron mixed phase in compact stars

We investigate systematically the quark-hadron mixed phase in dense stellar matter, and its influence on compact star structures. The properties of quark matter and hadronic matter are fixed based on various model predictions. Beside adopting constant values, the surface tension $\Sigma$ for the quark-hadron interface is estimated with the multiple reflection expansion method and equivparticle model. To fix the structures of quark-hadron pasta phases, a continuous dimensionality of the structure is adopted as proposed by Ravenhall, Pethick, and Wilson. The corresponding properties of hybrid stars are then obtained and confronted with pulsar observations. It is found that the correlation between radius and tidal deformability in traditional neutron stars preserves in hybrid stars. For those permitted by pulsar observations, in almost all cases the quark phase persists inside the most massive compact stars. The quark-hadron interface plays an important role on hybrid star structures once quark matter emerges. The surface tension $\Sigma$ estimated with various methods increases with density, which predicts stiffer EOSs for the quark-hadron mixed phase and increases the maximum mass of hybrid stars. The EOSs of hybrid star matter are well constrained at densities $n\lesssim 0.8$ fm${}^{-3}$, while larger uncertainty is expected at higher densities.

Hybrid star within the framework of a lowest-order constraint variational method

The hadron-quark phase transition in the core of heavy neutron star (NS) has been studied. For the hadronic sector, we have used the lowest-order constraint variational method by employing $ AV_{18} $, $ AV_{14}$, $ UV_{14}$, and Reid $ 68 $ two-body nucleon-nucleon forces supplemented by the phenomenological Urbana-type three-body force. We have adopted the MIT bag model as well as three-flavor version of the Nambu- Jona-Lasinio (NJL) model to describe the quark phase. The equation of state (EOS) of a hybrid star (HS) is presented by combining two EOS of the hadronic sector and quark sector of a star, which are derived from independent models or theories. The hadron-quark transition is constructed by considering a sharp phase transition, i.e., Maxwell construction. The structure of the HS is calculated and reported by solving Tolman-Oppenheimer-Volkoff equations. Finally the radii and tidal deformability of purely NS and HS for the mass of $ 1.4M_{\odot} $ is computed and new constraints on these quantities are checked. The maximum mass of HS is found more than $ 2 M_{\odot} $ for both the NJL and MIT bag models. However, the maximum mass of $ 1.796 M_{\odot} $ ($ 1.896 M_{\odot} $) was the best result that would be calculated for a stable HS with the pure quark core within the MIT (NJL) model. All the hybrid EOS fulfill the constraints on radii and tidal deformability extracted from the binary GW170817 for HSs. A comprehensive analysis on the structure of purely NS and HS and also compactness, tidal Love number, and tidal deformability for the star with the mass of 1.4 $ M_{\odot} $ has been conducted for various EOS of the hadron sector and several parameter sets of the quark EOS. The results achieved in this study are in good concurrence with the other calculations reported on this subject.

Hadron-quark deconfinement phase transition in hybrid stars

Astronomical statistics shows that the mass of neutron star is of the order of the solar mass, but the radius is only about ten kilometers. Therefore, the neutron star is highly condensed and there may be a variety of competing material phases inside the compact star. Hadron-quark deconfinement phase transition that is poorly understood at high density can be studied by the matter properties of hybrid star. The hybrid star contains many kinds of material phases, which cannot be described uniformly by one theory. So, different material phases are described by different theories. The hadronic phase is described by the relativistic mean-field theory with parameter set FSUGold including <i>ω</i><sup>2</sup><i>ρ</i><sup>2</sup> interaction term, and the quark phase is described by an effective mass bag model in which the quark mass is density-dependent. The hadron-quark mixed phase is constructed by the Gibbs phase transition, and the properties of hybrid star in <i>β</i> equilibrium is studied in this model. It is found that the bag constant <i>B</i> has a great influence on the starting point and ending point of the hadron-quark deconfinement phase transition and the particle composition in the hybrid star. Comparing with the starting point of phase transition, the influence of <i>B</i> on the ending point of phase transition is very obvious. For the hybrid star, the equation of state of matter becomes stiffer at low density and softer at high density as <i>B</i> increases. The overall effect is that the slope of the mass-radius curve increases with <i>B</i> increasing. The calculated results show that the maximum mass of hybrid star is between 1.3 solar mass and 1.4 solar mass (<i>M</i><sub>☉</sub>), and the radius is between 9 km and 12 km. In addition, the influence of attractive and repulsive <i>Σ</i> potential on the properties of hybrid stars are studied. The results show that the <i>Σ</i> potential has a great influence on the particle composition in the hybrid star. We also find that the repulsive <i>Σ</i> potential makes the hybrid star have a greater maximum mass then an attractive <i>Σ</i> potential. For the attractive <i>Σ</i> potential, the maximum mass of hybrid star is 1.38<i>M</i><sub>☉</sub>, while for the repulsive <i>Σ</i> potential, the maximum mass of hybrid stars is 1.41<i>M</i><sub>☉</sub>.

Contraction of cold neutron star due to in the presence a quark core

Motivated by importance of the existence of quark matter on structure of neutron star. For this purpose, we use a suitable equation of state (EoS) which include three different parts: (i) a layer of hadronic matter, (ii) a mixed phase of quarks and hadrons, and, (iii) a strange quark matter in the core. For this system, in order to do more investigation of the EoS, we evaluate energy, Le Chatelier’s principle and stability conditions. Our results show that the EoS satisfies these conditions. Considering this EoS, we study the effect of quark matter on the structure of neutron stars such as maximum mass and the corresponding radius, average density, compactness, Kretschmann scalar, Schwarzschild radius, gravitational redshift and dynamical stability. Also, considering the mentioned EoS in this paper, we find that the maximum mass of hybrid stars is a little smaller than that of the corresponding pure neutron star. Indeed the maximum mass of hybrid stars can be quite close to the pure neutron stars. Our calculations about the dynamical stability show that these stars are stable against the radial adiabatic infinitesimal perturbations. In addition, our analyze indicates that neutron stars are under a contraction due to the existence of quark core.

Strange quark mass effect on the structure of hybrid stars

We study the strange quark mass effect on the phase diagram of strong interaction and the structure of compact stars with a thermodynamically enhanced perturbative QCD model by matching quark matter onto nuclear matter using the Gibbs conditions. It is found that the mass effect of strange quark matter can obviously stiffen the equation of state of mixed phases and result in more massive hybrid stars (HSs), while that usually lowers the maximum mass of pure quark stars. Given reasonable model parameters, the maximum mass of HSs can reach two times the solar mass and the stars always have mixed-phase core in a considerably wide range of model parameters.

Maximum Mass of Hybrid Stars in the Quark Bag Model

The effect of model parameters in the equation of state for quark matter on the magnitude of the maximum mass of hybrid stars is examined. Quark matter is described in terms of the extended MIT bag model including corrections for one-gluon exchange. For nucleon matter in the range of densities corresponding to the phase transition, a relativistic equation of state is used that is calculated with two particle correlations taken into account based on using the Bonn meson-exchange potential. The Maxwell construction is used to calculate the characteristics of the first order phase transition and it is shown that for a fixed value of the strong interaction constant $\alpha_s$, the baryon concentrations of the coexisting phases grow monotonically as the bag constant B increases. It is shown that for a fixed value of the strong interaction constant $\alpha_s$, the maximum mass of a hybrid star increases as the bag constant $B$ decreases. For a given value of the bag parameter $B$, the maximum mass rises as the strong interaction constant $\alpha_s$ increases. It is shown that the configurations of hybrid stars with maximum masses equal to or exceeding the mass of the currently known most massive pulsar are possible for values of the strong interaction constant $\alpha_s>0.6$ and sufficiently low values of the bag constant.

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 $2.1$ ${M}_{\ensuremath{\bigodot}}$.

Strange quark matter in explosive astrophysical systems

Explosive astrophysical systems, such as supernovae or compact star binary mergers, provide conditions where strange quark matter can appear. The high degree of isospin asymmetry and temperatures of several MeV in such systems may cause a transition to the quark phase already around saturation density. Observable signals from the appearance of quark matter can be predicted and studied in astrophysical simulations. As input in such simulations, an equation of state with an integrated quark matter phase transition for a large temperature, density and proton fraction range is required. Additionally, restrictions from heavy ion data and pulsar observation must be considered. In this work we present such an approach. We implement a quark matter phase transition in a hadronic equation of state widely used for astrophysical simulations and discuss its compatibility with heavy ion collisions and pulsar data. Furthermore, we review the recently studied implications of the QCD phase transition during the early post-bounce evolution of core-collapse supernovae and introduce the effects from strong interactions to increase the maximum mass of hybrid stars. In the MIT bag model, together with the strange quark mass and the bag constant, the strong coupling constant αs provides a parameter to set the beginning and extension of the quark phase and with this the mass and radius of hybrid stars.