Narrow Results

In this work, we consider static quark star (QS) within the framework of Rastall gravity. Rastall gravity purports to be the nonconservative theory of gravity and an unusual nonminimal coupling between matter and geometry. In our study, we consider a Quantum chromodynamics (QCD)-motivated Equation of State (EoS) to determine the properties of QSs in Rastall gravity. Depending on the values of parameters, we seek to determine the mass–radius relations for QSs in Rastall gravity, identifying the deviation from standard general relativity (GR) counterparts. Interestingly, we find the value of the maximum gravitational mass to be more than 2$M_{\odot }$ for the given equation of state (EoS). We present the essential features regarding the stability of QSs.

We present an analytical description of the phase transitions from a nucleon gas to nuclear matter and from nuclear matter to quark matter within the same model. The equation of state for quark and nuclear matter is encoded in the effective potential of a linear sigma model. We exploit an exact differential equation for its dependence upon the chemical potential μ associated to conserved baryon number. An approximate solution for vanishing temperature is used to discuss possible phase transitions as the baryon density increases. For a nucleon gas and nuclear matter we find a substantial density enhancement as compared to quark models which neglect the confinement to baryons. The results point out that the latter models are not suitable to discuss the phase diagram at low temperature.

This paper provides a short overview of the multifaceted, possible role of quark matter for compact stars (neutron stars and strange quark matter stars). We began with a variational investigation of the maximum possible energy densities in the cores of neutron stars. This is followed by a brief discussion of the possible existence of quark matter in the cores of neutron stars and how such matter could manifest itself in neutron star observables. The possible presence of color superconducting strange quark matter nuggets in the crusts of neutron stars is reviewed next, and their impact on the pycnonuclear reaction rates in the crusts of neutron stars is discussed. The second part of the paper discusses the impact of ultra-strong electric fields on the bulk properties of strange quark matter stars and presents results of a preliminary study that models the thermal evolution of radio-quiet, X-ray bright, central compact objects (CCOs).

Quark matter is expected to exist in the interior of compact stellar objects as neutron stars or even the more exotic strange stars, based on the Bodmer–Witten conjecture. Bare strange quark stars and (normal) strange quark-matter stars, those possessing a baryon (electron-supported) crust, are hypothesized as good candidates to explain the properties of a set of peculiar stellar sources such as the enigmatic X-ray source RX J1856.5-3754, some pulsars such as PSR B1828-11 and PSR B1642-03, and the anomalous X-ray pulsars and soft γ-ray repeaters. In the MIT bag model, quarks are treated as a degenerate Fermi gas confined to a region of space having a vacuum energy density B_bag (the Bag constant). In this note, we modify the MIT bag model by including the electromagnetic interaction. We also show that this version of the MIT model implies the anisotropy of the bag pressure due to the presence of the magnetic field. The equations of state of the degenerate quarks gases are studied in the presence of ultra strong magnetic fields. The behavior of a system made up of quarks having (or not) anomalous magnetic moment is reviewed. A structural instability is found, which is related to the anisotropic nature of the pressures in this highly magnetized matter. The conditions for the collapse of this system are obtained and compared to a previous model of neutron stars that is built on a neutron gas having anomalous magnetic moment.

We investigate the hadron-quark phase transition inside neutron stars and obtain mass–radius relations for hybrid stars. The equation of state for the quark phase using the standard NJL model is too soft, leading to an unstable star and suggesting a modification of the NJL model by introducing a momentum cutoff dependent on the chemical potential. However, even in this approach, the instability remains. In order to remedy the instability we suggest the introduction of a vector coupling in the NJL model, which makes the EoS stiffer, reducing the instability. We conclude that the possible existence of quark matter inside the stars require high densities, leading to very compact stars.

In high density quark matter under a strong external magnetic field, possible phases are investigated by using the two-flavor Nambu–Jona–Lasinio (NJL) model with tensor-type four-point interaction between quarks, as well as the axial-vector-type four-point interaction. In the tensor-type interaction under the strong external magnetic field, it is shown that a quark spin polarized phase is realized in all regions of the quark chemical potential under consideration within the lowest Landau level approximation. In the axial-vector-type interaction, it is also shown that the quark spin polarized phase appears in the wide range of the quark chemical potential. In both the interactions, the quark mass in zero and small chemical potential regions increases which indicates that the chiral symmetry breaking is enhanced, namely the magnetic catalysis occurs.

In this chapter, we investigate the structure and composition of hot neutron star matter and proto-neutron stars. Such objects are made of baryonic matter that is several times denser than atomic nuclei and tens of thousands of times hotter than the matter in the core of our Sun. The relativistic finite-temperature Green function formalism is used to formulate the expressions that determine the properties of such matter in the framework of the density-dependent mean-field approach. Three different sets of nuclear parameterizations are used to solve the many-body equations and to determine the models for the equation of state of ultra-hot and dense stellar matter. The meson–baryon coupling schemes and the role of the Δ(1232) baryon in proto-neutron star matter are discussed in great detail. The use of the non-local three-flavor Nambu–Jona-Lasinio model to describe quark matter, the hadron-quark composition of dense baryonic matter at zero temperature is discussed. General relativistic models of non-rotating as well as rotating proto-neutron stars are presented in part two of our study.

The Bodmer-Terazawa-Witten hypothesis of absolutely stable quark matter made of up, down, and strange quarks ((u,d,s) matter) is of much astrophysical and fundamental interest. One consequence is a large binding energy release associated with the conversion of a neutron star to a quark star. A quantitative understanding of the dynamic aspect of the conversion is necessary in order to find out whether this energy is released quietly or in an explosive manner. We address numerically (i.e. solving the reaction-diffusion-advection equations for (u,d) to (u,d,s) combustion) the dynamic processes through which the conversion appears. We find fundamentally very different results from semi-analytic calculations, with front speeds that are several orders of magnitude higher for the former. Resolving the hadronic-quark-matter interface is necessary, since approximations like Coll’s condition may quench the burning, while properly resolving the flame can make combustion always thermodynamically favourable if the hypothesis of absolutely stable strange quark matter is true. We find that lepton physics, including weak decays, electron equation-of-state (EoS), neutrino EoS, and neutrino transport are at the very least as important to the physics of the burning front as the EoS of highly dense matter. In concert, these effects induce novel wrinkling instabilities (such as the deleptonization instability) possibly leading to a deflagration-detonation and/or a quark-core collapse Quark-Nova.

We present a novel treatment of calculating the in-medium quark condensates. The advantage of this approach is that one does not need to make further assumptions on the derivatives of model parameters with respect to the quark current mass. The normally accepted model-independent result in nuclear matter is naturally reproduced. The change of the quark condensate induced by interactions depends on the incompressibility of nuclear matter. When it is greater than 265 MeV, the density at which the condensate vanishes is higher than that from the linear extrapolation. For the chiral condensate in quark matter, a similar model-independent linear behavior is found at lower densities, which means that the decreasing speed of the condensate in quark matter is merely half of that in nuclear matter if the pion-nucleon sigma commutator is six times the average current mass of u and d quarks. The modification due to QCD-like interactions is found to slow the decreasing speed of the condensate, compared with the linear extrapolation.

In this article, we study higher-dimensional cosmological models with quark–gluon plasma in the context of general relativity. For this purpose, we consider quark–gluon plasma as a perfect fluid in the higher-dimensional universes. After solving Einstein's field equations, we have analyzed this matter for the different types of universes in the higher- and four-dimensional universes. Also, we have discussed the features of obtained solutions.

We analyze the magnetic field evolution in dense quark matter with unbroken chiral symmetry, which can be found inside quark and hybrid stars. The magnetic field evolves owing to the chiral magnetic effect in the presence of the electroweak interaction between quarks. In our study, we also take into account the magnetohydrodynamic turbulence effects in dense quark matter. We derive the kinetic equations for the spectra of the magnetic helicity density and the magnetic energy density as well as for the chiral imbalances. On the basis of the numerical solution of these equations, we find that turbulence effects are important for the behavior of small scale magnetic fields. It is revealed that, under certain initial conditions, these magnetic fields behave similarly to the electromagnetic flashes of some magnetars. We suggest that fluctuations of magnetic fields, described in frames of our model, which are created in the central regions of a magnetized compact star, can initiate magnetar bursts.

We explore the possibility of formation of $\mathrm{\Delta }$ baryons (1232MeV) in neutron star matter in an effective chiral model within the relativistic mean-field framework. With variation in delta-meson couplings, consistent with the constraints imposed on them, the resulting equation-of-state (EoS) is obtained and the neutron star properties are calculated for static and spherical configuration. Within the framework of our model, the critical densities of formation of $\mathrm{\Delta }s$ and the properties of neutron stars (NS) are found to be very sensitive to the iso-vector coupling compared to the scalar or vector couplings. We revisit the $\mathrm{\Delta }$ puzzle and look for the possibility of phase transition from nonstrange hadronic matter (including nucleons and $\mathrm{\Delta }s$) to deconfined quark matter, based on QCD theories. The resultant hybrid star configurations satisfy the observational constraints on mass from the most massive pulsars PSR J1614-2230 and PSR J0348+0432 in static condition obtained with the general hydrostatic equilibrium based on GTR. Our radius estimates are well within the limits imposed from observational analysis of QLMBXs. The obtained values of $R_{1.4}$ are in agreement with the recent bounds specified from the observation of gravitational wave (GW170817) from binary neutron star merger. The constraint on baryonic mass from the study of binary system PSR J0737-3039 is also satisfied with our hybrid EoS.

Spontaneous magnetization and magnetic susceptibility originated from the pseudovector-type four-point interaction between quarks are calculated in quark matter with zero temperature and finite quark chemical potential by using the two-flavor Nambu–Jona-Lasinio model. It is shown that both the chiral condensate and spin polarized condensate coexist in a narrow region of the quark chemical potential. And then, it is also shown that, in this narrow region, the spontaneous magnetization appears. Also, the magnetic susceptibility due to quarks with the positive energy is evaluated in the spin polarized phase.

A possibility of a quark spin polarization originating from a pseudovector condensate is investigated in the three-flavor Nambu–Jona–Lasinio model with the Kobayashi–Maskawa–’t Hooft interaction which leads to flavor mixing. It is shown that a pseudovector condensate related to the strange quark easily occurs compared with pseudovector condensate related to light quarks. Further, it is shown that the pseudovector condensate related to the strange quark appears at a slightly small chemical potential by the effect of the flavor mixing due to the Kobayashi–Maskawa–’t Hooft interaction.

To obtain the equation of state of quark matter and construct hybrid stars, we calculate the thermodynamic potential in the three-flavor Nambu–Jona-Lasinio model including the tensor-type four-point interaction and the Kobayashi–Maskawa–’t Hooft interaction. To construct the hybrid stars, it is necessary to impose the $\beta$ equilibrium and charge neutrality conditions on the system. It is shown that tensor condensed phases appear at large chemical potential. Under the possibility of the existence of the tensor condensates, the relationship between the radius and mass of hybrid stars is estimated.

We investigate the properties of the hadron-quark mixed phase in compact stars using a Brueckner-Hartree-Fock framework for hadronic matter and the MIT bag model for quark matter. We find that the equation of state of the mixed phase is similar to that given by the Maxwell construction. The composition of the mixed phase, however, is very different from that of the Maxwell construction; in particular, hyperons are completely suppressed.