Neutron stars, hybrid stars and the equation of state

Gross properties of hybrid stars consisting of a core of strange matter surrounded by ordinary neutron matter are investigated. We discuss star models based on phenomenological equations of state from nuclear reactions including a phase transition between the hadronic phase and the quark-gluon plasma. For certain parameters, such equations of state support the existence of hybrid stars. The identification of such objects could provide detailed information on the properties of strange quark matter.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

A new parametric equation of state and quark stars

It is still a matter of debate to understand the equation of state of cold matter with supra-nuclear density in compact stars because of unknown non-perturbative strong interaction between quarks. Nevertheless, it is speculated from an astrophysical view point that quark clusters could form in cold quark matter due to strong coupling at realistic baryon densities. Although it is hard to calculate this conjectured matter from first principles, one can expect that the inter-cluster interaction will share some general features with the nucleon-nucleon interaction successfully depicted by various models. We adopt a two-Gaussian component soft-core potential with these general features and show that quark clusters can form stable simple cubic crystal structure if we assume that the wave function of quark clusters have a Gaussian form. With this parametrization, the Tolman-Oppenheimer-Volkoff equation is solved with reasonably constrained parameter space to give mass-radius relations of crystalline solid quark stars. With baryon number densities truncated at 2_n0 at surface and the range of the interaction fixed at 2 fm we can reproduce similar mass-radius relations to that obtained with bag model equations of state. The maximum mass ranges from 0.5M_⊙ to 3M_⊙. The recently measured high pulsar mass ( 2M_⊙) is then used to constrain the parameters of this simple interaction potential.     

A general class of Euclidean stars

In this paper we revisit the problem of modeling radiating stars in which the areal radius is equal to the proper radius throughout the stellar evolution. We provide a new family of solutions that completely describes the dynamical behaviour of these so-called Euclidean stars. The solution satisfies all the energy conditions, and importantly, admits a barotropic equation of state.     

Effects of magnetic fields on equation of state of rotating stars

The evolution of rotating stars with magnetic fields has been studied with focus given to the following aspects: the effects of magnetic fields on equation of state for stellar matter and the thermodynamic quantities; the effects of magnetic energy and pressure on the internal structure of stars. The differences between the structure and evolution of a 15M⊙rotating star with and without magnetic fields are discussed. Our results show that the magnetic fields have an effect on the structure and evolution of the star mainly during the central helium burning phase; and this influences the physical quantities in the stellar envelope where hydrogen and helium are partially ionized. This may influence stellar pulsation.     

Gluon condensates,quark matter equation of state and quark stars

We consider here quark matter equation of state including strange quarks and taking into account a nontrivial vacuum structure for QCD with gluon condensates. The parameters of condendsate function are determined from minimisation of the thermodynamic potential. The scale parameter of the gluon condensates is fixed from the SVZ parameter in the context of QCD sum rules at zero temperature and zero baryon density. The equation of state for strange matter at zero temperature as derived is used to study quark star structure using Tolman Oppenheimer Volkoff equations. Stable solutions for quark stars are obtained with a large Chandrasekhar limit as 3.2M and radii around 17 kms.     

Generalized pressure-volume equations mimicking the Stacey reciprocal K-primed equation of state

Two generalized polynomial expressions, one based on a logarithmic form and the other on an exponential form have been set up that give pressure-volume (P-V) relationship and higher derivative properties mimicking the Stacey reciprocal K-primed equation of state. The results have been obtained for pressure P, bulk modulus K and its pressure derivative K′ for six metals viz. Ag, Al, Au, Cu, Mo and W at different values of compression down to V/V₀=0.5. The zero-pressure values of input parameters K₀ and have been taken from the literature, whereas and have been fixed to match the Stacey reciprocal K-primed equation. The polynomial equations thus formulated can be used as a substitute for the Stacey equations of state (EOS) for determining P-V relationship and higher derivative properties such as K and K′.     

Observations of neutron stars and the equation of state of matter at high densities

We summarize the constraints on the equation of state of high-density nuclear matter derived from neutron star observations. The most stringent constraints are provided by the largest mass, the largest radius, the highest rotational frequency, and the maximum surface gravity observed for neutron stars. The combination of these constraints allows only nuclear equations of state which are quite stiff.     

Dependence of the tidal deformability of neutron stars on the nuclear equation of state

Within the Bayesian framework, using an explicitly isospin-dependent parametric equation of state (EOS) for the core of neutron stars (NSs), we studied how the NS EOS behaves when we confront it with the tidal deformabilities \begin{document}$ \Lambda_{1.4} $\end{document} of canonical NSs with different error and different lower boundaries, and with the tidal deformabilities of massive NSs. We found that it does not significantly improve the constraints on the NS EOS but has a weak effect on narrowing down the slope parameter of the symmetry energy by decreasing the measurement errors of \begin{document}$ \Lambda_{1.4} $\end{document}. Both the isospin-dependent and isospin-independent parts of the NS EOS were significantly constrained and raised as the tidal deformabilities of massive NSs were adopted in the calculations, especially in high-density regions. We also found that \begin{document}$ \Lambda_{1.4} $\end{document} is more competent to limit the curvature parameter than the slope parameter of the symmetry energy, whereas the opposite occurs for the radius of canonical NSs \begin{document}$ R_{1.4} $\end{document}. The tidal deformability of an NS with two times the solar mass \begin{document}$ \Lambda_{2.0} $\end{document} is more sensitive to skewness than the curvature parameter of the symmetry energy, and \begin{document}$ \Lambda_{1.4} $\end{document} and \begin{document}$ R_{1.4} $\end{document} have no correlation with the former.     

Influence of the nuclear equation of state on the hadron-quark phase transition in neutron stars

We study the hadron-quark phase transition in the interior of neutron stars, and examine the influence of the nuclear equation of state on the phase transition and neutron star properties. The relativistic mean field theory with several parameter sets is used to construct the nuclear equation of state, while the     

Euclidean image of the soliton coherent state

A euclidean correspondence of a soliton coherent state is constructed by making use of the Guerra-Ruggiero realization of the euclidean Markov field. As a result, the euclidean image of a soliton coherent state is found to be a gaussian Markov field.     

Diffusive and dynamical radiating stars with realistic equations of state

We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.     

Regular models with quadratic equation of state

We provide new exact solutions to the Einstein–Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein–Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.     

Generalized two-mode coherent-entangled state with real parameters

The coherent-entangled state |α, x; λ> with real parameters λ is proposed in the two-mode Fock space, which exhibits the properties of both the coherent and entangled states. The completeness relation of |α, x; λ> is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operator is derived, with its own squeezing properties. Furthermore, generalized P-representation in the coherent-entangled state is constructed. Finally, it is revealed that superp...     

Maximum elastic deformations of compact stars with exotic equations of state

I make the first estimates of maximum elastic quadrupole deformations sustainable by alternatives to conventional neutron stars. Solid strange quark stars might sustain maximum ellipticities (dimensionless quadrupoles) up to a few times rather than a few times for conventional neutron stars, and hybrid quark-baryon or meson-condensate stars might sustain up to . Most of the difference is due to the shear modulus, which can be up to rather than in the inner crust of a conventional neutron star. Maximum solid strange star ellipticities are comparable to upper limits obtained for several known pulsars in a recent gravitational-wave search by LIGO. Maximum ellipticities of the more robust hybrid model will be detectable by LIGO at initial design sensitivity. A large shear modulus also strengthens the case for starquakes as an explanation for frequent pulsar glitches.