Superdense Stars Research Articles

On the Stability of Most General Exact Solution for Isentropic Superdense Stars

On the Stability of Most General Exact Solution for Isentropic Superdense Stars

RELATIVISTIC SUPERDENSE STAR MODELS OF PSEUDO SPHEROIDAL SPACE–TIME

The physically viable models of compact stars like SAX (J1808.4-3658) can be obtained using Vaidya–Tikekar ansatz prescribing spheroidal geometry for their interior space–time. We discuss here the suitability of an alternative ansatz in this context. The models of superdense star are proposed using a general three parameter family of solutions of relativistic field equations obtained adopting the alternative ansatz. The setup is shown to admit physically viable models of superdense stars and strange matter stars such as Her. X-1.

A superdense star model as charged analogue of Schwarzschild?s interior solution

A charged analogue of Schwarzschild’s interior solution has been derived by considering the non-gravitational energy density to be constant along with a special choice of electric intensity. The charged fluid sphere so obtained is seen to be more general than that of P.S. Florides and joins smoothly with the Reissner-Nordstrom metric at the pressure-free interface. Also the new charged fluid sphere is capable of representing a superdense star with surface density of 2×1014 g cm−3 which can occupy maximum mass 1.502408 times the solar mass. In the process of deriving the solution, the authors have also come across A. L. Mehra’s gaseous charged fluid model which is found to be unphysical as it has negative pressure at least at the center of the model.

CORE-ENVELOPE MODELS OF SUPERDENSE STAR WITH ANISOTROPIC ENVELOPE

A core-envelope model for superdense matter distribution with the feature — core consisting of isotropic fluid distribution and envelope with anisotropic fluid distribution — is studied on the background of pseudo-spheroidal spacetime. In the case of superdense stars core-envelope models, with isotropic pressure in the core and anisotropic pressure in the envelope, may not be unphysical. Physical plausibility of the models have been examined analytically and using numerical methods.

Exotic phases in compact stars

We discuss how the co-existence of hyperons, antikaon condensate and colour superconducting quark matter in neutron star interior influences the gross properties of compact stars such as the equation of state and mass–radius relationship. We compare our results with the recent observations. We also discuss about superdense stars in the third family branch which may contain a pure colour-flavour-locked (CFL) core.

Color superconducting quark matter core in the third family of compact stars

We investigate first order phase transitions from $\beta$-equilibrated hadronic matter to color flavor locked quark matter in compact star interior. The hadronic phase including hyperons and Bose-Einstein condensate of $K^-$ mesons is described by the relativistic field theoretical model with density dependent meson-baryon couplings. The early appearance of hyperons and/or Bose-Einstein condensate of $K^-$ mesons delays the onset of phase transition to higher density. In the presence of hyperons and/or $K^-$ condensate, the overall equations of state become softer resulting in smaller maximum masses than the cases without hyperons and $K^-$ condensate. We find that the maximum mass neutron stars may contain a mixed phase core of hyperons, $K^-$ condensate and color superconducting quark matter. Depending on the parameter space, we also observe that there is a stable branch of superdense stars called the third family branch beyond the neutron star branch. Compact stars in the third family branch may contain pure color superconducting core and have radii smaller than those of the neutron star branch. Our results are compared with the recent observations on RX J185635-3754 and the recently measured mass-radius relationship by X-ray Multi Mirror-Newton Observatory.

Transport properties and equation of state of quark-nuclear matter

Transport equations for composite nucleons and deconfined quarks in quark-nuclear matter (QNM) are derived. QNM is a many-body system containing hadrons and deconfined quarks. The starting point is a microscopic quark-meson coupling (QMC) Hamiltonian with a density-dependent quark-quark interaction. An effective quark-hadron Hamiltonian containing canonical hadron and quark field operators is constructed using a mapping procedure. For high densities, the effective Hamiltonian contains interactions that lead to quark deconfinement. Transport equations of the Ueling-Ullenbeck-Vlasov type for quarks and nucleons are obtained using standard many-body techniques with the effective quark-hadron Hamiltonian. I Introduction The study of the properties of high density hadronic matter is one of the most important problems in contemporary physics. The possibility of creating in laboratory a new state of matter through collisions of heavy nuclei has become feasible in recent years, with widespread opportunities for understanding several aspects of the strong interactions and matter in superdense stars and at the origin of the universe. One of the central questions in this field is the identification of the appropriate degrees of freedom to describe the different phases of hadronic matter. At densities much higher than the nuclear saturation density, a phase of deconfined matter composed of quarks and gluons is expected to occur. The study of the properties of such a state is possible with the methods of perturbative quantum chromodynamics (QCD). On the other hand, the study of matter at densities not much higher than the saturation density of nuclear matter - like the one existing in dense stars - is very complicated. The complication is due to the fact that this phase of matter is characterized by nonperturbative QCD phenomena and the use of tractable models and drastic approximations is presently the only practical way of tackling the problem. The quark-meson coupling (QMC) model [1] is a very useful model to study the different phases of hadronic matter. It is formulated in terms of quark-gluon degrees of freedom and is devised in such a way to incorporate in an explicit way hadron structure in the nuclear many-body problem. In this model, low-density hadronic matter is described as a system of independent baryons interacting through effective scalar- and vector-meson degrees of freedom which couple directly to the quarks. At very high density the quarks and gluons become deconfined and the entire system is confined by a bag, or potential. For a list of references and recent work, see Ref. [2].

Causality Principle for a Reissner–Nordstrom Field in the RTG: The Small-Charge Case q 2 ≤m 2

We analyze the validity of the causality principle for the external electrovac solution generated by a static spherically symmetric and electrically charged body in the relativistic theory of gravity with a vanishing graviton mass, i.e., the Reissner–Nordstrom solution. We show that this principle restricts values of the constant in the external solution and also sets a lower bound for the source radius. We demonstrate that the external field of superdense star configurations satisfies the causality principle.

A model of low-mass neutron stars with a quark core

We consider an equation of state that leads to a first-order phase transition from the nucleon state to the quark state with a transition parameter λ>3/2 (λ=ρQ/(ρN+P0/c2)) in superdense nuclear matter. Our calculations of integrated parameters for superdense stars using this equation of state show that on the stable branch of the dependence of stellar mass on central pressure dM/dPc>0) in the range of low masses, a new local maximum with Mmax=0.082⊙ and R=1251 km appears after the formation of a toothlike kink (M=0.08M⊙, R=205 km) attributable to quark production. For such a star, the mass and radius of the quark core are Mcore=0.005M⊙ and Rcore=1.73 km, respectively. In the model under consideration, mass accretion can result in two successive transitions to a quark-core neutron star with energy release similar to a supernova explosion: initially, a low-mass star with a quark core is formed; the subsequent accretion leads to configurations with a radius of ∼1000 km; and, finally, the second catastrophic restructuring gives rise to a star with a radius of ∼100 km.

Third family of superdense stars in the presence of antikaon condensates

The formation of ${K}^{\ensuremath{-}}$ and ${K}^{0}$ condensation in $\ensuremath{\beta}$-equilibrated hyperonic matter is investigated within a relativistic mean field model. In this model, baryon-baryon and (anti)kaon-baryon interactions are mediated by the exchange of mesons. It is found that antikaon condensation is not only sensitive to the equation of state but also to the antikaon optical potential depth. For large values of the antikaon optical potential depth, ${K}^{\ensuremath{-}}$ condensation sets in before the appearance of negatively charged hyperons. We treat ${K}^{\ensuremath{-}}$ condensation as a first-order phase transition. The Gibbs criteria and global charge conservation laws are used to describe the mixed phase. Nucleons and $\ensuremath{\Lambda}$ hyperons behave dynamically in the mixed phase. A second-order phase transition to ${K}^{0}$ condensation occurs in the pure ${K}^{\ensuremath{-}}$ condensed phase. Along with ${K}^{\ensuremath{-}}$ condensation, ${K}^{0}$ condensation makes the equation of state softer, thus resulting in smaller maximum mass stars compared with the case without any condensate. This equation of state also leads to a stable sequence of compact stars called the third family branch, beyond the neutron star branch. The compact stars in the third family branch have different compositions and smaller radii than that of the neutron star branch.

HER X-1: A QUARK–DIQUARK STAR?

Using a general solution to the Vaidya–Tikekar model for a spherically symmetric superdense star, we show that the equation of state (EOS) of a star with values of mass and radius within the experimental ranges for Her X-1 (a compact X-ray binary pulsar), agrees accurately with the EOS obtained by Horvath et al.,1 who considered a quark–diquark mixture in equilibrium. Nevertheless, we note that the boundary condition chosen for bosonic (diquark) component in Ref. 1 is not appropriate and the identification of Her X-1 as a quark–diquark star remains inconclusive.

On most general exact solution for Vaidya-Tikekar isentropicsuperdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)2 < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc 2, (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c 2, when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ ⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 1014 gm cm-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R 2 by −R2 in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ2 > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres.

Relativistic fluid sphere on pseudo-spheroidal space-time

A new exact closed form solution of Einstein's field equations is reported describing the space-time in the interior of a fluid sphere in equilibrium. The physical 3-space,t=constant of its space-time has the geometry of a 3-pseudo spheroid. The suitability of this solution for describing the model of a relativistic superdense star is discussed and the stability of the model under radial pulsations is examined.

Moment of inertia of a neutron star. II. Relativistic corrections

In part I we suggested an approximate equation to determine the contribution of relativistic effects to the moment of inertia of a superdense star. In the present paper it is tested on model neutron stars with nine different variants of the equation of state of superdense matter. It is established that the approximation error does not exceed 5% for stable configurations. A more accurate version of the Ravenhall—Pethick equation [D. G. Ravenhall and C. J. Pethick, Astrophys. J., 424, 846 (1994)] for the moment of inertia as a function of the mass and radius of a neutron star is derived.

Moment of inertia of a neutron star. I. Relativistic equation for the accumulated moment of inertia

A relativistic, first-order differential equation is derived for the accumulated moment of inertia of a spherically symmetric celestial body. An approximate equation is proposed to describe the contribution of relativistic effects to the moment of inertia of a superdense star. For configurations of an incompressible fluid, this approximation describes the results of the numerical calculations of Chandrasekhar and Miller to within 5% in the entire range of central pressures from 0 to ∞.

Neutron stars in the multidimensional einstein theory of gravitation

The radius, mass, total number of baryons, and other parameters of static, spherically symmetric, superdense stars are calculated. A model with one Ricci-flat inner space of arbitrary dimensionality and the approximation p1=−0.5e + ap for additional components of the energy — momentum tensor are used (e and ρ are the total energy density and the pressure of the stellar matter and a is a fitting parameter). In the case of white dwarfs, the results of the multidimensional theory do not depend on the dimensionality D of space-time for −10 ≲ a ≲ 10 and coincide with the analogous data of the general theory of relativity (GTR). For neutron stars there is a dependence on D and a. For D>4, in particular, the greatest mass Mmax of a neutron star as a function of a has a maximum at 3<a(D) ≲ 4, which exceeds the greatest mass M max 0 =2.14 M⊙ in the GTR. A comparison of theoretical results with observational data determines the allowable values of a. Data for PSR 1913 + 16 lead to 0.2 ≤ a ≤ 9.2 in the case of D=26, while the results of [P. C. Joss and S. A. Rappaport, Annu. Rev. Astron. Astrophys.,22, 537 (1984)] lead to the stricter limits 1 ≤ a ≤ 7.4.

Space-time modes of relativistic stars

The problem of relativistic stellar pulsations is studied in a somewhat ad hoc approximation that ignores all fluid motions. This {\em Inverse Cowling Approximation} (ICA) is motivated by two observations: 1) For highly damped ($w$-mode) oscillations the fluid plays very little role. 2) If the fluid motion is neglected the problem for polar oscillation modes becomes similar to that for axial modes. Using the ICA we find a polar mode spectrum that has all features of the $w$-mode spectrum of the full problem. Moreover, in the limit of superdense stars, we find the ICA spectrum to be qualitatively similar to that of the axial modes. These results clearly show the importance of general relativity for the pulsation modes of compact stars, and that there are modes whose existence do not depend on motions of the fluid at all; pure ``spacetime'' modes.

Imploding stars, shifting continents, and the inconstancy of matter

Two revolutionary concepts of the twentieth century—continental drift and the existence of superdense stars and black holes—had extended histories which ran in curious parallel for five decades. Between the wars each encountered a fierce and emotionally charged resistance which may have had a common psychological root. Each threatened man's instinctive faith in the permanence of matter.

Exact solutions for the Tikekar superdense star

We analyze a relativistic model for superdense stars proposed by Tikekar [R. Tikekar, J. Math. Phys. 31, 2454 (1990)]. In this model the hypersurfaces generated by {t=const} have the geometry of the 3-spheroid which gives the solutions a clear geometrical characterization. The solution of the Einstein field equations is reduced to integrating a second order ordinary differential equation. New classes of solutions are presented by restricting the choice of the spheroidal parameter K so that polynomial solutions are admitted for the first solution and then we find that there exists another solution which is a product of polynomials and algebraic functions. A remarkable feature of the class of solutions generated is that they are expressible completely in terms of polynomials and algebraic functions. Some physical aspects of the solutions are briefly considered. We regain the Tikekar solution as a special case when K=−7. As another example we explicitly present the form of the solution when K=−2.

On the interior of the neutron star (II)

With the assumption, the physical 3-spacet = constant in a superdense star is spheroidal and the matter-density on the boundary surface of the configurationρa = 2 × 1014 g cm−3(∼ the average matter density in a neutron star) Vaidya and Tikekar (1982) proposed an exact relativistic model for a neutron star. They suggested that their model can describe the hydrostatic equilibrium conditions in such a superdense star with densities in the range of 1014-1016 g cm−3. Based on this model Parui and Sarma (1991) estimated the maximum limit of the density variation parameter λ for a stable neutron star (both for charged and uncharged) which is equal to 0.68, i.e. λmax = 0.68.