Phase transition to color-flavor-locked matter and condensation of Goldstone bosons in neutron star matter

Deconfinement phase transition and condensation of Goldstone bosons in neutron star matter are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. It is shown that the hadronic-CFL mixed phase (MP) exists in the center of neutron stars with a small bag constant, while the CFL quark matter cannot appear in neutron stars when a large bag constant is taken. Color superconductivity softens the equation of state (EOS) and decreases the maximum mass of neutron stars compared with the unpaired quark matter. The K⁰ condensation in the CFL phase has no remarkable contribution to the EOS and properties of neutron star matter. The EOS and the properties of neutron star matter are sensitive to the bag constant B, the strange quark mass m_s and the color superconducting gap Δ. Increasing B and m_s or decreasing Δ can stiffen the EOS which results in the larger maximum masses of neutron stars.     

Conversion of dark matter axions to photons in magnetospheres of neutron stars

We propose a new method to detect observational appearance of dark matter axions. The method utilizes radio observations of neutron stars. It is based on the conversion of axions to photons in strong magnetic fields of neutron stars (the Primakoff effect). If the conversion occurs, the radio spectrum of the object has a very distinctive feature—a narrow spike at the frequency corresponding to the rest mass of the axion. For example, if the coupling constant of the photon-axion interaction is M = 10¹⁰ GeV, the density of dark matter axions is ρ = 10⁻²⁴ g cm⁻³ and the axion mass is 5 μeV; then the flux from a strongly magnetized (10¹⁴ G) neutron star at the distance 300 pc from the Sun is expected to be about few tenths of millijansky at a frequency of about 1200 MHz in a bandwidth of about 3 MHz. Close-by X-ray dim isolated neutron stars are proposed as good candidates to look for such radio emission. The article is published in the original.     

Gravitational wave background from neutron star phase transition

We study the generation of a stochastic gravitational wave (GW) background produced by a population of neutron stars (NSs) which go over a hadron-quark phase transition in its inner shells. We obtain, for example, that the NS phase transition, in cold dark matter scenarios, could generate a stochastic GW background with a maximum amplitude of h _BG ~ 10⁻²⁴, in the frequency band ν _obs ≃ 20–2,000 Hz for stars forming at redshifts of up to z ≃ 20. We study the possibility of detection of this isotropic GW background by correlating signals of a pair of Advanced LIGO observatories.     

Nuclear matter properties and relativistic mean-field theory

Nuclear matter properties are calculated in the relativistic mean-field theory by using a number of different parameter sets. The result shows that the volume energy a₁ and the symmetry energy J are around the acceptable values 16MeV and 30MeV, respectively; the incompressibility K₀ is unacceptably high in the linear model, but assumes reasonable value if nonlinear terms are included; the density symmetry L is around 100MeV for most parameter sets, and the symmetry incompressibility K _s has positive sign which is opposite to expectations based on the nonrelativistic model. In almost all parameter sets there exists a critical point (,), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero, falling into ranges 0.014fm^-3 < < 0.039fm^-3 and 0.74 < ≤0.95; for a few parameter sets there is no critical point and the pure neutron matter is predicted to be bound. The maximum mass M _NS of neutron stars is predicted in the range 2.45M ?M _NS? 3.26M , the corresponding neutron star radius R _NS is in the range 12.2km ?R _NS? 15.1km. Received: 5 May 2000 / Accepted: 28 November 2000     

Gravity waves accompanying supernova explosions

Gravitational radiation arising during the formation of a protoneutron star is studied. Here it is mainly large-scale nonuniformities that develop inside the star. The entropy and density profiles of such nonuniformities resemble the “mushroom cloud” of a nuclear explosion. A bubble of hot neutron matter floats to the surface of the star, like the “mushroom cloud” of an explosion in the earth’s atmosphere. Depending on the symmetry of the problem, from two to six bubbles can float upward at the same time. The characteristic masses of such bubbles are 0.01M _⊗ and the radial velocities reach ∼0.1c. The energy radiated in the form of gravitational waves in one cycle of bubbles floating to the surface is ∼10⁻² M _⊗ c ²−10⁻¹⁰ M _⊗ c ². Such cycles occur repeatedly as the neutron star cools. This phase can last up to seconds. The total energy radiated in the form of gravitational radiation can reach 10⁻¹ M _⊗ c ². Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 817–822 (25 December 1996)     

Superfluidity in dense nuclear matter

We discuss the onset of superfluidity in neutron stars, where the model of nuclear matter is realized in a high-density and asymmetry state. In particular, we present the study of the effects of microscopic three-body forces on the proton pairing in the ¹ S ₀ channel and neutron pairing in ³ PF ₁ channel for β-stable neutron star matter. It is found that the main effects of three-body forces are to shrink the domain of existence of the ¹ S ₀ below the threshold of the direct URCA process and to stretch the density range of the ³ PF ₁ pairing in a broad domain so to cover most part of the neutron-star core. The text was submitted by the authors in English.     

Limiting angular velocity of realistic relativistic neutron star models

The Keplerian velocity as well as those frequencies at which instability against gravitational radiation-reaction sets in are calculated for rotating neutron star models of gravitational mass 1.5M . The investigation is based on four different, realistic neutron star matter equations of state. Our results indicate that the gravitational radiation instability sets in wellbelow (i.e., 63–71% of) the Keplerian frequency, and thatyoung neutron stars are limited to rotational periods greater than about 1 ms. In young and therefore hot (T10¹⁰ K) neutron stars them=5(±1) modes and in old stars after being spun up and reheated by mass accretion, them=4 and/orm=3 modes may set the limit on stable rotation.Dedicated to Prof. Dr. H.J. Mang on the occasion of his 60th birthday.     

Contribution of the massive photon decay channel to neutrino cooling of neutron stars

We consider massive photon decay reactions via intermediate states of electron-electron-holes and proton-proton-holes into neutrino-antineutrino pairs in the course of neutron star cooling. These reactions may become operative in hot neutron stars in the region of proton pairing where the photon due to the Higgs-Meissner effect acquires an effective mass m _γ that is small compared to the corresponding plasma frequency. The contribution of these reactions to neutrino emissivity is calculated; it varies with the temperature and the photon mass as T ^3/2 m _γ ^7/2 exp(−m _γ /T) for T<m ^γ . Estimates show that these processes appear as extra efficient cooling channels of neutron stars at temperatures T≅10⁹–10¹⁰ K. Zh. éksp. Teor. Fiz. 114, 385–397 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Dense stars with exotic configurations

In this paper, we consider dense stars with configurations expected from the SU(3)_C×SU(2)_W× U(1) standard model of strong and electroweak interactions. Following a recent suggestion that strange matter, a form of (uds) quark matter, may be the true ground state of hadronic matter, we investigate the prospect for the existence of dense stars consisting partially, or entirely, of strange matter by comparing the relative stability between neutron matter and strange matter. It is found that the restriction on the maximum star mass holds in all cases, including a pure strange star, a pure neutron star, and a neutron star with a quark core. It is also found that the choice of both the bag constantB and the strong coupling constant _s has a decisive effect on the relative stability between strange matter and neutron matter. For currently accepted values of (B, _s), anA= dense starcannot consist entirely,nor partially, of strange matter. Nevertheless, such conclusion may be subject to change if corrections ofO ( _s ² ) or other effects are taken into account. Finally, we use the framework of Tolman, Oppenheimer, and Volkoff to analyze two cases of boson stars: gluon stars and stars consisting of massive scalar particles (massive bosons). It is found that, in the case of gluon stars, the presence of the bag constant in the QCD vacuum yields results very similar to that found in quark stars. On the other hand, soliton stars consisting of massive bosons exist if there is some background pressure which plays the role similar to the bag constant for lowering the matter pressure. The stability problem for both gluon stars and soliton stars is briefly discussed.     

Stars of strange matter?

We investigate suggestions that quark matter with strangeness per baryon of order unity may be stable. We model this matter at nuclear matter densities as a gas of close packed Λ-particles. From the known mass of the Λ-particle we obtain an estimate of the energy and chemical potential of strange matter at nuclear densities. These are sufficiently high to preclude any phase transition from neutron matter to strange matter in the region near nucleon matter density. Including effects from gluon exchange phenomenologically, we investigate higher densities, consistently making approximations which underestimate the density of transition. In this way we find a transition density ρ_tr≳7ρ₀, where ρ₀ is nuclear matter density is not far from the maximum density in the center of the most massive neutron stars that can be constructed. Since we have underestimated ρ_tr and still find it to be ∼7ρ₀, we do not believe that the transition from neutron to quark matter is likely in neutron stars. Moreover, measured masses of observed neutron stars are ≅1.4 M_⊙, where M_⊙ is the solar mass. For such masses, the central (maximum) density is ρ_c<5ρ₀. Transition to quark matter is certainly excluded for these densities.     

Triplet superfluidity in neutron matter with Skyrme forces at subnuclear and supranuclear densities in a strong magnetic field

Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T _c,1(n, H) and T _c,2(n, H) (which are nonlinear functions of density, n, and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases ³He - A₁ and ³He - A₂) in steady and homogeneous sufficiently strong magnetic field (but |μ _n |H ≪ E _c < ɛ _F (n), where μ _n is the magnetic dipole moment of a neutron, E _c is the cutoff energy and ɛ _F (n)is the Fermi energy in neutron matter). General formulae for T _c,1,2(n,H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density n (at sub- and supranuclear densities) from the interval 0.7 n ₀ ≲ n < n _c (Skyrme)< 2 n ₀, where n ₀ =0.17 fm⁻³ is the nuclear density and n _c (Skyrme)is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.     

Quark matter formation in dense stellar objects

It is expected that at very large densities and/or temperatures a quark-hadron phase transition takes place. Lattice QCD calculations at zero baryon density indicate that the transition occurs at T _c ∼ 150–170 MeV. The transition is likely to be second order or a cross over phenomenon. Although not much is known about the density at which the phase transition takes place at small temperatures, it is expected to occur around the nuclear densities of few times nuclear matter density. Also, there is a strong reason to believe that the quark matter formed after the phase transition is in colour superconducting phase. The matter densities in the interior of neutron stars being larger than the nuclear matter density, the neutron star cores may possibly consist of quark matter which may be formed during the collapse of supernova. Starting with the assumption that the quark matter, when formed consists of predominantly u and d quarks, we consider the evolution of s quarks by weak interactions in the present work. The reaction rates and time required to reach the chemical equilibrium are computed here. Our calculations show that the chemical equilibrium is reached in about 10⁻⁷ seconds. Further more during the equilibration process enormous amont of energy is released and copious numbers of neutrinos are produced. Implications of these on the evolution of supernovae will be discussed.     

Well Behaved Charged Generalization of Buchdahl’s Fluid Spheres

In the present article, we have obtained a class of well behaved charged analogues of Buchdahl (Phys. Rev. 116:1027–1034, 1959) neutral perfect fluid solution, which reduces to its neutral counter part in the absence of charge. The solutions so obtained are utilized to depict the super-dense stars models such as models for neutron stars and strange star. It is observed that the models are well behaved for restricted range of the parameter K (1<K≤1.64). Over all the maximum mass and corresponding radius is 2.4495M _Θ and 16.7289 respectively and moment of inertia . Also the pulsars character of the super-dense stars so obtained and has been analyzed with the help of moment of inertia. The analysis of the models reveals both vela and crab pulsars.     

3PF2 neutron superfluidity in neutron stars and three-body force effect

We investigate the ^3PF2 neutron superfluidity in H-stable neutron star matter and neutron stars by using the BCS theory and the Brueckner-Hartree-Fock approach. We adopt the Argonne V18 potential supplemented with a microscopic three-body force as the realistic nucleon-nucleon interaction. We have concentrated on studying the threebody force effect on the ^3PF2 neutron pairing gap. It is found that the three-body force effect is to enhance remarkably the ^3PF2 neutron superfluidity in neutron star matter and neutron stars.     

Axion emission from a magnetized neutron gas

By using the polarization density matrix for a neutron in a magnetic field, the axion luminosity of magnetic neutron stars that is associated with the flip of the anomalous magnetic moment of degenerate nonrelativistic neutrons is calculated. It is shown that, at values of the magnetic-field induction in the region B ≳ 10¹⁸ G, this mechanism of axion emission is dominant in “young” neutron stars of temperature about a few tens of MeV units. At B ∼ 10¹⁷ G, it is one of the basic mechanisms. The Fermi energy of a degenerate neutron gas in a magnetic field is found, and it is shown that there is no such mechanism of axion emission in the degenerate case.     

Effect of binarity on the local stellar mass density

Summary Considering the existence of many unresolved binary systems among the stars used to derive the stellar luminosity function, we have estimated the increase in the total mass density in the solar neighbourhood. Such an increase depends on the fraction of stars which are unresolved binaries, but conservative estimates give a value larger than 0.004M _⊙ pc⁻³. Paper presented at the Congress ?Galactic and Extragalactic Dark Matter?, Roma, 28 to 30 June 1983.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System

In a previous work [1] matter models such that the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1, were considered in the context of Buchdahl’s inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, [R ₀, R ₁], R ₀ > 0, satisfies R ₁/R ₀ < 1/4. Moreover, given a sequence of solutions such that R ₁/R ₀ → 1, then the limit supremum of 2M/R ₁ was shown to be bounded by ((2Ω + 1)² − 1)/(2Ω + 1)². In this paper we show that the hypothesis that R ₁/R ₀ → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of 2M/R ₁ is bounded, but that the limit is ((2Ω + 1)² − 1)/(2Ω + 1)² = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R ₁ arbitrary close to 8/9, which is interesting in view of [3], where numerical evidence is presented that 8/9 is an upper bound of 2M/R ₁ of any static solution of the spherically symmetric Einstein-Vlasov system.