An Upper Bound on Neutron Star Masses

We derive an upper bound on neutron star masses by using model equations of state in the nuclear matter density region and the causality limited equation of state in the ultradense region. Supposing that the model equations of state describe neutron star matter at nuclear matter density correctly we find as bound 3.75 M_⊙. For large fiducial densities one gets a maximum mass which is above a previous estimate.     

Hyperonic equation of state

An equation of state for cold matter at neutron star densities, >10¹⁴ gm/cm³, is evaluated. The gas is considered to be a degenerate mixture of neutrons, protons, leptons, hyperons and massive baryons. We derive the equilibrium equations including the effects of nuclear interactions among all the hadrons.     

Neutrinooszillationen in Neutronensternmaterie

According to the suggestion of T. J. Mazurek (1979) neutrino oscillations occuring during the dynamic stellar collapse (M ≥ 10M) could be result in a transfer of leptonic zero-point energy to baryons. Then the adiabatic index increases above γ ≥ 4/3, and such an increase is necessary to reverse the collapse. From the theory of neutrino oscillations of B. Pontekorvo (1967) we derive the oszillation length L of neutrinos in vacuum and the characteristic oscillation lengh L^* of neutrinos taking into consideration the refraction index n_e of neutron star matter. The comparison of both oscillation lenghts shows that for electron densities, characteristically of neutron star matter, the oscillation lenght L is considerable larger than the oscillation lenght L^*. Therefore neutrino oscillations cannot influence the scenario for neutrino emission of the neutron star.     

Constraints the properties of neutron star matter from the mass of neutron star PSR J1614-2230

The constraints on the properties of neutron star matter from the mass of neutron star PSR J1614-2230 are examined in the framework of the relativistic mean field theory. We find that there are little differences between the σ potentials of large mass neutron star and those of canonnical mass neutron star. For potentials of ω, ρ, neutrons and electrons, the values corresponding to the large mass neutron star are larger than those to the canonnical mass neutron star as the baryon number density is more than a certain value. We also find that for the relative particle number density of electrons, muons, neutrons and protons and the pressure of the neutron star, the values corresponding to the large mass neutron star are far larger than those to the canonnical mass neutron star. For the relative particle number density of hyperons Λ, Σ^?, Σ⁰, Σ⁺ and Ξ^?, the values corresponding to the large mass neutron star are far smaller than those to the canonnical mass neutron star. These mean that the larger mass of neutron star is more advantageous to the production of protons but is not advantageous to the production of hyperons.     

Hydrogen molecular ion in the magnetic field of a neutron star

A two-dimensional potential energy surface of an H ₂ ⁺ molecular ion is calculated for the case of the strong magnetic field of the neutron starB=10¹¹–10¹³ G. It is shown that the dependence of the potential energy from the angle between the magnetic field direction and the internuclear axis becomes very sharp as the magnetic field increases. The obtained potential energy surfaces can be used for studying the vibrational-rotational structure of the H ₂ ⁺ spectrum in a strong magnetic field and the development of the observational methods for the determination of the magnetic field of a neutron star.     

Neutron star models

Neutron star models are calculated using an equation of state discussed in an earlier paper. A maximum mass for a neutron star of 1.74 solar masses is found. The central density of thie star is 3.3×10¹⁵ g/cm³. The lightest stars have masses of 0.02 (resp. 0.03) solar masses with central densities 2.2×10¹⁴ g/cm³ (resp. 1.9×10¹⁴).     

On the collapse of neutron stars and stellar cores to pion-condensed stars

The transition from a neutron star to a pion-condensed star is investigated in Newtonian hydrodynamics. It is shown that in a certain range of ultradense equations of state, there occurs a mass ejection with energies comparable with usual supernova outputs. But the ejected mass is only in the order of 0.02M _⊙. Therefore, the observable consequences of this transition are not so dramatic as conjectured recently. In a realistic scenario including a stiff ultradense equation of state and a weak effect of pion condensation the mass ejection disappears. Additionally the collapse of a stellar core to a neutron star with pion-condensed core is considered. In comparison with a standard supernova scenario we find only a slightly reduced explosion energy. Further, the possible consequence of pion condensation during the secular evolution of the bounced core of a collapsing star to the cool final neutron star is discussed.     

Equation of state constraints from neutron stars

Recent measurements of thermal radiation from neutron stars have suggested a rather broad range of radiation radii ( ). Sources in M13 and Omega Cen imply R _∞∼12–14 km, but X7 in 47 Tuc implies R _∞∼16–20 km and RX J1856-3754 R _∞>17 km. If these measurements are all correct, only a limited selection of EOS’s could be consistent with them, but a broad range of neutron star masses (up to 2 M_⊙) would also be necessary. The surviving equations of state are incompatible with significant softening above nuclear saturation densities, such as would occur with Boson condensates, a low-density quark-hadron transition, or hyperons. Other potential constraints, such as from QPO’s, radio pulsar mass and moment of inertia measurements, and neutron star cooling, are compared. US DOE Grant DE-FG02-87ER-40317.     

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 configurationa = 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 for a stable neutron star (both for charged and uncharged) which is equal to 0.68, i.e. _max = 0.68.In this paper we have shown variation of central density per unit equilibrium radius (0/a), variation of mass, upper limit of density variation parameter both for charged and uncharged neutron stars at densities 10¹⁵ and 10¹⁶ g cm^–3, respectively. We have obtained _max = 0.68, i.e. the same as before. The important is that the duration of stability among the neutron star's constituents around _max will be shorter and shorter at higher densities as we proceed near the centre of the neutron star. In case of a charged neutron star, once stability among the constituents has been established, then unstability appears gradually maintaining linear relation between change in central density per unit equilibrium radius and change in mass whereas in case of uncharged neutron star, linear relation does not maintain.     

Neutron star models based on an improved equation of state

Using an equation of state for cold degenerate matter which takes nuclear forces and nuclear clustering into account, neutron star models are constructed. Stable models were obtained in the mass range above 0.065M and density range 10^14.08 to 10^15.4 gm/cm³. All of these models were found to be bound. The outer crystalline layer of the star was found to have a thickness of 200 m or more depending on the mass of the model.     

Neutron star models including the effects of hyperon formation

A new series of neutron star models has been computed. The equation of state used included the effects of nuclear dissolution, nuclear forces, and the presence of hyperons. The nuclear forces were introduced through use of a generalized form of the Levinger-SimmonsV andV potentials. The maximum stable masses obtained were 2.28 and 2.37M , respectively. Details are given of the structure of the outer layers which are expected to be crystalline. Expressions are given for the angular momentum and rotational energy of a neutron star and the relevant moment of inertia is tabulated for the models.     

Upper bound on the mass of non-rotating neutron stars

The problem of placing an upper bound on the mass of a non-rotating neutron star is investigated under minimal assumptions on the equation of state above nuclear densities. In particular causality (dp/dq<1) is not assumed in this region. An upper bound of about five solar masses is found.Supported in part by the National Science Foundation.     

Theory of superdense matter and degenerate stellar configurations

During the last two decades the theory of degenerate stellar configurations has been developed in works by Ambartsumian and Sahakian, as well as in some other papers. This article is further progress in this direction. Systematic investigations of thermodynamic properties of the ground and metastable states of degenerate plasma have been carried out over the total range of pressures. It was found that in the range of densities 3×10¹⁰???3×10¹⁴ g cm^?3 there exists a pionization effect which plays an important role in the thermodynamics of degenerate plasma. The pion condensate present in nuclear matter promotes the existence of metastable nuclear clusters with the nuclear numberA?10⁶. The equation of state of degenerate stellar matter has been notably revised and, accordingly, the neutron star parameters have been calculated anew. The role of the pion condensate in generating strong magnetic fields observed in the pulsars is discussed.     

High frequency oscillations during magnetar flares

The recent discovery of high frequency oscillations during giant flares from the Soft Gamma Repeaters SGR 1806-20 and SGR 1900+14 may be the first direct detection of vibrations in a neutron star crust. If this interpretation is correct it offers a novel means of testing the neutron star equation of state, crustal breaking strain, and magnetic field configuration. We review the observational data on the magnetar oscillations, including new timing analysis of the SGR 1806-20 giant flare using data from the Ramaty High Energy Solar Spectroscopic Imager and the Rossi X-ray Timing Explorer. We discuss the implications for the study of neutron star structure and crust thickness, and outline areas for future investigation.      

Heat blanketing envelopes and thermal radiation of strongly magnetized neutron stars

Strong (B?10⁹ G) and superstrong (B?10¹⁴ G) magnetic fields profoundly affect many thermodynamic and kinetic characteristics of dense plasmas in neutron star envelopes. In particular, they produce strongly anisotropic thermal conductivity in the neutron star crust and modify the equation of state and radiative opacities in the atmosphere, which are major ingredients of the cooling theory and spectral atmosphere models. As a result, both the radiation spectrum and the thermal luminosity of a neutron star can be affected by the magnetic field. We briefly review these effects and demonstrate the influence of magnetic field strength on the thermal structure of an isolated neutron star, putting emphasis on the differences brought about by the superstrong fields and high temperatures of magnetars. For the latter objects, it is important to take proper account of a combined effect of the magnetic field on thermal conduction and neutrino emission at densities ρ?10¹⁰ g?cm^?3. We show that the neutrino emission puts a B-dependent upper limit on the effective surface temperature of a cooling neutron star.     

Massive fluid spheres with isothermal cores

We can define some adiabatic exponents for neutron star cores. The equality of and ₃ leads to an equation of stateE=P ln(K/P) orP=K exp(–E/P). This equation has been solved alongwith equations for hydrostatic equilibrium for different physical conditions at the centre. The parameters of isothermal neutron star cores have been computed by taking surface densityE _a=2×10¹⁴ g cm^–3. ForP ₀=E ₀ the maximum mass and radius of neutron star core are 3.25M and 17.14 km, respectively.     

Slowly rotating relativistic stars

Equations are given which determine the moment of inertia of a rotating relativistic fluid star to second order in the angular velocity with no other approximation being made. The equations also determine the moment of inertia of matter located between surfaces of constant density in a rotationally distorted star; for example, the moments of inertia of the crust and core of a rotationally distorted neutron star can be calculated in this way. The method is applied ton=3/2 relativistic polytropes and to neutron star models constructed from the Baym-Bethe-Pethick-Sutherland-Pandharipande equation of state. Supported in part by the National Science Foundation. Alfred P. Sloan Research Fellow.     

Exotic bulk viscosity and its influence on neutron star r-modes

We investigate the effect of exotic matter in particular, hyperon matter on neutron star properties such as equation of state (EoS), mass-radius relationship and bulk viscosity. Here we construct equations of state within the framework of a relativistic field theoretical model. As hyperons are produced abundantly in dense matter, hyperon–hyperon interaction becomes important and is included in this model. Hyperon–hyperon interaction gives rise to a softer EoS which results in a smaller maximum mass neutron star compared with the case without the interaction. Next we compute the coefficient of bulk viscosity and the corresponding damping time scale due to the non-leptonic weak process including Λ hyperons. Further, we investigate the role of the bulk viscosity on gravitational radiation driven r-mode instability in a neutron star of given mass and temperature and find that the instability is effectively suppressed.      

Maximum mass of a hot neutron star with a quark core

We have considered a hot neutron star with a quark core,a mixed phase of quark-hadron matter,and a hadronic matter crust and have determined the equation of state of the hadronic phase and the quark phase.We have then found the equation of state of the mixed phase under the Gibbs conditions.Finally,we have computed the structure of a hot neutron star with a quark core and compared our results with those of the neutron star without a quark core.For the quark matter calculations,we have used the MIT bag model...     

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=ρ_Q/(ρ_N+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/dP_c>0) in the range of low masses, a new local maximum with M_max=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 M_core=0.005M_⊙ and R_core=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.