Advanced evolutionary phase of a first-generation star

The theoretical evolution of a first-generation star of 3M after the core helium-exhaustion phase has been investigated. The star displays the character of a double shell burning model. Shell hydrogenburning produces energy mostly by the p-p chain reaction. CN-cycle reaction is only operating in the inner edge regions where sufficient amount of carbon is formed by the 3-reactions. Hence, the shell burning time of the star is longer than that of normal stars, thus lengthening the total evolutionary lifetime of the first-generation stars.Prior to carbon-burning phase, the mass of the complete hydrogen-exhausted region is 1.14M and that of complete helium-exhausted region is 0.83M . A carbon-oxygen core of about 0.87M has developed within the star in which the ratio of carbon to oxygen is about 0.85, but decreases down to a value of 0.50 near the boundary of the core.     

Relativistic mean-field theory equation of state of neutron star matter and a Maxwellian phase transition to strange quark matter

The equation of state of neutron star matter is examined in terms of the relativistic mean-field theory, including a scalar-isovector δ-meson effective field. The constants of the theory are determined numerically so that the empirically known characteristics of symmetric nuclear matter are reproduced at the saturation density. The thermodynamic characteristics of both asymmetric nucleonic matter and β-equilibrium hadron-electron npe-plasmas are studied. Assuming that the transition to strange quark matter is an ordinary first-order phase transition described by Maxwell's rule, a detailed study is made of the variations in the parameters of the phase transition owing to the presence of a δ-meson field. The quark phase is described using an improved version of the bag model, in which interactions between quarks are accounted for in a one-gluon exchange approximation. The characteristics of the phase transition are determined for various values of the bag parameter within the range B ∈ [60,120]MeV/fm³ and it is shown that including a δ-meson field leads to a reduction in the phase transition pressure P ₀ and in the concentrations n _N and n _Q at the phase transition point. Translated from Astrofizika, Vol. 52, No. 1, pp. 147–164 (February 2009).     

A two-dimensional hydrostatically equilibrium atmosphere of a neutron star with given differential rotation

An analytic solution has been found in the Roche approximation for the axially symmetric structure of a hydrostatically equilibrium atmosphere of a neutron star produced by collapse. A hydrodynamic (quasione-dimensional) model for the collapse of a rotating iron core in a massive star gives rise to a heterogeneous rotating protoneutron star with an extended atmosphere composed of matter from the outer part of the iron core with differential rotation (Imshennik and Nadyozhin, 1992). The equation of state of a completely degenerate iron gas with an arbitrary degree of relativity is taken for the atmospheric matter. We construct a family of toroidal model atmospheres with total masses M≈ 0.1?2M _⊙ and total angular momenta J≈(1?5.5)×⁴⁹ erg s, which are acceptable for the outer part of the collapsed iron core, in accordance with the hydrodynamic model, as a function of constant parameters ω₀ and r ₀ of the specified differential rotation law Ω=ω₀exp[?(rsinθ)²/r ₀ ² ] in spherical coordinates. The assumed rotation law is also qualitatively consistent with the hydrodynamic model for the collapse of an iron core.     

Spectroscopic observations of the classical symbiotic star V1413 AQL at the phase of its transition to quiescence

We present the results of our spectroscopic and photometric observations of the classical symbiotic star V1413 Aql in 2003–2007, which cover the transition phase of its hot component from activity to quiescence. Various quiescence criteria for the hot component of the system are analyzed. Judging by its photometric characteristics, the system had not yet returned to quiescence by 2007, although a fairly strong He II λ4686 Å line observed previously during quiescence in 1993 appeared in its spectrum. We model the continuum energy distribution for V1413 Aql based on a standard three-component model and a model with an accretion disk. Analysis of the forbidden [O III] and [Ne III] lines shows that the neon abundance in V1413 Aql may be enhanced with respect to the oxygen abundance. The cool component of V1413 Aql has been found to be a variable M5-type red giant, with the variability amplitude at λ = 7500 Å being at least 2 ^m .     

The Chandrasekhar’s condition of the equilibrium and stability for a star in the nonextensive kinetic theory

The idea of Chandrasekhar’s condition of the equilibrium and stability for a star is revisited in the nonextensive kinetic theory based on Tsallis entropy. A new analytical formula generalizing Chandrasekhar’s condition is derived by assuming that the stellar matter is kinetically described by the generalized Maxwell–Boltzmann distribution in Tsallis statistics. It is found that the maximum radiation pressure allowed at the center of a star of a given mass is dependent on the nonextensive parameter q. The Chandrasekhar’s condition in the Maxwellian sense is recovered from the new condition in the case of q = 1.     

Planet formation process as a phase transition

We discuss an adiabatic phase transition between a nebular ring and a protoplanet, taking into account the gravitational corrections to the perfect gas entropy. We compare the results of this model with those found in a previous paper from different assumptions, and we try a qualitative comparison with the structure of the real solar system, using the data for the four giant planets. We discuss the relevance of some primordial phenomena in the formation process of these planets such as a mass depletion within the asteroidal belt, a mass loss from the external regions of the nebula and a decrease of Neptune's orbital radius due to ejection of cometary material. The first and the second process seem to be significantly supported by the results of the phase transition model.     

Planet formation process as a phase transition

We discuss the condensation of ring-shaped nebular matter into a protoplanet such as an isothermal phase transition. Within an elementary model for this process, we analyze the effect of the relevant physical parameters (mass and temperature of the nebular matter) on the critical width of the ring which allows the transition.     

The development of a cocoon star

A newly-formed massive star is likely to be surrounded by dense gas and dust as it approaches the main sequence. Radiation pressure must push some of the inner material outward before the star begins to produce ionizing radiation; this affects the formation of theHii region. A remarkably dense dust front may precede the ionization front.The observable radio and infrared spectra are discussed. If the dust cloud is composed of small graphite grains, extraordinarily large far-infrared fluxes are possible.     

Thermal evolution of a rotating strange star in the colour superconductivity phase

Under the combination effect of recommencement heating due to the spin-down of strange stars (SSs) and heat preservation due to the weak conduction heat of the crust, Cooper pair breaking and formation (PBF) in colour superconducting quark matter arises. We investigate the cooling of SSs with a crust in the colour superconductivity phase including both deconfinement heating (DH) and the PBF process. We find that DH can delay the thermal evolution of SSs and the PBF process suppresses the early temperature rise of the stars. The cooling SSs behave within the brightness constraint of young compact objects when the colour superconductivity gap is small enough.     

Hydrostatic equilibrium of causally consistent and dynamically stable neutron star models

We show that the mass–radius  ( M – R )  relation corresponding to the stiffest equation of state (EOS) does not provide the necessary and sufficient condition of dynamical stability for equilibrium configurations, because such configurations cannot satisfy the 'compatibility criterion'. In this regard, we construct sequences composed of core–envelope models such that, like the central condition belonging to the stiffest EOS, each member of these sequences satisfies the extreme case of the causality condition,   v = c = 1  , at the centre. We thereafter show that the M – R relation corresponding to the said core–envelope model sequences can provide the necessary and sufficient condition of dynamical stability only when the 'compatibility criterion' for these sequences is 'appropriately' satisfied. However, the 'compatibility criterion' can remain satisfied even when the M – R relation does not provide the necessary and sufficient condition of dynamical stability for the equilibrium configurations. In continuation of the results of a previous study, these results explicitly show that the 'compatibility criterion' independently provides, in general, the necessary and sufficient condition of hydrostatic equilibrium for any regular sequence. In addition to its fundamental result, this study can explain simultaneously the higher and the lower values of the glitch healing parameter observed for the Crab-like and Vela-like pulsars respectively, on the basis of the starquake model of glitch generation.     

The formation of X-ray radiation in a boundary layer during disk accretion onto a neutron star

We present computed radiation spectra for the boundary layer (BL) of the accretion disk that is formed near the surface of a neutron star. Both free-free processes and Comptonization were taken into account. Our computations are based on the hydrodynamic solution obtained by Popham and Sunyaev (2001) for the BL structure. The computed spectra are highly diluted compared to the Planck spectra of the same surface temperature. They are complex in shape; in particular, an intense Wien emission component is formed in their high-energy region at high accretion rates. In general, the computed spectra are harder than those observed in actual X-ray sources. This is the result of a very high temperature found by Popham and Sunyaev (2001) for the BL. We show that such temperatures could result from an oversimplified treatment of radiative transfer in their paper, which completely ignored the frequency dependence of the matter opacity and radiation intensity. Our computations indicate that at moderate accretion rates, a proper treatment of radiative transfer with allowance for Comptonization leads to appreciably lower plasma temperatures and to softer radiation spectra.     

Variational principle for stars with a phase transition

The variational principle for stars with a phase transition has been investigated. The term outside the integral in the expression for the second variation of the total energy of a star is shown to be obtained by passage to the limit from the integration over the region of mixed states in the star. The form of the trial functions ensuring this passage has been found. All of the results have been generalized to the case where general relativity is applicable. The known criteria for the dynamical stability of a star when a new phase appears at its center are shown to follow automatically from the variational principle. Numerical calculations of hydrostatically equilibrium models for hybrid stars with a phase transition have been performed. The form of the trial functions for the second variation of the total energy of a star that describes almost exactly the stability boundaries of such stellar models is proposed.     

The spectrum of the Ap star HR 465 near the rare-earth minimum phase

Four spectra of the long-period Ap star HR 465 were taken in 1969–70 near its rare-earth minimum phase and analysed. Equivalent widths or upper limits were obtained for lines of 23 elements. Lines of Cr were very strong. The relative abundances of the iron-peak elements were derived by a differential curve-of-growth analysis using Gem as the comparison star. The Sc/Fe, Ti/Fe, V/Fe, and Ni/Fe abundance ratios were found to be abnormally low, while the Cr/Fe ratio was abnormally high (0.08). The equivalent widths in 1969–70 were compared with those measured by Aller on a spectrum taken in 1960 near the rare-earth maximum phase. Ionized lines of Sc, Ti, V, Te, Nb, Mo, and the rare-earths all vary out of phase with the Cri and Crii lines. Although Mo and Cr occupy corresponding positions in the periodic table, the Mo/Cr abundance ratio was apparently at least 180 times higher in 1960 than in 1969–70.     

The maximum mass of a neutron star

We consider the possibility that gravitational energy may play a local as well as global role in the behavior of matter in strong gravitational fields. A particular idealized equation, suggested as representing uniform energy density in general relativity, is examined, and its stability with respect to oscillatory and convective perturbations shown to be consistent with general relativistic hydrodynamics, subject to a new physical effect predicted for the behavior of fluids moving in strong fields. We calculate from this idealized equation the mass of a non-rotating neutron star, obtaining a maximum surface redshift ofz=2.48 and a maximum core mass of 9.79 ₁₄ ^–1/2 M. This compares withz=2.00 and 11.4 ₁₄ ^–1/2 M for a Schwarzschild star (=const.) and 6.8 ₁₄ ^–1/2 M for a causal star (dP/d1).     

Magnetic braking during star formation I

We study the transport of angular momentum from a cool massive gas cloud by Alfvén waves travelling along the distorted magnetic field linking the cloud with the hot galactic background. The efficiency of braking is never so great as to keep the cloud even roughly corotating with the back-ground. The mathematical approximations are not quite sharp enough to give a definitive answer to the question: is the braking ever so efficient that the centrifugal forces are kept well below gravity, so that the cloud contracts at the (magnetically-diluted) free-fall rate?; or is the cloud maintained in approximate centrifugal balance, with the rate of contractiondetermined by the loss of angular momentum?