There are serious discrepancies among some of the recent neutron star cooling calculations by various groups. We have been investigating the possible source of these discrepancies. In this paper, we report our findings. We also report the preliminary result of our most recent cooling calculations without assuming an isothermal stellar evolution code. In this work, we used the currently existing best energy transport theories, as well as general relativity, both in thermodynamics and hydrodynamics.

For material accreting along the magnetic field axis of a neutron star, electrons are quantized into Landau orbits. Collisional excitation of the first excited Landau level, followed by radiative decay, leads to the emission of a cyclotron line. The expected line is broad, because the optical depth is large, and its shape is difficult to calculate. Redshifts due to the recoil of a scattering electron and blueshifts due to scattering from the infalling accretion column are being calculated by I. Wasserman, as well as the proton stopping length in the presence of a magnetic field.

The energy liberated by nuclear burning of matter accreting onto degenerate dwarfs can be more than an order of magnitude greater than that available from the release of gravitational potential energy. Nuclear burning therefore significantly alters the characteristics of X radiation from such stars. Here we report the results of two-fluid calculations in which steady burning occurs at various rates, and compare them with our earlier calculations which assumed no burning. If the star has a weak or no magnetic field, we find that nuclear burning enhances the soft X-ray flux emitted from the stellar surface, increases Compton cooling of the emission region and therefore reduces the hard X-ray luminosity and softens the hard X-ray spectrum. On the other hand, if the star has a strong magnetic field we find that nuclear burning enhances the soft X-ray flux emitted from the stellar surface but has little effect on the hard X-ray luminosity and spectrum. We apply the results of our calculations to the AM Her sources and to cataclysmic variables such as SS Cyg and U Gem, and discuss the evidence for and against nuclear burning of accreted material in these objects.

We report the Monte Carlo simulation of the unsaturated Comptonization to probe the phyiscal state of the accreting plasma near a compact object. We calculate the emission spectrum and the Compton cooling rate of the plane-parallel hot plasma layer with the finite optical depth to the Thomson scattering, τ. The distribution of electrons is assumed to be a relativistic Maxwellian with the temperature Te. The energy and angular distribution of the soft photons impinging on the plasma layer is taken to be Planckian with the temperature Tph. We use the Klein-Nishina formula for the scattering between a photon and an electron.

Does rotation influence stellar evolution? Does it cause observational effects other than line broadening? Can rotation be responsible for mixing of chemical elements throughout the star? Do evolved stars have rapidly rotating cores? This, for instance, is of interest if one wants to compute the details of supernova events. We are not sure whether rotation has really important effects on the life of a star. There might be no rapidly rotating cores. If we think that a fossile general magnetic field couples core and envelope of an evolved star, the core will always be slowed down by the big inertial momentum of the outer regions.

Magnetic fields are now observed or inferred in a wide variety of stellar objects. The class of early-type stars with strong large-scale fields extends from types B to F, with effective fields from 300 gauss up to several x 104 gauss (Borra and Landstreet 1980). Fields between 4 × 106 and 108 gauss have been inferred in a small percentage of white dwarfs, and of over 1012 gauss in neutron stars. Some Cepheids show measurable fields. Evidence has built up of solar-type activity in late-type stars. The pioneering work by Wilson (1978) on Ca activity has shown convincingly the occurrence of periodicity reminiscent of the solar cycle in a number of G, K and M stars. Ca II emission appears to be a good predictor of simultaneous X-ray emission from hot coronae around cool stars (Vaiana 1979, Mewe and Zwaan 1980). Fields of some 2 × 103 gauss have been reported in two late-type main sequence stars (Robinson, Worden and Harvey 1980).

Equilibria of rigidly rotating polytropic gas with small compressibilities are computed in order to investigate the relation between the incompressible and compressible equilibria. The equilibrium figure varies from a spheroid-like shape to a concave hamburger as the angular velocity increases. This result is supported by the fact that a concave hamburger equilibrium is obtained even in the complete incompressible case. Thus the Maclaurin spheroid does not represent the incompressible limit of the rotating polytropic gas because of its restriction of the figure. The computed sequence of equilibria clarifies the relation between the Maclaurin spheroid and the Dyson-Wong toroid. Moreover it is the sequence of minimum-energy configuration. These results suggest that our solutions are more physical and probably stabler than any other equilibrium of incompressible fluids.

A technique used in the numerical computation of Newtonian rotating polytropes has been generalized and applied to the rapidly rotating polytropes in general relativity.

The occurrence of rotation in Globular Cluster stars has been suggested (see e.g. Renzini 1977) as a mechanism producing the observed colour spread in actual Horizontal Branches. If this is the case, canonical results on evolutionary properties of HB stars have to be revisited in order to account for rotation-driven structural variations: faster Main Sequence rotators delay the He flash increasing the mass-size Mc of the He core at the flash and loosing a greater amount of mass during the Red Giant stage.

Among the observational astronomers it is quite customary to assume potential magnetic fields in calculating the strength and the direction of the magnetic fields on the stellar surface. People use this assumption because

1. 1. it is easy to calculate,

2. 2. it is possible to fit the observations with the calculations to some extent using the parameters inherent to the model,

3. 3. at a first glance, there is no difficulty in assuming both potential magnetic fields and static stellar atmosphere because they do not interact each other (except at the pole).

Influence of convection on the pulsational stability of stars is examined based on Unno's (1967) theory of time-dependent convection. This theory is an extension of Vitense's local mixing-length theory of convection to the time-dependent problem. The equations of linear non-adiabatic pulsations, which include the thermal interaction between convection and pulsation, have been solved numerically on a series of Cepheid models. It is found that the thermal eigenfunctions (of δ T/T and δ L/L) exhibit spatial oscillations with short wavelength in cool stellar models where the energy is mostly transported by convection. This phenomenon of spatial oscillations is interpreted, and it is shown that they arise because of the phase lag of the convective flux to pulsation and they are related to the local character of the convection theory. It is found that the spatial oscillations play a determinant role in the pulsational stability in the region of the red edge of the Cepheid instability strip, as far as the thermal convection-pulsation coupling is concerned. The details of this study have been pulbished in Astronomy and Astrophysics.

Turbulent diffusivities are often used for representing nonlinear interactions of turbulent elements on the motion of a larger scale. In turbulent convection, the average life of a representative element is substantially lengthened by bouyancy. Taking this effect into account, we calculate turbulent viscosities, thermal and electrical conductivities for Boussinesq fluids on the basis of a spectral theory of turbulent convection (Nakano, Fukushima, Unno, and Kondo, 1979). The effect of bouyancy results in the increase of turbulent diffusivities, compared with the case without bouyancy. We also propose the generalization of the method such that a stellar convection zone can be theoretically constructed without recourse to the mixing length.

The presence of a mild turbulence inside rotating stars has been considered by Howard et al (1967) and by Bretherton et al (1968) in connection with the problem of the solar flattening, raised by Dicke (1970). The possibility of using abundance determination to test the existence of that turbulence has been considered by Schatzman (1969).

The number ratios of horizontal branch stars to red giant stars were obtained for globular clusters and Draco dwarf galaxy and the helium abundance was estimated using model results without semiconvection zone (SCZ) and with fully developed one. The analysis was confined to the four clusters (M4, M5, M13, and 47 Tuc) and the Draco galaxy, for which fairly precise star counts had been carried out. The effect of the difference in radial distribution between horizontal and red giant branch stars were taken into account, if necessary. The statistically significant difference in R exists among these objects. The cause may be the difference in the helium abundance and/or in the development of the SCZ. In the case of the fully developed SCZ, the helium abundance for M5 and Draco is appreciably smaller than the value given by the big-bang cosmology. It may be taken as an evidence against the full development of the SCZ for the horizontal branch stars in these objects.

Type II supernovae probably arise predominantly in stars of 8–15 M⊙ which leave neutron star remnants but accomplish little in the way of nucleosynthesis. Stars in the mass range ~ 15-70 M⊙ may either explode or collapse. Their evolution and final outcome, including their contribution to nucleosynthesis, may depend strongly on processes of mass loss. Type I supernovae probably involve a deflagrative explosion in a carbon-oxygen core surrounded by a distended helium envelope. The evolutionary origin of such a configuration is obscure.

Presupernova evolution and the hydrodynamic behavior of supernova explosions in stars having electron-degenerate cores are summarized. Carbon deflagration supernovae in C+O cores disrupt the star completely. On the other hand, in electron capture supernovae, O+Ne+Mg cores collapse to form neutron stars despite the competing oxygen deflagration.

Also discussed are white dwarf models for Type I supernovae (SN I). Supernova explosions in accreting white dwarfs are either the detonation or deflagration type depending mainly on the accretion rate. The carbon deflagration model reproduces many of the observed features of SN I.

In our paper (Haubold and John 1978) we succeeded in a closed-form evaluation of the reaction rate by means of a special function, known as Meijer's G-function

This representation of the rate is appropriate to perform analytical operations (e.g. for the computation of energy generation in a fusion plasma).

The enhancement factor for the rate of thermonuclear reactions which involve two kinds of nuclei with charges Zi and Zj in the strong-screening regime is given for general cases of surrounding nuclear plasmas by the formula, exp[1.25Γij −0.095τij(3Γij/τij)2]. Here, Γij = 2ZiZje2/(ai+aj)T; ai = [3Zi/4πΣkZknk]1/3; τij = [(27π2/4)(2μijZi2Zj2e4Th2)]1/3; μij is the reduced mass for the two reacting nuclei Zi and Zj; and nk is the number density of nuclei Zk. The calculation is based on the recent results of Monte Carlo computations for binary ion mixtures, which have shown that the screening functions hij(r) at intermediate distances [0.5 ≤ r/[(ai+aj)/2] ≤ 1.6] can be expressed to a good degree of accuracy by

Application to the calculation of carbon ignition in the carbon-oxygen core of a highly evolved star is discussed. The carbon ignition temperature is found to be single-valued as a function of the density in contrast to the work of Graboske.

In this report I consider dynamic instability when the non-equilibrium neutronization of matter plays the main role. The model of the deflagration supernova has been developed during more than ten year in our group. In 1973 it was shown that thermal flash evolves in the deflagration regime. In our computations the deflagration regime is stipuleted by joint effect of compression of matter and weak shock waves, obtained at the pulsing regime of burning. Fig. 1 shows the graduated growth of entropy in mass zone through passage of weak shock waves.

The collapse of dense cores in massive stars proceeds as follows. Initially, leptons dominate the pressure because neutrinos become trapped at high densities. This results in the formation of a cool inner core that collapses homologously. At around nuclear densities the pressure from nucleons increases rapidly and halts the collapse, giving a core bounce. A shock forms at the surface of the inner core and propagates into the infalling envelope. These basic features have emerged in the hydrodynamic studies of collapse by various researchers. However, the question of final outcome of collapse is unresolved at present. The evolution of the core after the shock has propagated through the envelope has not been addressed in detail. This communication summarizes some current results of the author's ongoing study of stellar collapse.