Some problems in constructing massive star models containing a chemically-inhomogeneous convective core with the local mixing-length theory

Some problems in constructing the massive star models which have a chemically-inhomogeneous convective core by using the local mixing-length theory are indicated. One problem is negative helium flux. Another one is a large discontinuity in velocity in the convective region. It does not seem easy to reconcile these problems with the present local mixing-length theory.     

The effects of convective overshooting on naked helium stars

Using stellar evolutionary models, we investigate the effects of convective overshooting on naked helium stars. We find that a larger value of overshooting parameter δ_(ov) results in a larger convective core,which prolongs the lifetimes of naked helium stars on the helium main sequence and leads to higher effective temperatures and luminosities. For naked helium stars with masses lower than about 0.8 M_⊙, they hardly become giant stars as a result of a weak burning shell. However, naked helium stars with masses between about 0.8 M_⊙ and 1.1 M_⊙can evolve into giant branch phases, and finally become carbon oxygen white dwarfs.     

Velocity of the local interstellar medium relative to the sun from interstellar helium flux measurements onboard the Ulysses and IBEX spacecraft

The question of determining the relative velocity of the local interstellar medium (LISM) based on direct interstellar helium flux measurements in the Solar system is considered. Such measurements were made onboard the Ulysses spacecraft in 1990–2007 at a distance of 2–5 AU from the Sun and have been made from 2009 to the present day onboard the Interstellar Boundary Explorer (IBEX) spacecraft at the Earth’s orbit. Recent works on analyzing the IBEX measurements have shown that the LISM velocity relative to the Sun determined from the IBEX data differs in magnitude (by ≈3 km s^?1) and direction (by ≈4°) from the LISM velocity obtained previously by Witte based on Ulysses measurements. We have modeled the Ulysses data (including the 2007 data that have not been considered previously by anybody) by taking into account various LISM velocity vectors and compare our numerical simulations with experimental data. The LISM velocity vector derived from the IBEX data is shown to contradict the Ulysses data in the position of the measured interstellar helium flux maximum on the sky map. In addition, the position of the flux maximum is shown to be determined exclusively by the LISM velocity vector and to be independent of other model parameters (the LISM temperature and ionization rate). This means that the Ulysses data (including the 2007 data obtained only two years before the IBEX measurements) cannot be explained in terms of the existing models with the LISM velocity vector from the IBEX data. Possible reasons for the detected contradictions are discussed.     

Nonlinear development of convective instability within slender flux tubes. II. The effect of radiative heat transport

Inclusion of radiative heat transport in the energy equation for a slender flux tube leads to oscillations of the tube. The amplitude of the oscillations depends on the radius of the tube when lateral heat exchange alone is considered. Longitudinal heat transport has a greater influence on the evolution of the instability than lateral heat exchange for the particular value of tube radius considered in the calculation. Heat transport is seen to reduce the efficiency of concentration of magnetic fields by convective collapse in the case of polytropic tubes.     

Fluctuation theory of the mass flux from the stars: The refutations

This third paper on the stellar mass loss as a fluctuation phenomenon addresses the refutations. It discusses the instability of the subphotosphere to outward mass flows, which develop into stochastic surges. By applying the principle of minimum free energy, the average outward velocity to which these flows are amplified is found to be just below the atmospheric escape velocity. Small fluctuations above this average value will therefore lead to mass loss. This justifies the Langevin equation, introduced previously to describe the mass loss, and a formal derivation of this equation is presented. The average value is, furthermore, related to the earlier postulated equipartition of kinetic and thermal power of the atmosphere. Finally, the paper discusses deviations of the stellar relaxation time fromGM ² /RL, when a strong concentration of matter is at the centre. These deviations explain the anomalous behaviour of the mass loss rate of red (super)giants, so that the essential prediction of the fluctuation theory for the loss rate is not refuted.     

Nonlinear development of convective instability within slender flux tubes. I. Adiabatic flow

The nonlinear development of convective instability within slender flux tubes is studied using the method of characteristics. It is seen that the initial magnetic field influences the development of the instability. The asymptotic state of the unstable tube depends on the boundary conditions. Flux tubes subjected to ’open’ boundary conditions show a better evidence for field amplification than those subjected to ’closed’ boundary conditions. In either case, convective instability results in the generation of significant gas flow within slender flux tubes.     

A generalized time-dependent local convection theory

The time-dependent convection theory given in [1] is generalized to include non-radial oscillations. Under some reasonable assumptions, dynamic equations are derived of the auto-correlation and cross-correlation functions of the velocity and temperature fluctuations. Steady and pulsating components are separated and solved for. Our steady component agrees with Vitense's formulae. The pulsating component contains a phase-lag, due to the inertia of the convective motion.     

Fluctuation theory of the mass flux from the stars

The mass flux from a star is adopted to result from a fluctuation of the photosphere, which is not in complete thermal equilibrium. Because of the large difference between the dynamical and thermal relaxation times, its state can be approximated by a partial equilibrium. Using a theory of thermodynamic fluctuations, the mass flux is expressed in a correlation function of gravitational perturbations of the photosphere. A hypothesis is proposed that the susceptibility to these perturbations, if normalized to the available thermal energy, is the same for all stars. Its value is obtained by considering the upper limit to the mass flux. This results in a mean mass loss ofL ^3/2 (R/M)^9/4/G ^7/4, where the symbols have their common meaning. The result is compared to empirical data on the mass flux from some 50 stars of various luminosities and luminosity classes. With a possible exception for late-type (super) giants the agreement is good, in many cases within a factor 2.     

The flux ejection dynamo with small diffusivity

A number of examples are worked out to illustrate the consequences of reverse flux ejection from the surface of a convective layer of conducting fluid. Generally the reverse flux ejection has the opposite effect of magnetic buoyancy, tending to bury the fields rather than bringing them through the surface. Even a weak flux ejection effect prevents the excape of magnetic field through the surface. Reverse flux ejection at the surface of an -dynamo profoundly alters the character of the solutions of the dynamo equations. Altogether, flux ejection serves to obscure the interpretation of magnetic observations. The outstanding problem now is to determine under what circumstances there exists cyclonic convection with rotations in excess of ±1/2 in the rising columns of fluid. Negative turbulent diffusion is expected to be a close companion of the flux ejection effect.This work was supported by the National Aeronautics and Space Administration under grant NGL 14-001-001.     

A statistical theory for the decay process of weak homogeneous convective turbulence

In this paper we have derived kinetic equations for the decay of kinetic and thermal energy of a weak homogenous turbulent flow in which the fluctuating temperature field is superimposed on the eddy velocity field. Random fluctuations of velocity and temperature in a one-dimensional model have been considered on the basis of wavenumbers in Fourier space together with linearized mode approximations. Energy decay equations have been obtained in closed form, using quasi-normal approximations and the Bogoliubov expansion method. The paper also discusses the cases off=v andf=0.     

The helium radiation in prominences

It is shown that the emission of quiescent and loop prominences in the helium D₃ line and in the 4686 Å line of He⁺ respectively, occurs at low temperatures, of the order of 7000 K.The ionization of neutral helium is produced by short-wave solar radiation, which is absorbed in the outer layers of filaments composing a prominence. The population of helium triplet levels in prominences is determined by recombinations and subsequent resonance scattering of photospheric radiation. Transitions from triplet to singlet levels caused by electron collisions considerably reduce the line brightness.Emission of ionized helium in the 4686 Å line arises in prominence surface layers as well. In quiescent prominences the emission is very faint and is due to recombination; the second ionization is caused by the far ultraviolet radiation.In flare-like events ionized helium emits due to charge-exchange collisions. The symmetrical resonance charge-exchange of -particles is caused by helium ions in corpuscular streams which are probably generated in photospheric layers. Due to increased radiation losses the temperature of the prominence under the action of the stream is negligibly increased. With a stream density equal to 5 × 10⁸ cm^-3 and velocity 300 km/s the theoretical intensity of the 4686 He⁺ line is some hundreds of microängströms and agrees with observations of Goldberg-Rogozinskaya (1962, 1965) and others.     

The epoch of helium reionization

We study the reionization of He  ii by quasars using a numerical approach that combines 3D radiative transfer calculations with cosmological hydrodynamical simulations. Sources producing the ionizing radiation are selected according to an empirical quasar luminosity function, and are assigned luminosities according to their intrinsic masses. The free parameters associated with this procedure are (1) a universal source lifetime, (2) a minimum mass cut-off, (3) a minimum luminosity cut-off, (4) a solid angle specifying the extent to which radiation is beamed, and (5) a tail-end spectral index for the radiative energy distribution of the sources. We present models in which these parameters are varied, and examine characteristics of the resultant reionization process that distinguish the various cases. In addition, we extract artificial spectra from the simulations and quantify statistical properties of the spectral features in each model.
We find that the most important factor affecting the evolution of He  ii reionization is the cumulative number of ionizing photons that are produced by the sources. Comparisons between He  ii opacities measured observationally and those obtained by our analysis reveal that the available ranges in plausible values for the parameters provide enough leeway to provide a satisfactory match. However, one property common to all our calculations is that the epoch of He  ii reionization must have occurred at a redshift in the range  3≲ z ≲4  . If so, future observational programmes will be able to directly trace the details of the ionization history of helium and to probe the low-density phase of the intergalactic medium during this phase of the evolution of the Universe.     

Percolation theory and the geometry of photospheric magnetic flux concentrations

The magnetic field in solar active regions forms a highly structured pattern without an apparent length scale. We study this pattern in detail for a plage and its surroundings observed with the Swedish Solar Observatory on La Palma. The magnetogram has a resolution of about 1/3, after image optimisation. We analysed the geometric properties of isolated patches of magnetic flux. Patches with a linear size up to 3 appear to be statistically self-similar, with a fractal dimension ofD _f = 1.54 ± 0.05 for the relation between area and linear size. This value agrees very well with the dimensionD _f = 1.56 which is found in percolation theory for clusters of tracers placed randomly on a lattice with a tracer density below a critical threshold. The distribution of observed cluster areas also agrees with that of clusters on such a random lattice. The correspondence between properties of observations and of clusters on randomly filled lattices suggests that- well after emergence - the magnetic flux on the Sun is randomly distributed at least up to sizes of about 3 and possibly larger.     

The space spectrum of convective instability

Growth rates are obtained for convective disturbances propagating in an atmosphere with a linear variation of entropy. The dispersion equation for small-scale disturbances in the parabolic entropy diagram case is considered by means of the WKB-approximation. It is shown for that case that the small-scale disturbances are reflected inside the convective zone and so cannot be observed at the Sun's surface. If the atmosphere is polytropic, it is shown that the small-scale disturbances can easily reach the sun's surface.     

The URCA process in convective cores

A Monte Carlo simulation has been carried out for URCA processes in a degenerate convective stellar core, such as would be obtained following degenerate carbon ignition. We find energy loss rates substantially less than obtained by Paczynski in his vibrational approximation for this process. We conclude that the loss rates should be computed by direct integration over the convective core assuming a uniform ratio of the abundances of the URCA pair.     

Fluctuation theory of the mass flux from the stars: Amplifications

Two critical points in an earlier paper on this theory are further discussed. The first is related to the physical average of the stochastic force driving the mass flux. A more accurate estimate has been made of the mean mass loss, viz. 0.40L ^3/2(R/M)^9/4/G ^7/4, where the symbols have their common meaning. The second has to do with the upper limit to the mass loss and is replaced by the postulate of equipartition of thermal power and mechanical power in the photosphere. This equipartition seems to be reached in stars of spectral type earlier than G8. Only for these stars the above mass loss formula is valid.     

Distribution functions in the statistical theory of convective MHD turbulence of an incompressible fluid

In this paper, we define a hierarchy of distribution functions for simultaneous velocity, magnetic, and temperature fields. Some properties of the constructed distribution functions such as reduction, separation, and coincidence are discussed. Equations for the evolution of one- and two-point distribution functions have been derived. Finally, a comparison of the equation for the single-point distribution function in case of zero viscosity, negligible diffusivity, and infinite electrical conductivity is made with first equation of BBGKY hierarchy in the kinetic theory of gases.On study leave from the Department of Mathematics, University of Rajshahi, Bangladesh.     

Solar wind interaction with interstellar helium

Solar wind interaction with neutral interstellar helium focused by the Sun's gravity in the downwind solar cavity is discussed in a hydrodynamical approach. Upon ionization the helium atoms “picked up” by the (single fluid) solar wind plasma cause a slight decrease in the wind speed and a corresponding marked temperature increase. For neutral helium density outside the cavity n_He^∞ = 0.01 atoms cm^?3 and for interstellar kinetic temperature T_He= 10,000 K, the reduction is speed of the solar wind on the downwind axis at 10 AU from the Sun amounts to about 2kms^?1; the solar wind temperature excess attains 7000 K. The resulting pressure excess leads to a non-radial flow of the order of 0.25 km s^?1. The possibility of experimental confirmation is discussed.