A relaxation method for the computation of model stellar atmospheres

A general Monte Carlo relaxation method has been formulated for the computation of physically self-consistent model stellar atmospheres. The local physical state is obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer. Anisotropic Thomson scattering is included in the equation of transfer and radiation pressure effects are included in the hydrostatic equation. The constraints of hydrostatic and radiative equilibrium are enforced. Local thermodynamic equilibrium (L.T.E.) is assumed as a boundary condition deep in the atmosphere. Elsewhere in the atmosphere L.T.E. is not assumed.The statistical equilibrium equations are solved with no assumptions made concerning detailed balance for the bound-bound radiative processes. The source function is formulated in microscopic detail. All atomic processes contributing to the absorption and emission of radiation are included. The kinetic energy balance equation for the electron gas is formulated in detail. All atomic processes by which kinetic energy is gained and lost by the electron gas are included.The method has been applied to the computation of a model atmosphere for a pure hydrogen early-type star. An idealized model of the hydrogen atom with five bound levels and the continuum was adopted. The results of the trial calculation are discussed with reference to stability, accuracy, and convergence of the solution.Contribution No. 385 from the Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Helium in stellar atmospheres

Helium, which was first discovered on the sun with the help of spectral analysis, plays, together with hydrogen, a principal role in astrophysics. We consider here two fundamental quantities: primordial helium abundance formed during Big Bang nucleosynthesis and the current initial helium abundances in nearby stars. It is shown that stellar atmospheres are enriched in helium during the main-sequence stage. Observational evidence for helium contamination in close OB-binaries is discussed. Stars with strong abundance anomalies are considered, such as chemically peculiar Ap and Bp helium-deficient stars and some types of objects with helium atmospheres.     

On convection in stellar atmospheres far from local thermodynamic equilibrium

Non-thermal effects generated by sub-photospheric convection are considered. It is shown that convective cells are destroyed by shocks generated when convective velocities reach the speed of sound. Terminologically this process is given the name of sonic-boom-interrupted convection. An estimate is made on the dependence of convective velocities on stellar parameters. It is suggested that the process being investigated could explain why some stars do not belong to any branch of the theoretical Hertzsprung-Russell diagram.     

Convective energy transport in stellar atmospheres

We discuss a theoretical method of computing the temperature structure of hot and cool streams in convective stellar atmospheres. The method is based on the model that the streams are due to organized cells whose diameters are greater than the thickness of the photosphere. The excess thermal energy of matter rising from the deeper layers, where the entropy is higher than in the photosphere, is converted to radiation in a steady front. This model, applied to the solar case, exhibits a peak-to-peak contrast of 30–40% between granules and lanes. This contrast agrees with the Stratoscope data reduced by Namba and Diemel (1969). As a necessary part of the theory, we obtain an expression for the perturbation in radiative heat exchange which may be used in a medium with a strongly preferred direction such as a stellar atmosphere.Supported in part by the National Science Foundation [GP-15911 (formerly GP-9433), GP-9114] and the Office of Naval Research [Nonr-220(47)].     

Convective energy transport in stellar atmospheres

The motion of convective cells in an environment which changes rapidly with depth is examined. In such an environment a cell may move through regions with different levels of ionization and with associated differences in heat capacity. The energy equation is cast in a manner which is independent of the history of these cells. The convective flux at a given level of the atmosphere is written as an average over an ensemble of cells originating at a range of other levels. A procedure for correcting the temperature gradient for these non-local effects is described and results for a model solar atmosphere are given. The principal results are: (1) The rms velocity varies smoothly and is non-zero well into the photosphere (e.g.,v _rsm=1.4 km/sec at =0.2); (2) Convective overshoot reduces the radiative flux to 60% and 90% of the total at =2.5 and 0.2 respectively; and (3) The interior adiabat of the convective envelope is less sensitive to the assumed value of the average cell size than in the usual treatment of convection.Supported in part by the National Science Foundation [GP-9433, GP-9114], the Office of Naval Research [Nonr-220(47)], and Air Force Grant AG-AFOSR-171-67.     

On nonstationary radiative transfer in a spectral line in stellar atmospheres

We consider nonstationary radiative transfer in a line in stellar atmospheres simulated as a stationary semi-infinite plane-parallel medium. We assume complete frequency redistribution in the elementary act of scattering. We assume that the time a photon spends in the medium is determined only by the mean time spent in the absorbed state. We obtain an explicit expression for the resolvent of the nonstationary integral equation of transfer, which is a bilinear expansion with respect to the eigenfunctions found in [12] for the corresponding stationary transfer equation.Translated fromAstrofizika, Vol. 37, No. 3, 1994.I am grateful to the American Astronomical Society for financial support of this work.     

The Rosseland mean opacity of stellar atmospheres

Rosseland mean opacities $\text{a}\text{?}{}_{\mathrm{R}}\text{(T,}\text{lgP}{}_{\mathrm{e}}\text{)}$ [see Table 2] per unit hydrogen particle are calculated in this paper for the atmosphere of the solar type [see Table 1].The sources of the continuous opacities under consideration in this paper are as follows: (1) H^?, HI, H^?₂, H⁺₂ He^?, HeI, HeII, CI, CII, CIII, NI, NII, NIII, OI, OII, NaI, MgI, MgII, AlI, AlII, SiI, SiII, CII, KI, CaII in the form of absorption. (2) HI, HeI, CI, NI, OI, H₂ in the form of Rayleigh scattering. (3) Free electrons in the form of Thomson scattering.     

Turbulence influenced line formation in stellar atmospheres

The influence of stochastic velocity fields with finite correlation lengths on the formation of spectral lines is taken into account without restrictions to specific velocity models. To construct a perturbation theory treating the influence of stochastic motion on the radiative transfer we start with the stochastic transfer equation for plane-parallel atmospheres and expand it to an infinite hierarchical system. An appropriate cut-off of the infinite system admits to achieve exactly the micro- and macroturbulent limit at every level of approach. The formalism is derived for n-point correlations of the absorption coefficient and specialised for 2-point correlations.     

Magnetodynamic phenomena in the solar and stellar outer atmospheres

Magnetic effects causing anomalous heating and drastic flarings in the atmospheres of various types of stars are discussed. The best studied examples of these magnetic effects with spatially resolved observations are those in the case of the Sun, but no simple application of the solar knowledge to the stellar cases is allowed, since there are generally very large differences in the physical conditions between the Sun and other types of stars. We examine possible effects of the magnetic field in the respective situations of several types of stars which show X-ray and radio emissions indicating the presence of such activities, and it is concluded that the magnetic field may be playing important roles in producing anomalous heating and drastic flarings also in those stars having very different physical conditions, in ways seemingly very different from, but intrinsically closely related to, those in the case of the Sun.Invited review paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

A new model for the structure of the DACs regions in the Oe and Be stellar atmospheres

As it is already known, the spectra of many Oe and Be stars present Discrete Absorption Components (DACs) which, because of their profiles' width as well as the values of the expansion / contraction velocities, they create a complicated profile of the main spectral lines. This fact is interpreted by the existence of two or more independent layers of matter, in the region where the main spectral lines are formed. Such a structure is responsible for the formation of a series of satellite components (DACs) for each main spectral line. In this paper we present a first approximation to a mathematical model reproducing the complex profile of the spectral lines of Oe and Be stars that present DACs. This model presupposes that the regions, where these spectral lines are formed, are not continuous but consist of a number of independent absorbing density layers of matter, followed by an emission region and an external general absorption region. When we fit the spectral lines that present DACs, with this model, we can calculate the values of the apparent rotation and expansion / contraction velocities of the regions where the DACs are formed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Pinchrosphere — The coolest layer in stellar atmospheres

An attempt is made to demonstrate the possibility of the existence of one more layer—pinchrosphere—in the structure of atmospheres of late-type stars—later than G5. Pinchrosphere is the coolest layer with very low electron temperature, 5500K, it is located on the photosphere and near the inner boundary of the chromosphere. Practically all elements in pinchrosphere, particularly hydrogen and magnesium, are in neutral state. The main physical parameters of the pinchrosphere are derived.     

On the influence of density and temperature fluctuations on the formation of spectral lines in stellar atmospheres

A method taking into account the influence of temperature and density flucuations generated by the velocity field in stellar atmospheres on the formation of spectral lines is presented. The influenced line profile is derived by exchanging the values in a static atmosphere by a mean value and a fluctuating one. The correlations are calculated with the help of the well-know hydrodynamic eqs. It results, that in normal stellar atmospheres the visual lines are only very weakly influenced by such fluctuations due to the small values of the gradients of the pressure and density and of the velocity dispersion.     

On the use of collocation methods for the construction of stellar models

Collocation with piecewise continuous polynomials is studied for use in the numerical modelling of stellar evolution. Accuracy and convergence of the method are demonstrated for a 5M star with a convective core. Collocation should be further studied since it is likely to lead to significant gains in computational efficiency for the construction of stellar models.