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.     

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.     

Curvature effects in extended stellar atmospheres — Pure absorption

The effects of curvature in an atmosphere with pure absorption are investigated. Numerical solution of the transfer equation has been obtained in the framework of the Discrete Space Theory of Radiative Transfer. Two cases have been considered: (a) the atmosphere is irradiated at the bottom and there is no incident radiation at the top of the atmosphere; and (b) no radiation is incident on either side of the atmosphere. It is found that the thermal sources inside the atmosphere dominantly influence the emergent radiation and this is very much so, in the spherical case and for large optical thickness. The emergent luminosities increase with the geometrical thickness although the emergent specific intensities are reduced and the former seems to be because of the larger surface area and later seems to be because of the effects of curvature.     

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.     

Upper limits in the toroidal component of force-free magnetic fields in stellar atmospheres in the context of solar and stellar flares

Doing numerical calculations of axially symmetric force-free fields, Milsom and Wright (1976) have noticed that there seem to be no solutions if the toroidal component of the field exceeds a certain limit. In the present paper this problem is reexamined in the approximation of a plane stellar surface using a very simple analytic approximation. The results of Milsom and Wright (1976) are confirmed but, in contrast to their interpretation, it is shown that these limitations do not indicate the possibility of sudden changes of the topology of the magnetic field. This is because in a stellar atmosphere the toroidal component of the surface magnetic field is no independent quantity but is produced by shearing motions in the star which will prevent the toroidal magnetic field from exceeding its maximum value. To study the possibility of sudden changes in the magnetic field, which could cause stellar flares, the calculations are re-done prescribing the motion of the magnetic footpoints (shear in the stellar surface) instead of the toroidal component of the surface field. Using the same mathematical formalism it is found that no sudden changes can occur for configurations where all field lines connect to the stellar surface but that sudden changes may be possible for a more complicated field topology.     

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.     

Non-LTE effects for Na I lines in X-ray illuminated stellar atmospheres

The formation of Na I lines in X-ray illuminated atmospheres is investigated by abandoning the assumption of local thermodynamic equilibrium (LTE). Calculations are performed on the basis of a 21-level Na I model atom for the LTE model atmospheres of irradiated F-G stars obtained with allowance for a reflection effect in the first approximation. The state of extreme “overrecombination” is shown to exist for the populations of all Na I levels in the case of external illumination. Absorption features in the profiles of “cool” and “normal” Na I lines have been found to be enhanced compared to the LTE approximation. Effects of the angle of incidence and intensity of the external radiation on the formation of level populations and line profiles when abandoning LTE are analyzed. The existence of overrecombination for Na I is explained by the small X-ray heating function and the large optical cooling function. Na I level populations are shown to depend weakly on the presence of “overionization” for Na II in the atmospheres of irradiated stars.     

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.     

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.     

On the construction of model stellar atmospheres

The construction of model atmospheres by means of differential corrections is discussed. Either flux or flux gradients may be minimized, with arbitrary weighting with depth. For the simple atmospheres studied, no convergence problems were encountered even when very poor first approximations were used; and flux constancy in the radiative case was generally attained in three or four iterations.Quantities computed in one iteration may be re-used, not only in subsequent iterations within the model, but also in the construction of other models with differentT _eff org; and so the method is particularly suited for grid computations.     

Polarization of radiation from stellar atmospheres. The grey case

An accurate numerical method is presented for the solution of the transfer equations in a plane-parallel atmosphere in which scattering occurs according to Rayleigh's law. Some results are given for the polarization and limb darkening of both integrated and monochromatic radiation emerging from grey atmospheres with various ratios of scattering to absorption. The method is equally applicable to non-grey atmospheres.     

The optical continuum of solar and stellar flares

A further development of the Kostyuk-Pikelner's model is presented. The response of the chromosphere heated by non-thermal electrons of the power-law energy spectrum has been studied on the basis of the numerical solution of the one-dimensional time-dependent equations of gravitational gas dynamics. The ionization and energy loss for the emissions in the Lyman and Balmer lines have been determined separately for the optically thin and thick L-line layers. Due to the initial heating, a higher-pressure region is formed. From this region, disturbances propagate upwards (a shock wave with a velocity of more than 1000 km s^-1) and downwards. A temperature jump propagates downwards, and a shock is formed in front of the thermal wave. During a period of several seconds after the beginning of this process, the temperature jump intensifies the downward shock wave and the large radiative loss gives rise to the high density jump ( ₂/ ₁ 100). The numerical solution has been analyzed in detail for the case heating of the ionized and neutral plasma, and a value of this heating is close to the upper limit of the admissible values. In this case, the condensation located between the temperature jump and the shock wave front, may emit in the observed optical continuum.In their essential features, the gas dynamic processes during the flares in red dwarf atmospheres are the same as those in the solar atmosphere. However, the high atmospheric densities, smaller height scale in red dwarf atmospheres, and greater energy of this processes in stellar flares, give rise, in practice, to the regular generation of optical continuum. The photometric parameters of a source with n 0¹⁵ cm^-3, T 9000 K, and _z 10 km are in a good agreement with observations.     

The transfer of polarized radiation in spectral lines: Solar-type stellar atmospheres

The polarization structure in several spectral lines in solar type stars is computed using the method described by McKenna (1981, 1984a). The frequency redistribution function used for these calculations is a linear combination ofR _II andR _III. The line profiles and polarization structures have been computed for several weak solar resonance lines includingKi 7664 Å, Sri 4607 Å, Baii 4554 Å, for various polar angles along the stellar disk. Both the line profiles and polarization structures as well as the center to limb behavior of the line center polarization agree well with observations.The somewhat stronger resonance line Cai 4227 Å shows a different polarization structure when compared to the weaker solar resonance lines. It is found that for strong resonance lines the proper redistribution function to be used is a linear combination ofR _III andR _v (see McKenna, 1981, 1984b; Heinzel, 1981). The major reason for this is that for strong resonance lines both the upper and lower levels are broadened by collisions. This violates the assumptions upon which the redistribution functionsR _II andR _III are based.     

Long-duration solar and stellar flares

According to one of the most popular classifications, solar flares may be assigned either to the category of small short-lived events, or to the category of large, long-duration two-ribbon (2-R) flares. Even if such abroad division oversimplifies the flare phenomenon, our knowledge of the characteristics of stellar flares is so poor, that it is worthwhile to investigate the possibility of adopting this classification scheme for stellar flares as well. In particular we will analyze Einstein observations of a long duration flare on EQ Peg to establish whether it might be considered as a stellar analogy of 2-R solar events. To this end we apply to EQ Peg data a reconnection model, developed originally for solar 2-R flares, and conclude that stellar observations are consistent with model predictions, although additional information is required to identify uniquely the physical parameters of the flare region. Application of the model to integrated observations of a 2-R solar flare, for which high spatial resolution data are also available, shows, however, that future integrated observations may allow us to solve the ambiguities of the model and use it as a diagnostic tool for a better understanding of stellar flares.     

Asteroseismology of solar and stellar models

I discuss several asteroseismology diagnostic techniques that can be applied to the high quality data on stellar oscillations obtained, and to be obtained in the future, from ground based and space based experiments. In particular I discuss techniques using the representation of oscillation frequencies in terms of inner and outer phase shifts which can be used both for model fitting and inversion procedures to probe the inner structure of stars, and hence to test and improve our modelling.