In section 1 practical details concerning the equivalence of observational and theoretical descriptions of stellar spectra are reviewed, particularly the difficulty of identifying the observed reference level (continuum) with the theoretical continuum in the case when many lines are present. In this connection thought must be given to how integrals over frequency should be normalised and evaluated because the effective continuous absorption coefficient does not remain constant over the range from 0 to ∞. The choice of spectroscopic details by which to determine Teff, log g and abundances requires careful consideration.

In section 2 the factors by which an extended atmosphere are recognized are summarized and the question is posed do all stars have extended atmospheres. Another question requiring an answer is whether the concepts microturbulence and macroturbulence are physically real concepts or whether they are merely fitting parameters to make a simple LTE theory account for the observed spectra of supergiants in which rather wide lines occur and many multiplets show rather steep gradients. In section 3 the types of line sensitive to non-LTE conditions are described. These are resonance lines, lines arising from metastable levels, subordinate lines for which the upper level is sufficiently separated from the continuum and other levels that this upper level is chiefly populated by radiative processes from the ground or other low lying levels and lines which go into emission in low density atmospheres as a result of optical-pumping (fluorescent) processes. Such lines should not be used for abundance determinations by means of LTE theory though this is frequently done.

Theoretical considerations are discussed in Section 4 where first the problem of the two-level atom is sketched and then the problem is generalised to a many-level atom. The parameter λ which gives the probability that a photon is lost from the line by de-excitation processes other than spontaneous emission is defined and it is pointed out that non-LTE physics has the effect of adding a scattering term to the expression for the source function. One example is given of the effect of changing the line source function from the Planck function to a form suitable for isotropic coherent scattering. The line becomes deeper and wider for the same number of atoms. Interpretational problems in stellar spectra are discussed in section 5. It is noted that many lines in main-sequence early type spectra show the effects of departures from LTE. These effects are shown to a conspicuous degree by the spectra of shell stars. The example of He I 5876 in 10 Lacertae, 09V, is discussed and the implication for interpreting the He I lines in all B type main-sequence stars are touched upon. Helium-weak and helium-strong spectra probably indicate variations in density of the outer U atmosphere rather than true abundance differences. The spectra of supergiants are also considered and it is pointed out that the Ia supergiants of type B may be hydrogen-poor.

Finally in section 6 the problem of choosing simplified physical representations of line forming when non-LTE physics must be used is discussed. Some relevant points concerning the observed spectral lines used for spectral classification are illustrated by means of partial energy-level diagrams.

The necessity of carefully defining the phenomenological basis for classification of atmospheres as being “extended” is emphasized, and four alternative bases for such classification are suggested (1) the necessity to include curvature terms; (2) the presence of an ejected shell surrounding a central star; (3) an observational discrepancy between predicted and observed density gradient; (4) an anomaly between predicted and observed phenomena in stars with “dynamic” atmospheres such as cepheids. A number of physical problems connected with the presence of an extended stellar atmosphere are then categorized according to these alternative bases.

Exploratory calculations on nongray, hydrostatic-equilibrium model envelopes for central stars of planetary nebulae of high temperature and possibly near the instability limit are reported. It is conjectured that these may be related to Wolf-Rayet type nuclei; it appears possible to obtain an OV absorption, and OVI emission, spectrum even in an LTE calculation.

Evaluating transition probabilities of N IV 2p3d 3 P ° to 2s4s 3S and 2p3p 3P and an emission feature at λ7410 it is shown that a disputed emission at λ5810 in WN stars may not be attributed to N IV.

Profiles and total intensities are computed for solar 01 resonance lines at λ1302 and λ1305 using a model atmosphere program that includes non-LTE effects in both hydrogen and oxygen and that includes microturbulence both as a line broadening mechanism and as a contribution to the gas pressure. Good agreement is obtained between computed and observed intensities. The computed profiles appear to have too much 'self-reversal.

Theoretical methods applicable to the study of line formation in steady-state extended atmospheres are reviewed. The formal solution of the transfer equation is considered, as well as numerical and analytical methods of determining the source function. Topics discussed include: the local frequency transformation, geometrical effects, and the case of large velocity gradients. A new plane-parallel approximation for spherically symmetric moving atmospheres is given that takes account of transverse velocity gradients.

I have not prepared any formal communication. Nevertheless I would like to mention the types of calculation that are now in progress in Paris.

I am handling transfer problems in moving atmospheres by using Monte Carlo techniques. A twolevel atom and an isothermal atmosphere are always assumed. Two types“of geometry are considered: a spherical atmosphere with a constant velocity of expansion, or a flat disk with constant velocities of expansion and rotation. Non-coherent scattering (either entirely incoherent or partially coherent) is assumed with respect to the “local frequency“ (as seen by the absorbing atoms).

Concerning the “creation” of photons, two problems have been handled: the photons are created via absorption of a continuous spectrum produced by an underlying photosphere (the Schuster problem) or they are created within the envelope via electronic collision or recombination from ionized states.

The most typical results concern the Schuster problem.

We discuss an integral equation method that permits the calculation of the line source functions and of the emergent profiles in finite and semiinfinite atmospheres with macroscopic motion normal to the surface. Solutions are presented for a semiinfinite atmosphere with a temperature rise in the outward direction and with a flow that decays with increasing depth. The computed profiles have the form of P Cygni lines.

The radiative transfer equation is written in microscopic form, and from some simplifications on the ratio of occupation numbers for upper and lower level, a laser action is suggested.

The flux divergence technique of Athay and Skumanich (1967) is generalized for application to media whose properties vary in more than one spatial dimension. In this method, the flux divergence is viewed as an integro-differential functional of the source function. The source function is then expanded in terms of basis functions along characteristic paths, and, with the help of various interpolations, the flux divergence is converted to an approximate linear algebraic operator on a discrete spatial grid. A large but finite set of linear, inhomogeneous, simultaneous algebraic equations with known matrix coefficients is thus generated and is solved by direct matrix inversion for the source function at each point of the spatial grid.

Some aspects of the accuracy, stability, and computational convenience of the technique are discussed. Sample solutions for depth dependent, axially symmetric variations of temperature are shown.

A progress report on theoretical work on the formation of a continuum in low-density stellar envelopes. Preliminary results are given on a comparison between the recombination case and the case for a semi-empirical approach including the effect of collisions from the ground state.

Accurate evaluation of a line source function, S, requires that the frequency bandwidth be sufficiently large to include properly transfer effects in the line wings. The bandwidth required to achieve a given level of accuracy in the evaluation of S can be specified, in units of the Doppler width, in terms of three parameters: the ratio of continuum to line opacity, ro, the probability for collisional deexcitation, ε, and the Voigt wing parameter . Bandwidths required to give S to an accuracy of 2 percent are given for values of ε and ro from 10-2 to 10-8 and for values of from 10-2 to 10-5.

Numerical methods are essential to the treatment of line formation in inhomogeneous non-LTE atmospheres. The new methods due to Hummer and Rybicki and to Feautrier now make it possible to make such calculations, although these are often quite timeconsuming.

We shall describe an alternative approach using discrete space techniques depending on concpets of invariance. The solution algorithm is closely related to the method of Hummer and Rybicki, whose equations are obtained as a limiting case. The stability and errors of our algorithm are susceptible to mathematical analysis, and make it possible to identify the critical parameters in the calculation with precision. The results for a two-level problem will be compared with those from an implementation of the Rybicki-Hummer equations and a comparison will be made of the performance of the two procedures in respect of speed of computation and storage requirements.

A discrete ordinate method is developed for solving the equation of coherent line formation, for arbitrary given variations with depth in an atmosphere of the temperature (or Planck function, assuming local thermodynamic equilibrium) and the line absorption and scattering coefficients. The direct solution thus obtained can then be used as the starting point of an iterative procedure. Results obtained for an exactly soluble case indicate the utility of the method.

Four problems in interpreting spectra to infer chromospheres-coronas are summarized. (1) The a priori difficulties in interpreting spectra lie in uncertainty on the range of possible models, coming from uncertainty as to which conservation equations may be applied, and from lack of an exhaustive list of spectral indicators that may be used for uniqueness tests. (2) As spectral indicators we consider: emission lines, self-reversed emission cores, the presence of He I lines in stars not of early type, coronal-type high ionization, excess continuum emission in the rocket UV and the far infrared. (3) To determine what we can infer from observations, we summarize information: inferred by comparison of models to data, on velocity fields, and on spectral variability which might suggest chromospheric activity. (4) We summarize the evidence for chromospheres in A stars, as being those where convection-induced acoustic heating is marginal.

Chromospheres-coronas satisfy the last two of the proposed classification schemes: inadequacy of the classical atmosphere (CA) model to represent observations and a priori rejection of the CA model So we survey the question of what is required for more knowledge from the standpoint of asking what conceptual modifications will increase knowledge and what new observations are required. We stress that continued progress requires a continual interchange of ideas between the solar situation and the range of stellar situations.

A summary of information on the extended atmosphere of the K component coming from three eclipsing binaries consisting of a K supergiant and a main sequence B star. Various anomalies exist: (1) Discrepancy between electron density and metallic density inferred from observations, noting that the electrons should come from the metals. This suggests a cloud structure in the atmosphere. (2) Anomalous excitation temperatures and populations of the second quantum level of hydrogen suggests a solar-chromosphere type behavior for these K atmospheres. (3) Significant changes in the profiles of the Ca+ lines from one eclipse to another. The necessity to distinguish between effects coming from radiation of the B star on the K atmosphere and chromosphericlike effects is emphasized.

Calculations on the expansion of novae shells are presented, from which the degree of ionization is obtained using a simplified form of a non-LTE ionization equation. From this, estimates of the time of vanishing of the Balmer absorption spectrum can be made.