The allegory alluded to in the subtitle of my review came to mind in the early morning hours when I was battling insomnia after a successful observing run at our McDonald Observatory. Similar bouts with insomnia are more widely classified as “jetlag,” a condition probably too familiar to many of the readers!

Imagine two villages connected by a bridge spanning a deep, fast-flowing river. In my village on the south bank live the astronomers. Across the bridge live the chemical physicists and the physical chemists who are engaged in determining by all possible theoretical and experimental means the structure and spectra of molecules (and atoms). The astronomical community can be sorted into various clans of whom I consider here only the stellar spectroscopists and, in particular, the small subclan fascinated by quantitative spectroscopy who to pursue their trade must establish and maintain excellent communications with the village on the other side of the bridge. The necessity for contacts between the two villages has grown with the development of the tools of the stellar spectroscopists’ trade: e.g., the advances of telescopes and spectrographs with respect to coverage of the electromagnetic spectrum and sensitivity, and the theoretical developments in the construction of model stellar atmospheres and the computation of synthetic stellar spectra. The recent decades of astronomical advances have been matched by exciting years in the village across the bridge: e.g., tunable lasers have spawned a renaissance in molecular (and atomic) spectroscopy, and theoretical work on molecular structure and spectra has advanced with the awesome growth of computers. Yet, a curious paradox may be sketched. These welcome and remarkable developments in the two villages have made it more difficult to maintain effective communications across the bridge. How can I possibly exploit fully the successes of MRD-CI calculations and appreciate their limitations? My counterparts across the bridge will echo my question: What experiments or quantum calculations might be usefully made in support of the astronomers’ programs ATLAS, MARCS, SOSMARCS, and their relatives?

Molecular data bases (including very different numbers of molecular lines, and based on computations spanning a wide range in quality) have been used in the construction of models of the stellar atmospheric structure, and effects of various molecules on the stellar structure and evolution have been described in the literature. A systematic study showing which molecules are of importance in which types of stars is, nevertheless, still lacking, and the line lists used in various model computations necessarily reflect what was at hand at the time of computation rather than a systematic effort to solve the molecular opacity problem. A pioneering investigation was presented in two extensive papers by Tsuji (1964, 1973) where the foundation of the reaction scheme used in most models today was laid down. Later Tsuji (1986) has given a review of the existing work on molecules known in stars, and Johnson (1986) and Gustafsson (1989) have touched upon the same subject in reviews covering a broader range of stellar aspects. Jørgensen (1992) has recently summarized the existing molecular data (and discussed the methods used) available for model atmosphere construction.

In this contribution we want to discuss M star atmospheres and their dependence on molecular opacities. A star belongs to the spectral class M if its optical and infrared spectrum shows strong bands of TiO and numerous strong metal lines so that for wavelengths < 4000 Å there is “hardly any flux left” (Jaschek & Jaschek 1987). M stars cover a very large range in luminosity: M dwarfs are the intrinsically faintest stars, whereas M giants and supergiants reach luminosities that are among the highest known. General properties of these objects are given in Table 1 (after Schmidt-Kaler 1982).

The term dwarf stars identifies objects of small radius in the Hertzsprung-Russell (H-R) Diagram, but encompasses more than one phase of stellar evolution. The M dwarfs (type dM) populate the main sequence at the low mass end; these are the coolest core hydrogen-burning stars. They belong generally to the Galactic disk, or Population I, have relatively small space motions with respect to the Sun, and have similar metallicities to the Sun (although perhaps only within a factor of several). In particular, this means that the abundance of oxygen is always greater than that of carbon. The M subdwarfs (sdM) are the Population II counterparts, showing low metallicities and high space motions. Because they have smaller radii, they define a main sequence at lower luminosity than the M dwarfs for a given temperature. Hence the term subdwarf.

It is the intention of this review to explain what white dwarfs are and why it is interesting to study them, and why the H+2 molecule is of special interest.

The evolution, from start to finish, of a star of mass less than about 2 solar masses (M⊙), can roughly be summarized as follows:

1. – A cloud of gas contracts from the interstellar medium until hydrogen ignites at the center and a main sequence (MS) star forms. H is transformed to He and the MS phase continues until H is exhausted in the stellar core.

2. – H continues burning in a shell outside the He core while the core contracts. He “ashes” are added to the core, and a red giant star is formed as the envelope expands. The star evolves up the Red Giant Branch (RGB) (i.e. it becomes more and more luminous and the surface cools).

3. – Towards the end of the RGB phase, mass-loss from the upper layers increases until helium to carbon burning in the core ignites suddenly under degenerate conditions – this is called the Helium Flash (HF). The HF terminates the RGB evolution, and therefore also the mass-loss and the growth of the stellar core.

4. – The star readjusts its structure and the He-core burns steadily on the horizontal branch (HB) (a phase of nearly-constant luminosity) until fuel is exhausted in the He-core.

5. – Then the C/O core contracts anew and the expansion of the envelope, and the growth of the core, during He-shell burning, mimics RGB evolution but relatively little mass is added to the core this time.

6. – The second ascent of the giant branch (the so-called Asymptotic Giant Branch, or AGB) continues with increased mass loss towards the end

7. – Rapid detachment of a considerable fraction of the remaining envelope and the hot core takes place, sometimes observable as the Planetary Nebulae (PN) phase.

8. – The PN is dispersed as the core contracts to a white dwarf (WD).

9. – The WD cools for a long time, as internal kinetic energy and latent heat is released.

For studies of radiative processes in stellar environment, knowledges on opacities are essential, and molecular line opacities play a dominant role in many cases where temperatures are roughly below 4,000K. Accurate treatments of molecular line opacities require high precision line data for millions (and up to billions?) of lines. Recent progress in theoretical as well as in experimantal molecular physics made it possible to realize such an approach, and dedicated efforts are being done to developing extensive databases for polyatomic (Jørgensen in this volume) as well as for diatomic (Kurucz in this volume) molecules. These accurate databases should be of fundamental importance in our understanding of astronomical observations that are progressing rapidly both in scope and in accuracy.

During the last two decades there has been a tremendous renewal of interest in the circumstellar environment of evolved stars. This renewal has been mainly driven by sensitive microwave observing techniques. Microwave spectroscopy has resulted in a number of fundamental discoveries in circumstellar shells, including the discovery of maser lines and complex circumstellar chemistry. Historically, interest in circumstellar shells originates from a desire to understand the mass-loss process. It has been known for at least 50 years that circumstellar gas is the origin of interstellar gas and dust. As such the circumstellar shell becomes the pathway through which elements created in the interior of the central star enrich galactic abundances. High resolution spatial and spectral techniques and an ever improving knowledge of stellar evolution has resulted in an increased but still incomplete understanding of the mass-loss process.

Red giant stars on the asymptotic giant branch (AGB), AGB-stars, lose copious amounts of matter in a slow stellar wind (Olofsson 1993). Mass loss rates in excess of 10-4 M⊙ yr-1 have been measured. The primary observational consequence of this mass loss is the formation of an expanding envelope of gas and dust, a circumstellar envelope (CSE), that surrounds the star. This is a truly extended atmosphere that continues thousands of stellar radii away from the star. At the highest mass loss rates (which probably occur at the end of the AGB evolution) the CSE becomes so opaque that the photosphere is hidden and essentially all information about the object stems from the circumstellar emission. At some point on the AGB a star may change from being O-rich (i.e., the abundance of O is higher than that of C) to becoming C-rich (i.e., a carbon star where the abundance of C is higher than that of O) as a result of nuclear-processed material being dredged up to the surface. The chemical composition of the CSE will follow that of the central star, although with some time delay so that there may be some rare cases of O-rich CSEs around carbon stars. The mass loss decreases and changes its nature as the star leaves the AGB and starts its post-AGB evolution. Eventually the star becomes hot enough to ionize the inner part of the AGB-CSE and a planetary nebula (PN) is formed. The ultimate fate of the star is a long life as a slowly cooling white dwarf. The CSE will gradually disperse and its metal-enriched matter will mix with the interstellar medium, and thereby it contributes to the chemical evolution of a galaxy. The intense mass loss makes it possible for stars as massive as 8 M⊙, i.e., the bulk of all stars in a galaxy, to follow this evolutionary sequence. Similar CSEs are also found around supergiants.

The aim of this review is to discuss our knowledge on molecules in the circumstellar environment of evolved stars. In particular the presence and the behaviour of various kinds of molecules with several or many carbon atoms, in relation to C-rich dust, is considered.

Such objects include mainly: (i) circumstellar shells of AGB carbon stars, either visible (such as Y CVn) or infrared (such as IRC+10216 (CW Leo)); (ii) planetary nebulae (PNe, e.g. NGC 7027); (iii) pre-planetary nebulae (PPNe, also called post-AGB stars, such as CRL 2688 or the Red Rectangle), probably in an intermediate evolution stage between the two former classes. I will not discuss more peculiar classes, such as R CrB stars and novae, for which very little is known about the presence of such molecular species.

Atoms and ions dominate the opacity of most astrophysical plasmas at temperatures above about 5000 K. In the range between 5000 K and about 1500 K, molecular processes are important contributors to the opacity. Depending upon the composition and pressure, grains may begin to condense at temperatures below about 1500 K. For the conditions of interest here, the grains which form are generally small (radius < 0.25 µm) compared to the wavelength of light near the peak of the Planck curve. Because their absorption and scattering cross section is so large compared to atoms or molecules, grains dominate the mean opacity whenever they are present and must, therefore, be taken into account whenever such temperatures are encountered. Our calculations indicate that failure to do so can lead to errors as large as five orders of magnitude in the mean opacity.

Cosmic dust is an ubiquiteous component of the interstellar medium, the presence of which has severe bearings both upon the observations and upon the physical description and realistic modelling of astronomical objects. In most dusty objects, the grain component is intimately interwoven with the gas component and the radiation field, and, hence strongly affects the thermodynamical, the hydrodynamical and the chemical structure of the object. Therefore any consistent description of the astrophysical dust complex has to rely upon a treatment where these aspects are properly taken into account. In general this complex comprises the following problems:

1. – Formation of small stable molecular clusters out of the gaseous phase

2. – Growth of these clusters to macroscopic specimens (primary condensates: grains, plates, etc.)

3. – Destruction of grains (e.g. thermal evaporation, sputtering, shattering), and

4. – Physical and chemical processing of already existing grains (e.g. coagulation, chemical and thermal transformation, etc....).

Opacity influences the transfer of radiation and is thus of decisive importance for (a) the interpretation of astronomical observations, (b) determining the thermal structure, (c) critically influencing molecular, atomic and thermonuclear processes and (d) affecting the overall dynamic evolution during the star formation process. Questions pertaining to the onset of instability of gas clouds, their subsequent fragmentation into smaller clumps, the formation of multiple systems, the initial mass function (IMF), the upper and lower mass limits, star formation efficiency and the fate of material not collected into stars cannot be considered without intimate knowledge of the opacity in this environment.

Molecules play a unique role in solar spectroscopy in allowing to derive, with high accuracy, the temperature structure of the photospheric layers from where the solar spectrum in the near ultraviolet, visible and infrared emerges. They also allow to observe the heterogeneous structure of the outer layers as well as the subtle convective motions in the layers just above the solar convection zone. Molecules play also a unique role in defining the solar chemical composition, at least as far as the very important elements like carbon, nitrogen and oxygen are concerned. They also offer the unique opportunity to derive meaningful isotopic ratios for C and O. Although we shall not deal with sunspots in the present review, it has to be recalled that molecules are the only tracers to derive the solar abundances of CI and F from the rotation-vibration lines of HC1 and HF present in the infrared sunspot spectra (Hall & Noyes 1972; Hall & Noyes 1969).

On the other hand, the Sun itself offers a unique opportunity to produce molecular transitions, in local thermodynamic equilibrium (LTE), at rather high temperatures (T ∼ 5000 K), higher in any case than in the laboratory, often in non LTE (see review by Johnson in this volume). Therefore, new lines and new transitions of higher excitation appear in the solar spectrum allowing to use the Sun as a “permanent laboratory source” in order to refine the molecular constants. Furthermore, the solar photosphere, where we believe the physical conditions and physical processes are better known than in any other stars, offers a unique possiblity to test basic molecular data like dissociation energies and transition probabilities.

Pressure-induced absorption arises in complexes of two or more inert atoms or molecules, due to dipole moments induced during the collisional interaction. The term “pressure-induced” still prevails in the astrophysical literature, yet “collision-induced” absorption (CIA), or “interaction-induced” absorption seems more appropriate and is commonly used elsewhere. Ordinary absorption processes in the infrared arise from individual, polar molecules interacting with electromagnetic radiation. As a consequence, the intensity of the allowed lines increases linearly with density. CIA, on the other hand, is most striking in gases composed of nonpolar, infrared-inactive molecules. Induced spectral lines are observed at rovibrational frequencies which are dipole-forbidden in single (i.e. non-interacting) molecules. Dipole transitions may, however, be induced in the interacting pair. The new symmetry of the electronic cloud of a collisional complex may be very different from those of the isolated molecules and thus commonly allows for a transient dipole, which then interacts with radiation. Collision-induced absorption increases quadratically in the low density limit, thus reflecting the two-body origin of the basic absorption process. At higher gas densities, ternary interactions become significant and cubic and higher-order contributions to the observable absorption are then commonly seen.

It is well known that molecules have much more complex electronic spectra than atoms due to their rotational and vibrational motions. Most molecular spectra observed in the laboratory and included in model atmospheres involve transitions between two bound electronic states. However, in contrast to atoms, molecules can also have bound-free transitions into states that are repulsive in at least one nuclear coordinate, even below the first ionization potential. These transitions not only lead to dissociation of the molecule, but also provide a source of continuous opacity which is usually not taken into account in model atmospheres. Moreover, photodissociation plays an important role in the non-LTE chemistry of stellar atmospheres and circumstellar envelopes (see Olofsson this volume). In this chapter, a brief overview of our current knowledge of cross sections for continuous absorption and photodissociation is given.

Molecules increase in importance in stellar atmospheres as the temperature falls along the spectral sequence for all luminosity classes. Among their many roles molecular features provide the basis for spectral classification (temperature and chemical composition) in M, S, and C stars; they constitute important opacity sources across the spectrum from the ultraviolet to the infrared; they influence the energy budget and hence the kinetic temperature in the outer photospheric layers; they may contribute significantly to the radiative levitation of the atmosphere; they form masers; they may cause or facilitate mass loss; and they are indicative of physical conditions and processes from the photosphere to the outer circumstellar envelope.

For a simple dissociation equilibrium

the equilibrium constant Kp at temperature T can be written in terms of partial pressures p or densities n in the form given by Equation 6 of Tatum (1966)

where m is the reduced mass of AB, k the Boltzmann constant, h the Planck constant, QA, QB, QAB the internal partition functions of the species, and D0 the dissociation energy of AB. This equation derives from a more general expression of Kp (T) for a chemical reaction that is demonstrated in all physicalchemistry textbooks treating statistical thermodynamics (see for example Atkins 1990). Partition functions are weighted Boltzmann factors

with ϵn corresponding to the energy of the eigenstates of degeneracy gn. Provided all the eigenvalues are known, Q values can be calculated exactly. Derivations and calculations of the partition functions can be found in textbooks or in reviews relating to astrophysics.

Let Iv(r, θ) be the intensity of radiation of frequency v, at a distance r from the centre of a star and in a direction making an angle θ to the outward normal. In a plane-parallel approximation the equation of radiative transfer is

where 𝛋v is the opacity and jv the emissivity. The net outward flux of radiant energy is

and the flux integrated over all frequencies is

Molecules in stellar atmospheres play key roles, not only as promoters of our understanding of stars, but also as actors affecting the structures of the atmospheres. In particular cool star atmospheres are affected by molecular opacities, and during recent years it has become clear that also weak molecular lines are of crucial structural importance. Extensive molecular data are thus needed in order to correctly model the structure of a stellar atmosphere and the transport of radiation through it. The basis for how such molecular data are acquired constitutes the theme of the present article. As will follow below, results from different subfields of molecular physics are needed in order to obtain a complete picture of the absorption of radiation by molecules. This article will only consider allowed molecular electronic transitions, i.e. dipole transitions between different electronic states; however, the presentation and the formulae may easily be modified to be valid for transitions between levels within a single electronic state.

In this section I briefly describe my efforts to improve the atomic and molecular line data. This work is described in more detail in Kurucz (1992a). In subsequent sections I briefly describe three methods for computing opacity and the models and spectra that result from using them.

My model calculations in the 1970s used the distribution-function line opacity computed by Kurucz (1979a,b) from the line data of Kurucz & Peytremann (1975). We had computed gf values for 1.7 million atomic lines for sequences up through nickel using scaled-Thomas-Fermi-Dirac wavefunctions and eigenvectors determined from least squares Slater parameter fits to the observed energy levels. We also collected all published data on g f values and included them in the line list whenever they appeared to be more reliable than the computed data (that work is ongoing, but I am running behind).