It is intimidating to attempt a review of the subject of late-type stars macroturbulence which follows so closely on the heels of David Gray’s (1978) fine review in Solar Physics. Therefore this paper will avoid many emphases of his review while filling in some areas where some progress has emerged in the last 1-1/2 years. My slant will come mainly from the standpoint of line broadening analysis.

I am very pleased to have this opportunity to present some recent observational work bearing on the depth dependence of motions in stellar atmospheres. I thank Dr. Gray for this invitation and also wish to acknowledge the patronage of the NAS-NRC.

A review of the orbits and dimensions of the ζ Aurigae systems is given, based on photometric and spectrographic observations. The Ca II K-line has been studied intensively to determine the extent and uneven structure of the chromospheres of these stars; the multiple structure of this line observed at several eclipses confirms the presence of large-scale clouds in the atmospheres. Measurements of line profiles and equivalent widths show that macroturbulent velocities up to 10 km/sec in the upper chromosphere, and up to 20 km/sec. in the lower chromosphere are present. Microturbulent velocities in the lower chromosphere are about 10 km/sec. Recent ultraviolet observations indicate that the B star in the 32 Cygni system may be within the outer chromosphere of the giant component and its radiation may affect the chromospheric structure more than had previously been suggested.

In the beginning of this review, I paraphrase three statements from Paul W. Merrill (1960). (1) In the spectra of long-period variables, absorption lines of neutral metals show a shortward displacement increasing algebraically with excitation potential, probably due to atoms moving outward in the star’s upper atmosphere with an expansion velocity of the order of 20 km s-1. (2) About 6 weeks after maximum light emission components appear within the broad absorption at H and K of Ca II, but displaced about -100 km s-1. A similar, but less extreme, behaviour is known for classical cepheids. (3) In quasi-constant red giants, the resonance lines of Ca II, Ca I, and SR II show circumstellar components displaced shortward relative to the normal stellar photospheric lines by a velocity which is correlated with the spectral type, typically -8 km s-1 for M6 II to -25 km s-1 for class M0 III.

The radial velocities measured in the spectrum of HD 92207 (AO Ia+) show a Balmer progression, which varies considerably within one week and reverses within one month (or less). These observations give strong evidence, that at least in some parts of the atmosphere the velocity field reverses with time. (To be published in Astronomy and Astrophysics).

The study of microturbulence in stars for itself, and not as a byproduct of abundance determinations, is relatively recent. The first comprehensive study on this topic was carried out in 1966, by Bonsak and Culver. They found general trends of the behaviour of microturbulence in the HR diagram. A decisive advance occured when ttarz and Kock (1969) revised the scale of oscillator strengths of iron and, as a consequence, the value of the microturbulent velocity in the solar photosphere. The use of microturbulent velocities determined before 1969 should be avoided.

Before describing what we know about the behaviour of microturbulence with stellar age, I shall make some statements, and describe how the microturbulent velocity is found, from observations, to depend on the atmospheric parameters.

Changes and differences in radial velocities between neutral and ionized metals have been found for three F5-type supergiants: HD 231195, HD 10494, and HD 17971. Fifteen high dispersion coudé spectrograms (6 Å/mm) were used and 33 to 165 lines were measured on each. Semi-regular time variations up to about 8 km s-1 in radial velocity have been found. In addition, Hα line profiles for 8 high luminosity F-K stars have been analyzed. All of the stars show Ha emissions, variable in time, which is probably a common phenomenon in very luminous stars. Metallic emission lines with low excitation potentials, in particular the Ca I 6572.8 and the Fe I 6574.2 lines, are present in 5 of these stars.

The stationary turbulent surface layer, whose depth is of the order of the pressure scale height in the subphotospheric layer, was investigated for B-type stars, using the momentum and the continuity equations with the inertia term neglected but the turbulence-viscosity term included. The mean velocity field is dominated by the horizontal component of the meridional circulation, driven by the pressure-density unbalance in the radiative envelope of the rotating star, and the differential rotation induced by the Coriolis force.

The model calculation for a B3IV-V star with the equatorial rotational velocity of 200 km/s led to the conclusions that the velocity field due to the differential rotation is of the order of 0.1-1 km/s, the velocity field of the meridional circulation itself is negligible, the velocity field of the three-dimensional shear turbulence is of the order of 0.1 km/s, and i t s scale is comparable to or less than the pressure scale height, the velocity field of the horizontal two-dimensional turbulence is of the order of 1-10 km/s, and i t s maximum scale ranges from a few times the pressure scale height to one-fiftieth of the stellar radius. If the index of the energy density law is close to 3.5, the turbulent surface layer may be dominated by the large scale (two-dimensional) barotropic eddies whose energy is fed by the small scale (three-dimensional) baroclinic turbulence in a way similar to the planetary atmospheres. In this case we may expect the tangential macroturbulence of the order of 1-10 km/s, though the interaction between this and the small-scale three-dimensional turbulence still remains to be investigated.

The influence of a stochastic velocity field with a finite scale length 1 on the transfer of line radiation is described by means of a generalization of the transfer equation. Micro- and macroturbulence are contained in this mesoturbulence approach as limiting cases 1 → O and 1 → ∞ respectively.

A general formalism for describing the radiation transfer in a medium with arbitrary velocity fields is presented. It is demonstrated that classical microturbulence and mesoturbulent models based on Markov processes can be considered as the two lowest order members within a hierarchy of model equations with an increasing degree of approximation to reality. Some preliminary results concerning the relevance of low order model equations are presented.

For realistic stellar atmospheres the equations describing mesoturbulent line formation are solved numerically. The general dependence of theoretical line profiles and equivalent widths on the correlation length 1 and the mean square turbulent velocity a is demonstrated. Also empirical relations between the basic parameters of the micro-macroturbulence description (vmic, vmac) and the fundamental mesoturbulence parameters (1,σ) are derived.

Almost all studies of spectral line formation in the presence of non-thermal velocity fields have been made assuming that the only effect of the velocity field is to produce a Doppler shift of the absorption and emission coefficients. However, a non-thermal velocity field will entail velocity-correlated fluctuations in temperature, pressure, level populations, and other parameters of the line formation problem. Using a time-dependent dynamical calculation describing the propagation of non-linear, radiatively-damped short period (P = 30s) acoustic waves in the solar photosphere, Cram, Keil and Ulmschneider (1980) have shown that velocity-correlated fluctuations in state variables (particularly the temperature) may lead to important effects in line broadening, line shifts and asymmetries, and in line-shift oscillations. Upwardly propagating waves generally produce significant redshifts in the cores of medium-strong Fe I lines, and the increased ratio of observed line shift to wave velocity amplitude would significantly modify the results of kinematic studies of high frequency line shifts such as those of Deubner (1976) and Keil (1980).

Cram (1980) has further explored dynamical effects in the formation of Fe I and Fe II lines by using the “microturbulence” limit, wherein an average is made over the phase of the wave before the transfer equation is solved. Except for weak, high EP Fe II lines, the predicted solar lines are redshifted and show a “red” asymmetry. For a model of Arcturus the lines are often shifted to the blue, but it does not appear that this model can account for the observed differences between solar and Arcturan line asymmetries (Gray 1980).

We have studied the formation of optically thick lines in time dependent, nonlinear hydrodynamic model of the solar chromosphere. Models of the 200 second, chromospheric oscillation indicate that the emission peaks of self-reversed profiles such as those of Mg II and Ca II are formed at very different depths depending on the phase of the oscillation, while the central absorption feature is emitted at a very nearly constant mass depth. The figure shows the Mg II k line emitted by the mean atmosphere, including “microturbulence” (triangles) and the mean profile (squares). In addition to the substantial intensity increase interior to the emission peaks, one should note that the peaks are broadened only towards line center; i.e. the intensity fluctuations are symmetric outside of the peaks and strengthen more than they weaken within the peaks. A more detailed version has been submitted to the Astrophysical Journal.

J.L. wishes to acknowledge support by NASA contracts NASA-3053 and 5-23758.

The results of numerical simulations of the solar granulation are used to investigate the effects on photospheric apectral lines of the correlated velocity and temperature fluctuations of the convective granular motions. It is verified that the granular velocity field is the main cause for the observed broadening and strengthening of photospheric spectral lines relative to values expected from pure thermal and pressure broadening. These effects are normally referred to as being due to “macro-turbulence” and “micro-turbulence”, respectively. It is also shown that the correlated temperature and velocity fluctuations produce a “convective blue shift” in agreement with the observed blue shift of photospheric spectral lines. Reasons are given for the characteristic shapes of spectral line bisectors, and the dependence of these shapes on line strength, excitation potential, and center to limb distance are discussed.

Ladies and Gentlemen, we now reveal to you the secrets of how to create chaos out of order. The existence of a chromosphere or corona requires the existence of motions. A chromosphere or corona requires some non-radiative heat input. There has to be some kind of motion, either oscillatory or quasi-static, to transport the energy up to the chromosphere or corona. This ordered motion may be observed as chaos: microturbulence, macroturbulence, line asymmetries or shifts. Of course, it is necessary to actually compute the effects of motions on line profiles in order to see what will really happen.

Important progress in our understanding of stellar chromospheres has occurred in the past few years as a result of new observations, developments in spectral line formation theory, and the application of that theory to the construction of detailed model chromospheres. Significant trends are beginning to emerge from such analyses, and we are on the threshold of a meaningful confrontation between purely theoretical models and the data. The range of stars thought to possess chromospheres may be widening, and we now have a better understanding of the enigmatic problem of why the Wilson-Bappu relation between Ca II emission core widths and stellar absolute visual magnitudes actually works.

We present three separate observational studies of mass flows above the photosphere of α Ori (M2 Ia-Ib). The Ca II infrared triplet lines and Hα are asymmetric showing a systematic blue shift with decreasing residual intensity. These lines remain fixed in wavelength although the weak photospheric lines vary by ±4 km/sec. Observations of the 4.6μ vibration-rotation spectrum of CO show two sharp, cold components expanding at velocities of 10 and 17 km/sec relative to the centre of mass. Direct photographs of the shell in the light of KI λ7699 show that the cold shell is asymmetric and extends outward to at least 50”.

Details of these studies are either in press or will be submitted to “The Astrophysical Journal”.

Recent observational and theoretical results are reviewed that pertain to the presence and characteristics of stellar coronae and winds in late-type stars. It is found that stars - principally dwarfs - exist with “hot” coronae similar to the Sun with thermally driven winds. For stars, at the lowest effective temperatures, and gravities characteristic of supergiant and giant stars, high temperature (~105K) atmospheres are absent (or if present are substantially weaker than in the dwarf stars), and massive winds are present. There also exist “hybrid” examples - luminous stars possessing both a “hot” corona and a supersonic stellar wind. Constraints for theoretical models are discussed.

The ionization zone in the envelope of the late type stars is reasonably considered as a heat engine to transform some of the radiative energy into mechanical energy. This idea is suggestive for explaining Linsky and Haisch’s (1979) observation, which shows the sharp division into solar-type and non-solar type stars in the outer atmosphere. Also non-thermal velocity fields in “microturbulence” and in Wilson-Bappu effect are proposed to be formed essentially from this engine. Therefore, their envelope structure dependence observationally obtained is possibly explained by the envelope parameters (g, Te) dependence of the generated mechanical energy flux in this layer. If “microturbulence” is not contaminated by the other surface activities, it is expected to show a clear relation with envelope parameters (g, Te) similar to Wilson-Bappu effect.

We have analysed high dispersion spectra of the supergiant γ Cyg (F8 Ib). On the basis of the curve of growth method it has been shown that there is no dependence of microturbulent velocity ξt on excitation potentials of spectral lines. Using model atmospheres we considered about 100 Fe I lines and found that no constant value ξt makes possible to remove the systematic discrepancy in iron abundance between groups of lines with different equivalent widths. The depth dependence of microturbulence in the atmosphere is investigated. It is shown that parameter ξt increases outwards from about 0-1 km/s at the optical depth τ5000 = 0.2 to 10 km/s at the depth τ5000 = 10-3. Deducted function ξt (τ5000) gives the same iron abundance log ε(Fe) = T = 7.45 ± 0.05 for all groups of Fe I lines. The detailed analysis will be published in Izv. Crimean Astrophys. Obs.