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The heating of stellar chromospheres and coronae by the dissipation of acoustic waves is an important heating mechanism. It is only in the lower solar chromosphere that short period acoustic wave heating seems undisputed. The arguments leading to the rejection of the so called acoustic heating theory are derived from comparisons of calculated acoustic energy fluxes with observational or theoretical requirements.
Model stars whose convection zones had been prepared in accordance with the standard mixing-length theory were used as a basis for the computation of unstable convective modes. It was found that no superposition of statistically independent, nonviscous, adiabatic, convective modes can reproduce the radial dependence of the convective flux of the model. This implies that the representation of a stellar convection zone as a superposition of unstable adiabatic linear modes is inconsistent with the mixing-length theory, and that conclusions based upon such a representation should be regarded with caution. It is also shown that if the linear scale of convective motions is greater than (or of the same order as) the pressure scale height, then the fractional deviation of the pressure from equilibrium will generally not be negligible, as assumed in the mixing-length theory, but will be at least of the same order as the fractional deviation of the density from equilibrium.
The source functions and the energy fluxes are derived for wave generation in magnetic flux tubes embedded in an otherwise magnetic- field free, turbulent, and compressible fluid. Specific results for the generation of longitudinal tube waves are presented.
The source functions and the energy fluxes for wave generation in magnetic flux tubes embedded in an otherwise magnetic field-free, turbulent, and compressible fluid are derived. The calculations presented here assume that the tube interior is not itself turbulent, e.g., that motions within the flux tube are due simply to external excitation. Specific results for the generation of longitudinal tube waves are presented.
Two-dimensional numerical simulations are used to investigate how fully compressible nonlinear convection penetrates into a stably stratified zone beneath a stellar convection zone. Estimates are obtained of the extent of penetration as the relative stability S of the stable to the unstable zone is varied over a broad range. The model deals with a perfect gas possessing a constant dynamic viscosity. The dynamics is dominated by downward-directed plumes which can extend far into the stable material and which can lead to the excitation of a broad spectrum of internal gravity waves in the lower stable zone. The convection is highly time dependent, with the close coupling between the lateral swaying of the plumes and the internal gravity waves they generate serving to modulate the strength of the convection. The depth of penetration delta, determined by the position where the time-averaged kinetic flux has its first zero in the stable layer, is controlled by a balance between the kinetic energy carried into the stable layer by the plumes and the buoyancy braking they experience there. A passive scalar is introduced into the unstable layer to evaluate the transport of chemical species downward. Such a tracer is effectively mixed within a few convective overturning times down to a depth of delta within the stable layer. Analytical estimates based on simple scaling laws are used to interpret the variation of delta with S, showing that it first involves an interval of adiabatic penetration if the local Peclet number of the convection exceeds unity, followed by a further thermal adjustment layer, the depths of each interval scaling in turn as S(exp -1) and S(exp -1/4). These estimates are in accord with the penetration results from the simulations.
This paper investigates mass loss in late-type giant stars produced by propagating shock waves, assuming both monochromatic waves and acoustic frequency spectra. In monochromatic wave computations, the wave period is varied by a factor of 50. The wave models show that short-period waves produced in stellar convective zones do not play any direct role in generating the observed mass loss, except for episodic mass-loss events. However, these waves are important for heating stellar chromospheres. Continuous mass-loss solutions are obtained when the wavelengths are comparable to or larger than a stellar radius. In the case of Arcturus, a mass-loss rate between 10 to the -10th and 10 to the -11th solar mass/yr is found, and the final flow speed of the wind is larger than 40 km/s, which are close to the observed values.
The two general classes of models that deal with the required heating of stellar chromospheres and coronae assume that outer stellar atmospheres are heated by hydrodynamic or by magnetohydrodynamic (MHD) waves and that these waves are generated by turbulent motions in the stellar convection zones. This paper considers the types of MHD waves and the source of these waves in stars like sun, the efficiency of the generation of MHD waves, and the manner of propagation and energy dissipation of MHD waves. It is shown that the basic criteria for the validity of any theory of MHD wave heating must account for the mean level of heating observed in stellar chromospheres and coronae, and for the range of radiative losses observed for a given spectral type. It is also required that the MHD wave heating theory accounts for the existence of inhomogeneities in stellar atmospheres. The results obtained indicate that magnetic tube waves might supply enough energy for the chromospheric and coronal heating and might also account for the observed range of variations of stellar radiative losses for a given spectral type.
An investigation is presented on the way in which the generation of magnetohydrodynamic waves by turbulent motions in stellar convection zones depends on the star's effective temperature, surface gravity, and magnetic field strength. It is shown that the emitted Alfven wave flux (and acoustic slow wave flux in a very strong magnetic field) is in reasonable agreement with the general trend of observed chromospheric radiative losses in stars, and with the observations of three stars for which magnetic field strength, surface area covered by strong fields, and radiative losses have all been measured.
The theoretical description of the dynamics of a stellar convection zone is considered, taking into account one of the most basic issues by studying compressible convection extending over multiple scale heights. A revised version of a code reported by Graham (1975) is employed. Two-dimensional simulations show that nonlinear compressible convection possesses cellular structures with strong localized downward-directed plumes and broader upflows. The horizontal flows which close the circulation within the cell satisfy an approximate Bernoulli integral along a considerable portion of the horizontal trajectory. Attention is given to details regarding the numerical methods, the properties of the numerical solutions, the overall effects of compressibility on nonlinear convection, and a comparison with anelastic modal solutions.
In the present investigation of penetrative convection within a simple compressible model, the middle one of the three layers of differing stratification prior to the onset of convection is a convectively unstable polytrope bounded above and below by two stably stratified polytropes. One- and two-mode steady solutions with hexagonal planforms have been studied for Rayleigh numbers up to aobut 1000 times critical, and for a range of Prandtl numbers, horizontal wavenumbers, and stratifications. These indicate that the penetration into the lower stable layer by downward plumes is substantially larger in a stratified medium than in a Boussinesq fluid, and produces an extended region of adiabatic stratification. The strong asymmetry between upward and downward penetration in compressible media has major implications for the mixing of stable regions above and below stellar convection zones.
Available chromospheric, transition region, and coronal observations of the early main-sequence F stars are examined in order to find that while these objects exhibit enhanced levels of magnetic field-related radiative emissions, significant inhomogeneities in surface activity are not present. This phenomenon is discussed within the context of the calculations published by Schmitt and Rosner (1983) for the production of flux ropes of various spatial scales at a given rotation rate at the bottom of a stellar convection zone. It is found that the spatial scales and area contrast of emergent magnetic flux in these stars that, as a class, are characterized by rapid rotation and thin convection zones are substantially reduced relative to that of the sun.
The structure of solar, and very likely stellar, surface magnetic fields is highly inhomogeneous: at the photospheric level, the fields are locally strong, and show concentration into a flux tube structure. In this case, the wave energy generated in stellar convection zones may be largely carried away by flux tube waves, which can then become important sources for the heating of the outer atmospheric layers. Such flux tube wave generation may help to explain the UV and X-ray fluxes observed by the IUE and Einstein observatories. The generation of longitudinal tube waves in magnetic flux tubes embedded in an otherwise magnetic field-free, turbulent, and stratified medium was considered. It is shown that compressible tube waves are generated by dipole emission and that the generation efficiency is a strong function of the magnetic field strength. Energy flux calculations are presented for different magnetic flux tubes, and show how the results depend on the magnetic field strength and the characteristics of the convective turbulence.
The problem of the internal rotation of stars with masses and internal evolution similar to the sun is investigated, emphasizing the need to construct models of stellar convection zones which are consistent with full interior models. The affect of the distribution of angular momentum within a star on the formation process in a gas cloud and on the internal evolution throughout the premain-sequence phase and the early postmain-sequence phase is considered. The generation of magnetic fields associated with chromospheric activity via the interaction of rotation with convection is discussed. It is noted that rotationally induced mixing can alter the rate of evolution, thus affecting the luminosity function of star clusters.
A method is proposed to eliminate the compressional instability of a shallow layer in the upper part of stellar convective zones in standard mixing-length models. By equating the radiative cooling time of mixing eddies to their convective turnover time, the effective sizes of the eddies are assumed to be the smallest of those which are not eliminated by radiative transfer. Computations of the models with this assumption leads to smooth temperature profiles in the previously unstable layers and reductions of the convective velocity above its maximum value.
We have revisited the problem of acoustic wave generation by turbulent convection in stellar atmospheres. The theory of aerodynamically generated sound, originally developed by Lighthill and later modified by Stein to include the effects of stratification, has been used to estimate the acoustic wave energy flux generated in solar and stellar convection zones. We correct the earlier computations by incorporating an improved description of the spatial and temporal spectrum of the turbulent convection. We show the dependence of the resulting wave fluxes on the nature of the turbulence, and compute the wave energy spectra and wave energy fluxes generated in the Sun on the basis of a mixing-length model of the solar convection zone. In contrast to the previous results, we show that the acoustic energy generation does not depend very sensitively on the turbulent energy spectrum. However, typical total acoustic fluxes of order F(sub A) = 5 x 10(exp 7) ergs/sq cm/s with a peak of the acoustic frequency spectrum near omega = 100 mHz are found to be comparable to those previously calculated. The acoustic flux turns out to be strongly dependent on the solar model, scaling with the mixing-length parameter alpha as alpha(exp 3.8). The computed fluxes most likely constitute a lower limit on the acoustic energy produced in the solar convection zone if recent convection simulations suggesting the presence of shocks near the upper layers of the convection zone apply to the Sun.
A study of stellar chromospheres based on the internal structure of particular stars is presented. Used are complex flow diagrams of the linkage paths between mass loss, angular momentum loss, magnetic field from the turbulent dynamo and its relations to differential rotations and the convection zone, and stellar evolution.
Density inversion in convective zone of stellar photospheres occurring in Eridani atmospheric model under certain conditions
Starspots and stellar activity can be detected in other stars using high precision photometric and spectrometric measurements. These observations have provided some surprises (starspots at the poles - sunspots are rarely seen poleward of 40 degrees) but more importantly they reveal behaviors that constrain our models of solar-stellar magnetic dynamos. The observations reveal variations in cycle characteristics that depend upon the stellar structure, convection zone dynamics, and rotation rate. In general, the more rapidly rotating stars are more active. However, for stars like the Sun, some are found to be inactive while nearly identical stars are found to be very active indicating that periods like the Sun's Maunder Minimum (an inactive period from 1645 to 1715) are characteristic of Sun-like stars.