Modeling of convective motions in the envelope of procyon. II. Asymmetry of the spectral lines

Principal Astronomical Observatory, Ukrainian Academy of Sciences. Translated from Astrofizika, Vol. 31, No. 3, pp. 589–600, November–December, 1989.     

Peculiarities of convective motions in the upper solar atmosphere. I

A convective field of intensities and velocities between the levels of continuum origination and the temperature minimum is investigated based on spectral observations of iron lines performed near the center of the solar disc using the 70-cm German vacuum tower telescope (VTT) located at del Teide observatory of the Institute of Astrophysics on the Canaries (Tenerife island). Convective elements in the process of their upward and downward motion change with height not only the sign of the relative contrast but also the direction of motion. The height at which this reversal occurs strongly depends on the velocity and contrast of the convective elements which they had at the level of continuous spectrum formation. On average, the reversal of the velocity takes place at the height of 240 ± 130 km, and that of the contrast occur at the height of 200 ± 65 km.     

Some properties of convective motions in the upper solar atmosphere. II

Using a three-dimensional hydrodynamical model of the solar atmosphere, we calculated profiles of the Fe I λ 639.361 nm and Fe II λ 523.462 nm lines with consideration for deviations from the local thermodynamic equilibrium. We determined heights for intensity contrast reversal and for velocity sign reversal of convective elements. Both of these parameters depend strongly on the convective velocity and intensity measured in the continuum. The larger the parameters, the greater is the atmosphere altitude where the reversal takes place. We compared all the calculated relations with the observations obtained at the German Vacuum Tower Telescope in Izana (Tenerife, Spain). In our opinion, the 3D hydrodynamical model of the solar atmosphere satisfactorily describes all the main features of observed convective velocities and intensities.     

Physical conditions in the convective envelope of stars

Summary The mechanical flux originating in the convective envelope of stars is shown to depend critically by the treatment of convection. In particular, in the framework of the mixing-length theory, in passing from a mixing lengthl=H _P to a mixing lengthl=H the presence of mechanical fluxes shifts from being a marginal phenomenon to a dominant one.Possible implications concerning atmospheric microturbulence in Main Sequence stars, as so asA _p andA _m stars, several types of variables and mass loss are briefly discussed.

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Sommario Si mostra come il flusso cinetico originato negli inviluppi convettivi di una stella dipenda criticamente dalle assunzioni fatte nel trattamento della convezione superadiabatica. In particolare, sulla base della teoria della lunghezza di rimescolamento, a seconda che si assumal=H _P o l=H i flussi cinetici passano dall'essere un fenomeno marginale a contributi determinanti.E' discussa una serie di possibili implicazioni riguardanti la microturbolenza atmosferica in stelle di sequenza principale, le stelleA _p eA _m, diversi tipi di variabili e la perdita di massa in fase di gigante.

     

On the occurrence of convective motions in the upper photosphere

We have examined whether the motion field in the photosphere in the range of optical depths 0.25< ₀< 0.6 is dominated by thermal convection or by vibrations. The observed asymmetries of infrared Fraunhofer lines indicate the presence of motions, and the fact that the asymmetry is zero for lines of low excitation and increases with the excitation potential shows that these motions are chiefly convective in this part of the photosphere: upward moving elements appear to be hotter than downward moving ones.Assuming furthermore that the photosphere can be described by a three-column model, with temperature differences as given by Edmonds (1967), we find that in the range of optical depths given above, where T seems to vary between 80 and 160 °K, average convective velocities of 2.3 to 3.2 km/sec should occur. This result is in numerical agreement with (a) a previous one by the present authors (1967) derived from the variation of line asymmetry with depth in lines of one multiplet, (b) a finding by Lambert and Mallia (1968) deduced from absolute wavelength measurements of Fraunhofer lines, and (c) a recent result of Beckers (1968) found from a comparison of two granulation pictures obtained simultaneously with a narrow-band filter centred on the two wings of a faint line.     

Granulation and supergranulation as convective modes in the solar envelope

The stability of linear convective modes in the solar convection zone is investigated by incorporating the mechanical and thermal effects of turbulence through the eddy transport coefficients. The inclusion of turbulent thermal conductivity and viscosity, calculated in the framework of the mixing length approximation, is demonstrated to have a profound influence on the convective growth rates. The solar envelope model of Spruit (1977) is used to show that that most rapidly growing fundamental mode and the first harmonic are in reasonable accord with the observed features of granulation and supergranulation, respectively.On leave of absence from Govt. Digvijai College, Rajnandgaon 491441, India.     

Seismic study of stellar convective regions: the base of the convective envelope in low-mass stars

The possibility of observing solar-type oscillations on other stars is of great relevance to investigating the uncertain aspects of the internal structure of stars. One of these aspects is the convective overshoot that takes place at the borders of the envelopes of stars of mass similar to, or lower than, the Sun. It affects the temperature stratification, mixing, rotation and magnetic-field generation. Asteroseismology can provide an observational test for the studies of the structure of such overshoot regions.
The seismic study of the transition in the Sun, located at the base of the convection zone, has been successful in determining the characteristics of this layer in the Sun. In this work we consider the extension of the analysis to other solar-type stars (of mass between 0.85 and 1.2 M_⊙) in order to establish a method for determining the characteristics of their convective envelopes. In particular, we hope to be able to establish seismologically that a star does indeed possess a convective envelope, to measure the size of the convective region and also to constrain the properties of an overshoot layer at the bottom of the envelope. The limitations in terms of observational uncertainties and stellar characteristics, and the detectability of an overshoot layer, are discussed.     

The common convective envelope model for W Ursae Majoris systems and the analysis of their light curves

The common convective envelope model for W UMa systems is used to analyse the light curves of the sixteen systems with spectroscopic mass ratios. From the derived photometric elements, an indication is found that Binnendijk's W-type systems have only shollow common envelopes, which is therefore suggested to be the cause of the difference between A- and W-type systems. It is also suggested that the structure of many contact binaries permits only a shallow common envelope and that further study of such envelopes will yield the modification in the model required if a closer fit to the W-type light curves is to be obtained.The model is also used with mass ratio as an additional photometric element to analyse the light curve of AW UMa. The solution obtained confirms the remarkably small mass ratio of 0.08 found by Mauder and by Mochnacki and Doughty.Originally presented at the IAU Colloquium No. 16 held at the University of Pennsylvania, Philadelphia, Pa., U.S.A., September 8–11, 1971.     

A grid search for three-dimensional motions and three new types of such motions

A grid search method aimed at locating ‘all’ doubly symmetric orbits of the three-dimensional restricted problems of one, two, etc. revolutions is developed and applied numerically on the CDC-3300 computer. Three new types of orbits have thus been located and a second order ‘predictorcorrector’ method is applied in order to determine a certain number of members of the families of which the ‘located’ orbits are members. The stability of these members is also discussed.     

Magnetic field effect on the fine structure of convective motions in the solar atmosphere

Statistical properties of solar granulation in an active region on the solar surface from the photosphere to the lower chromosphere are studied. We use the values of the velocity, intensity, and magnetic field that were obtained at different heights in the solar atmosphere according to the observation data on the VTT telescope at Observatorio del Teide, Tenerife. The changes in the line??s parameters (central depth of the line, halfwidth, equivalent width, and central depth shift) and convective velocity are presented as functions of the value of the magnetic field. We propose a 16-column model of solar granulation depending on the direction of motion of convective elements and on the sign of contrast at two heights??in the continuous spectrum and in the highest layer (h = 650 km). We found that the magnetic field impedes the change in the sign and motion direction of convective elements.     

The interaction between the secondary and the common convective envelope in a contact binary

It has been suggested that a contact system almost certainly cannot exist in static equilibrium undergoing periodic thermal relaxation oscillation. The energy transfer in a common convective envelope (CCE) makes the secondary have a complex structure, so the interaction between the secondary and CCE may play an important role in the structure and evolution of the contact system. The present paper tests the TRO theory and investigates this interaction with polytropic stellar model from the observational datum of 22 contact systems directly. It shows that the A-type systems are expanding with a velocity of 25.04 m yr^–1, and the W-type systems are contracting at velocity of 3.10 m yr^–1 by the calculations about these contact systems. Also, we calculate the ratio of energy transfer and the interaction coefficient for them. The HS (hot secondary) model is supported by our calculations. These results may help to understand the TRO theory and the W-phenomenon.     

Numerical investigation of motions of resonant asteroids in the three-dimensional space

Motions of asteroids in mean motion resonances with Jupiter are studied in three-dimensional space. Orbital changes of fictitious asteroids in the Kirkwood gaps are calculated by numerical integrations for 10⁵ – 10⁶ years. The main results are as follows: (1) There are various motions of resonant asteroids, and some of them are very complicated and chaotic and others are regular. (2) The eccentricity of some asteroids becomes very large, and the variation of the inclination is large while the eccentricity is large. (3) In the 3:1 resonance, there is a long periodic change in the variation of the inclination, when (7 : ) is a simple ratio (7: longitude of perihelion, : longitude of node). (4) In the 7:3 resonance, the variation of the inclination of some resonant asteroids is so large that prograde motion becomes retrograde. Some asteroids in the 7:3 resonance can collide with the Sun as well as with the inner planets.     

Stellar pulsation: (I) analysis of stability of envelope

The life-time of the star on AGB is approximately 6 × 10⁴ yr. We divide it into front half and back half of AGB (including to optical Mira variable and OH/IR star) according to their evolution character. The observations show that the star has non-pulsation, but constant mass loss rate ( 5 × 10^–7 M yr^–1) on front half of AGB. Its circumstellar envelope is formed. When the star has pulsation on back half of AGB, its mass loss rate is relative with time, and increases gradually. In this time the star is on the stage of optical Mira variable. When the mass loss rate reaches the value of 3 × 10^–6 M yr^–1, the star evoluted from the stage of optical variable into the stage of radio bright OH/IR star. On the end of AGB the mass loss rate reaches 10^–4 M yr^–1. (Band and Habing 1983, Hermen and Habing 1985).     

Dynamo action in the ionosphere and motions of the magnetospheric plasma I. Symmetric dynamo action

In order to envisage the circulation pattern of the magnetospheric plasma produced by the dynamo action in the ionosphere, the distribution of the dynamo-induced electrostatic field resulting from basic ionospheric wind systems is studied. It is then shown by use of Maeda's field distribution that there exists a remarkable large-scale circulation of the magnetospheric plasma, inward (earthward) on the evening side of the magnetosphere and outward on the morning side. This motion is comparable to the motion produced by the Earth's rotation and by zonal winds in the ionosphere. It is shown also that the electrostatic field can cause a considerable radial motion of some of the energetic particles in the radiation belt.     

Chemical mixing by turbulent convection in the overshooting region below the convective envelope of RGB stars

Based on the turbulent convection model(TCM),we investigate chemical mixing in the bottom overshooting region of the convective envelope of intermediatemass stars,focusing on its influence on the formation and extension of blue loops in the Hertzsprung-Russell(HR) diagram.A diffusive mixing model is adopted during the Red Giant Branch(RGB) phase.The properties of the blue loop are changed by modification of the element profiles above the H-burning shell,which results from the incomplete mixing in the bottom...     

Regular motions in double bars – I. Double-frequency orbits and loops

Bars in galaxies are mainly supported by particles trapped around stable periodic orbits. These orbits represent oscillatory motion with only one frequency, which is the bar driving frequency, and miss free oscillations. We show that a similar situation takes place in double bars: particles get trapped around parent orbits, which in this case represent oscillatory motion with two frequencies of driving by the two bars, and which also lack free oscillations. Thus the parent orbits, which constitute the backbone of an oscillating potential of two independently rotating bars, are the double-frequency orbits. These orbits do not close in any reference frame, but they map on to closed curves called loops. Trajectories trapped around the parent double-frequency orbit map on to a set of points confined within a ring surrounding the loop.     

Relative motions of fragments of the split comets.: I. A new approach

A new approach is formulated for the study of motions of the split comets. It is based on the assumption that two fragments of a comet separate at a rate that is determined primarily by a slight difference between their effective solar attractions rather than by the impulse imparted on them at the time of splitting. The net dynamical effect is interpreted as due to differential nongravitational forces, which depend on the size, density, structure, composition, and spin rate of the fragments. Since at least at smaller distances from the Sun these forces vary inversely as roughly the square of heliocentric distance, their dynamical effect resembles that of radiation pressure, so that the formalism developed for the motion of a dust particle in a cometary tail is applicable in principle. The calculations show that this approach provides reasonably good to excellent fits of the observed separations for a great majority of the split comets, and that it fails only in the case of Comet 1957 VI. The correlation between the differential nongravitational forces and the endurance of the fragment is investigated in terms of the physical behavior of the fragments, with the emphasis on the short-lived objects. Some of the unusual phenomena accompanying the split comets are discussed, and comments are also offered on the sequence of splitting for comets with multiple nuclei and on the distribution of the points of splitting in space.     

The role of the Coriolis force on the stability of rotating magnetic stars and the origin of convective motions

Based on the method of the energy principle, the effect of the Coriolis force in the stability of rotating magnetic stars is examined and the conditions for instability is derived. It is shown that, in these stars, the effect of this force is to inhibit the onset of convective motion. Discussion is given on the possibility of hydromagnetic dynamo processes in respect to the convective motion inside these stars.