Equivalent widths of hydrogen Lyman alpha line in an expanding spherical atmosphere

We have calculated the profiles of hydrogen Lyman a line in an expanding spherical atmosphere containing dust and gas. We have investigated the variation of equivalent widths with velocities of expansion of the atmosphere, together with the amount of dust present in the medium. We have drawn curves of growth for different velocities and dust optical depths     

Theoretical study of partial frequency redistribution function in irradiated, moving atmospheres of close binary components

We have studied the effects of partial frequency redistribution function with angle-averaged   R _II-A  in irradiated and moving atmospheres of close binary components. We have considered the atmospheric extension of the primary component to be twice the radius of the primary component in a close binary system. We have considered two cases: (i) when the atmosphere is at rest and (ii) when the atmosphere is moving. In both the cases, we have computed the line profiles along the line of sight for a given optical depth. The irradiation from the secondary component is assumed to be one, five and 10 times the self-radiation. The line fluxes in the line of sight are calculated by using the total source functions due to self-radiation of the primary component and due to the irradiation from the secondary component. We have noted double-peaked emission lines in the case of a static medium and a reduction of emission peaks in the case of velocity field.     

A study of the H-alpha line in late G and K supergiants

A spectroscopic study of H_α has been carried out to investigate the properties of expanding chromospheres of late G and K supergiants. Spectra of 23 stars brighter thanV = 6.0 have been obtained at dispersions of 4–10 å mm^-1 using the coude and the coudé-echelle spectrographs at the 102-cm telescope of Kavalur Observatory. The H_α profiles are all asymmetric in the sense that the absorption core is shifted to the blue by amounts ranging between -4 and -24 km s^-1. H_α profiles were theoretically computed using radiative transfer in spherically symmetric expanding atmospheres covering a large range of integrated optical depths. These were compared with the characteristics of the observed line in the programme stars. The analysis shows that the H_α line is formed in a region with velocity increasing outward. The computed equivalent widths and line core displacements were matched with those observed to obtain hydrogen column densities and expansion velocities. From these, the rates of mass loss in these stars were determined to be in the range of 10⁶10^-7 M_⊙ yr^-1.     

Inhomogeneities of the stellar winds of hot supergiants

The causes of variability of line profiles in the spectra of O supergiants are analyzed. It is suggested that the main cause of the variability is the motion in the atmosphere of dense clumps of matter (inhomogeneities or clouds) along the Une of sight between star and observer. The profiles of C IV and Si IV UV resonance lines in the spectra of bright OB supergiants are calculated for spherically symmetric atmospheres and for atmospheres with inhomogeneity along the line of sight. The dependence of the line profiles on the distance of the inhomogeneity from the center of the star is investigated. It is shown that the formation and evolution with time of discrete absorption components (DACs) in the profiles of C IV and Si IV UV resonance lines can be explained within the framework of the proposed model of variability of line profiles. The parameters of the inhomogeneities moving in the atmosphere to produce DACs are estimated. Translated from Astrofizika, Vol. 41, No. 3, pp. 423–441, July–September, 1998.     

Lines formed in rotating and expanding atmospheres

Spectral lines formed in a rotating and expanding atmosphere have been computed in the frame of the observer at infinity. Two kinds of velocity laws are employed: (i) a uniform radial velocity of the gas and (ii) velocity increasing with radius (i.e. velocity gradients). The atmosphere has been assumed to be rotating with constant velocity. We have considered maximum radial and rotational velocities to be 10 and 3 mean thermal units respectively in an atmosphere whose geometrical thickness is 10 times the stellar radius. The total radial optical depth at line centre is taken to be about 100. In all cases, Doppler profile and a source function which is varying as 1/r ² have been used. Generally, the lines are broadened when rotation is introduced. However, when radial motion is also present, broadening becomes asymmetric and the red emission and blue absorption are enhanced.     

Ionization structure of the atmospheres and line profiles in the spectra of Wolf-Rayet stars

The ionization structure of the atmospheres of Wolf-Rayet (WR) and WC stars is studied. The stellar atmospheres were assumed to consist of helium, hydrogen, and carbon. Profiles of the C III l 5696 line are calculated, both for a spherically symmetric atmosphere with a density that decreases monotonically outward and for an atmosphere containing a dense condensation (inhomogeneity). The dependence of line profiles on the parameters of the inhomogeneity is investigated. It is shown that profiles of the C III λ 5696 line calculated assuming no inhomogeneities in the atmosphere are too weak, whereas assuming the existence of inhomogeneities enables one to reconcile the observed and calculated profiles. An equation is obtained relating the mass of an inhomogeneity to the flux in the detail of the total profile of the CIII λ 5696 line formed by that inhomogeneity. This equation is used to construct a stochastic cloud model of the atmosphere of a WR star, consisting of a large number of inhomogeneities in a homogeneous, spherically symmetric stellar wind. In the proposed model, the formation of inhomogeneities was treated as a random process. It is shown that in this model it is possible both to obtain an average line profile corresponding to the observed one and to reproduce the amplitude and overall pattern of variability of profiles in the spectra of Wolf-Rayet stars. Translated from Astrofizika, Vol. 42, No. 3, pp. 373–398, July–September, 1999.     

Radiative transfer effects in rotationally distorted stars

A general expression for the gravity darkening of the tidally and non-uniformly rotating Roche components of close binary systems is used to calculate the uniform rotational effects on line profiles in an expanding atmosphere. We consider a non-local thermodynamic equilibrium (non-LTE) two-level atom approximation in an extended atmosphere, and use Von Zeipel's theorem for the incident radiation at the maximum optical depth  (τ=τ_max)  in the atmosphere. These calculations are performed with uniform rotational velocities of 1, 4 and 8 mtu (mean thermal units). It is found that rotation dilutes the radiation field which is similar to the expansion velocity.
We also study rotational aspects, which make the outer layers of the star distorted. The equation of line transfer is solved in the comoving frame of the expanding atmosphere of the primary using complete redistribution in the line. We use a linear law for the velocity of expansion such that the density varies as r ⁻³, where r is the radius of the star, satisfying the law of conservation of mass. It is found that rotation broadens the line profile, and P-Cygni-type line profiles are obtained.     

Half-widths, their temperature dependence, and line shifts for the HDO-CO2 collision system for applications to CO2-rich planetary atmospheres

Measurements of water vapor in the atmospheres of Venus or Mars by spectroscopic techniques in the infrared range are being made routinely by instruments onboard the Venus Express and the Mars Reconnaissance Orbiter. The interpretation of these measurements in the 2250-4450 cm⁻¹ region is being complicated by the presence of HDO lines absorbing radiation in this region. These spectra cannot be modeled properly because line shape parameters for CO₂ broadening (principal gas in these atmospheres) of HDO are not available. Here semi-classical line shape calculations for the HDO-CO₂ collision system are made using the Robert-Bonamy formalism for some 2300 rotational band transitions of HDO. From these calculations, the half-width, its temperature dependence, and the line shift are determined to aid in the reduction of the measured spectra. These data will greatly reduce the uncertainty of the reduced profiles from the Venus and Mars measurements and will also allow better estimates of the D/H ratio on these planets.     

NLTE formation of the resonance Ba II line λ 455.4 nm in the solar atmosphere

We consider the NLTE formation of the resonance Ba II line λ 455.4 nm in the solar spectrum for three one-dimensional and one three-dimensional hydrodynamic models of the quiet solar atmosphere. The sensitivity of the line to atomic parameters, microturbulent and macroturbulent velocities, as well as to oscillator strength and barium abundance uncertainties was examined. The wings of the barium line are shown to be most sensitive to the van der Waals broadening constant. Another important parameter is the barium abundance. Our NLTE estimate of the solar barium abundance (A _Ba = 2.16) derived with allowance made for the nonuniform solar atmosphere structure is in good agreement with earlier results. The influence of granular convective motions on the line profile shape was studied, and the profiles formed in granules and in intergranular lanes are shown to be asymmetric and differently shaped. We demonstrate that the theoretical profiles match well the observed ones when the NLTE effects and the granular structure are taken into account.     

Magneto-induced Line Broadening of Magneto-sensitive Lines in Solar Magnetized Atmospheres

We analyze the spectral line broadening of those magneto-sensitive lines in solar magnetized atmospheres. The broadening at the line wings is due to the increase of the effective width of energy levels involved in Zeeman splitting, and the broadening at the line core also originated in Zeeman splitting under the condition that the Zeeman components are mixed. Therefore, the magnetoinduced or Zeeman broadening take effects on the whole line. The observed Stokes parameter data in a sunspot and outside it acquired by Solar Stokes Spectrum Telescope (S3T) are analyzed for the demonstration of this mechanism, and the Zeeman broadening rates are calculated for FeI6302.5 under some assumptions. Our result shows that the broadening is increased as the magnetic field strength becomes stronger, but the rate of increase at the line core is decreased as the field strength increases, while the rate at the wing does not show such an obvious regularity. The broadening is more effective in the line core than in the wings.     

Polarization of resonance lines formed in extenned spherical atmospheres

The problem of polarization of the resonance lines formed in extended spherical atmospheres is studied in detail. In this paper, the atmosphere is assumed to be at rest. The basic problem of resonance line polarization in spherical atmospheres as compared to the conventionally used plane-parallel atmospheres, is studied in Nagendra (1988). Our main interest in this paper is to understand the behaviour of polarized radiation fields in extended model spherical atmospheres so that some constraints can be placed on the model parameters in the modelling work conected with observations of polarization across resonance lines. A comparison of polarized lines formed under three kinds of line-scattering mechanisms is also made. They are CS=coherent scatteirng, CRD=complete redistribution, and PRD=partial frequency redistribution which, in the increasing order of generality, provide a good approximation in the two-level atom approach, to the resonance line polarization. The dependence of polarization on the opacity laws, extendedness and on optical depth is studied in detail. The distribution of line intensity and polarization across the visible disk of an extended model stellar atmosphere is studied, in view of the possible disk-resolved observations in future, of the extended atmospheres of the stars.     

Formation depths of lithium resonance absorption lines in the atmospheres of late-type stars and brown dwarfs

A numerical technique for determining absorption line formation depths in the atmospheres of late-type stars and substellar-mass subdwarfs is proposed. The technique is based on estimating individual absorptions contributed by certain layers of the stellar model atmosphere to the resulting equivalent width of a spectral line. In particular, the proposed technique can be used when considering lithium absorption lines formed at the background of molecular bands. The technique is applied to the formation of lithium lines in stellar atmospheres, specifically, in the atmosphere of the Sun (spectral type G2V) and those of the red giant star in the binary system RS Oph (M2III), the giant carbon star WZ Cas (C6), and the brown dwarf LP944-20 (M9V).     

Effects of Thomson scattering on the shape of a spectral line

The effect of Thomson scattering and Compton effect on the shape of a spectral line is studied in the case of a plane-parallel atmosphere. The theoretical values of red shift and intensity at the top of the line, having an equivalent width 5√π10^?10 cm, and of the red asymmetry are tabulated for 62 different values of the optical thickness τ′; from τ′=0.2/√3 to τ′=2.6/√3. The case of solar atmosphere is considered and it is shown that all main features of the observed red shifts can be interpreted by means of a scattering theory, with an error smaller than one milliängström. The need of further measurements is pointed out.     

High-resolution Martian atmosphere modeling

A multilayer radiative transfer, high-spectral-resolution infrared model of the lower atmosphere of Mars has been constructed to assess the effect of scattering on line profiles. The model takes into account aerosol scattering and absorption and includes a line-by-line treatment of scattering and absorption by CO₂ and H₂O. The aerosol complex indices of refraction used were those measured on montmorillonite and basalt chosen on the basis of Mars ir data from the NASA Lear Airborne Observatory. The particle sizes and distribution were estimated using Viking data. The molecular line treatment employs the AFGL line parameters and Voigt profiles. The modling results indicate that the line profiles are only slightly affected by normal aerosol scattering and absorption, but the effect could be appreciable for heavy loading. The technique described permits a quantitative approach to assessing and correcting for the effect of aerosols on lineshapes in planetary atmospheres.     

Semi-empirical solar line blanketing

The line blanketing procedure described in an earlier paper has been tested by a series of blanketed solar model atmosphere calculations incorporating methodological and data variations. The results of those tests show the method to be reasonably insensitive to data uncertainties and to certain assumptions employed. The method was also checked by calculating several blanketed stellar atmospheres for comparison with blanketed atmospheres computed by other investigators. Except at the highest atmospheric levels the comparisons of the model structures were good and the blanketing method appears to be validated.Central solar intensities were computed for two semi-empirical solar models and for a theoretical model using the present blanketing method. The results are compared with the observations of Labs and Neckel (1968) in the region 3300 Å to 6500 Å. It is found the blanketing improves agreement of the model predictions with observations in a substantial way, particularly at short wavelengths. Limb-darkening predictions with blanketing were also made for these models at four wavelengths and compared with observations. The blanketing generally produces an important improvement in the comparisons; however, the amount of blanketing to be included for limb-darkening is uncertain.The temperature distribution of the blanketed theoretical model was compared with semi-empirical solar models and a blanketed model by Athay (1970) including non-LTE effects. Over a large range in optical depth the agreement is reasonably good; at small optical depths (₀ 0.01) large divergences are seen which may be due to the effects of non-LTE and to the neglect of strong lines in the present blanketing method. In addition to the good structural comparisons, the quality of the blanketed theoretical model in terms of comparison with central intensity and limb darkening is nearly as good as the semi-empirical models. We conclude that theoretical model atmospheres of solar type or nearly solar type computed with current constant-flux programs and with blanketing included are of high quality.Possible improvements in the blanketing method of importance in some instances are suggested; these include the use of a picket-fence procedure, the inclusion of strong lines, and the consideration of non-LTE effects. Further applications to the solar UV region and to stellar atmospheres are suggested.Publications of the Goethe Link Observatory, Indiana University, No. 131.     

Plasma laser star model of QSOs

Varshni maintained that the emission lines observed in QSOs can be satisfactorily explained as being due to laser action in certain atomic species in the expanding envelope of a star and having no appreciable redshift. In order to test this hypothesis we have examined the conditions conducive to laser action in the stellar atmosphere and compared all the emission lines of 633 QSOs discovered till August 1976 (as listed by Burbidgeet al.) with the laser transitions found in the laboratory till April 1976 (as listed by Willett and Becket al.). It was found that 88% of the QSO lines agreed to within 10 Å with the laser lines and 94% agreed to within 20 Å. The main reason Greenstein and Schmidt failed to fit the spectral lines of 3C 48 and 3C 273 with known emission lines is that laser transitions in hydrogen do not occur in stellar atmospheres. The spectra are explained on the basis of the new theory and the broadening of lines explained.     

On the small-scale turbulence parameters in the atmosphere of venus and their use in the global circulation models

Vertical profiles of the turbulence parameters calculated for the planet-averaged conditions from the experimental data on the turbulent fluctuations of temperature and wind velocity are presented. Improved formulas accounting for the difference between the atmospheric gas on Venus and an ideal one, and the large difference in its thermal capacity at different altitudes, are used. The commonly used formula for the potential temperature describing the atmospheres of the Earth and Mars is inapplicable to the atmosphere of Venus. It has been shown that the opinion on the absence of turbulence in the atmosphere of Venus is based on overestimated values of the dynamic Richardson number obtained from the smoothed profiles of wind velocity, while its actual values are below unity due to the large wind velocity gradients produced by buoyancy waves. To improve the global circulation models of the atmosphere of Venus, it is necessary to use the currently available turbulence parameters calculated from experimental data.     

Models of the millimeter-centimeter spectra of the giant planets

Hitherto Jupiter's spectrum at short millimeter wavelenghts showed a clear discrepancy with model calculations (e.g., G.L. Berge and S. Gulkis, 1976, In Jupiter (T. Gehrels, Ed.), pp. 621–692. Univ. of Arizona Press, Tucson). A similar although less pronounced, discrepancy appears to exist for Uranus and Neptune. One explanation of this discrepancy is that additional absorbers not included in the model calculations are present in the atmosphere. It was suggested that uncertainties in the absorption coefficient of ammonia, especially at millimeter wavelengths, may be responsible for at least part of the discrepancy. A comparison of various model atmosphere calculations with data for all four giant planets is shown. The absorption profile of ammonia at centimeter wavelengths was assumed to be rightly represented by a Ben Reuven line profile, which enabled the derivation of information on the vertical distribution of ammonia in these planets' atmospheres. It appeared that ammonia must be depleted in the upper atmospheres of all four planets by a factor of 4–5 with respect to the solar abundance for Jupiter (and Saturn) and by a factor of 100–200 for Uranus and Neptune. At deeper layers the optical depth is larger, due either to a larger abundance of ammonia or to absorption by the presence of water. Given the vertical ammonia distribution in the atmospheres as derived from the centimeter data, a best fit to the millimeter spectra of all four planets was found by changing the high frequency tail of the ammonium lineshape profile. This, we feel, is legitimate since the profile at millimeter wavelenghts is not or is only poorly known due to the absence of laboratory spectra for ammonia as a trace constituent in an otherwise hydrogen gas. It was found that a line profile which at millimeter wavelenghts more closely resembles a Van Vleck-Weisskopf lineshape than the usually adopted Ben Reuven profile gives a rather satisfactory fit to the data of all four gaseous planets.     

Time variations of aerosol properties in the atmosphere of uranus

In the present paper, variations in the vertical structure of the cloud layer of the atmosphere of Uranus in 1981, 1993, and 1995 were analyzed from the data on the geometric albedo of Uranus in the profiles of the absorption bands of methane at λ = 543, 619, 702, 727, 842, 864, 887 nm (Neff, et al., 1984; Karkoschka, 1994; 1998). We used Morozhenko’s method that allows us to identify how much the vertical structure of the atmosphere diverges from the conditions of homogeneity. This method is based on the estimation of the optical depths of the layers which form the intensity in the optically-thick vertically homogeneous gasaerosol atmosphere, i.e., the effective optical depths. It has been shown that, at the depths of formation of these absorption bands, there are two extensive cloud layers, the strength of which was maximum in 1981 and minimum in 1995. They are approximately positioned at the levels that correspond to the pressure intervals from 1.4 to 2 bar and from 3.5 to 5.8 bar.