Helium in stellar atmospheres

Helium, which was first discovered on the sun with the help of spectral analysis, plays, together with hydrogen, a principal role in astrophysics. We consider here two fundamental quantities: primordial helium abundance formed during Big Bang nucleosynthesis and the current initial helium abundances in nearby stars. It is shown that stellar atmospheres are enriched in helium during the main-sequence stage. Observational evidence for helium contamination in close OB-binaries is discussed. Stars with strong abundance anomalies are considered, such as chemically peculiar Ap and Bp helium-deficient stars and some types of objects with helium atmospheres.     

Rayleigh-Cabannes scattering in planetary atmospheres II. Constant internal sources in nonconservative atmospheres

The vector equation of radiative transfer is solved for non-conservative homogeneous plane-parallel atmosphere using the method of discrete ordinates. The scattering processes in the atmosphere bounded by a Lambert bottom are described by the Rayleigh-Cabannes phase matrix. The primary radiation field is generated by constant internal sources. A package of FORTRAN subroutines is compiled to find the axial radiation field for such an atmosphere at arbitrary optical depth.     

Rayleigh-Cabannes scattering in planetary atmospheres III. The Milne problem in conservative atmospheres

The discrete ordinale method by Chandrasekhar is used to solve the conservative Milne problem in a homogeneous plane-parallel atmosphere which scatters the radiation according to the Rayleigh-Cabannes law.The approximate solution which is supposed to converge uniformly to an exact one when increasing the order of approximation is obtained explicitly. In addition to a tabulation of the Hopf vector for different factors of depolarization, the extrapolation distance, the values of c, q and the Rubenson degrees of polarization at the limb are given.     

Photoelectron fluxes in cometary atmospheres

The photoelectron fluxes in cometary atmospheres are calculated by a Monte Carlo method. This is the first quantitative model calculation of this kind. A pure H₂O atmosphere is assumed with a sublimation rate of 10³⁰ molecules sec^?1 at 1 AU. Discussions of the energetics of electron gas and of the elementary collisional processes in determining the fluxes largely concern this water atmosphere. Influences on the photoelectron fluxes are also investigated for CO, another possible constituent. The excitation rate of the ${}^1\text{D}$ level of atomic oxygen in electron impacts is evaluated. It is highly improbable that the photoelectrons are responsible for the observed 6300 Å emission of the order of 1 kR at a heliocentric distance of 1 AU. The structure of the heat equation for thermal electrons is analyzed and a drastic change of the plasma behavior within the coma region is expected.     

Rayleigh scattering in planetary atmospheres

The vector equation of radiative transfer is solved both for conservative and non-conservative planetary atmospheres using the method of discrete ordinates. The atmosphere, bounded by a Lambert bottom, is considered plane-parallel and homogeneous. The scattering in the atmosphere obeys the Rayleigh or Rayleigh-Cabannes law. The compiled package of FORTRAN codes allows us to find the Stokes parameters for such an atmosphere at arbitrary optical depth.     

Nucleosynthesis in neutron star atmospheres

The composition of neutron star atmospheres is calculated as a function of time including effects of diffusion, cooling and thermonuclear reactions. A seven-component nuclear reaction network with includes He⁴, C¹², O¹⁶, Ne²⁰, Mg²⁴, Si²⁸ and Fe⁵⁶ is utilized. Neutron star models with different initial nuclear abundances are compared as to subsequent nucleosynthesis. It is found that the final abundances are independent of original composition assuming He⁴ as the major initial constituent. The final composition of the atmosphere is predominantly Fe⁵⁶. Mass loss from an evolving neutron star is examined as a possible source of cosmic rays. It is found that a neutron star contributes only Fe⁵⁶ significantly to the cosmic-ray spectrum.     

Ray propagation in oblate atmospheres

We evaluate the departures from Bouguer's law for the case of an oblate atmosphere. We show that, to lowest order, the plane of refraction is defined by the normal to the atmosphere at closest approach. In next order, however, the ray path is “warped” by the oblateness, which changes slightly the plane of refraction.     

Multiple scattering in planetary atmospheres

Methods for solving radiative transfer problems within the extended visible spectrum in planetary atmospheres are reviewed for use by the nonspecialist. Emphasis is placed on rapid, approximate procedures for the determination of such quantities as the plane and spherical (Bond) albedo, surface illumination, absorbed energy, limb darkening, phase curve, and spectra. Precise numerical methods and analytical results are also discussed. Recent approaches to such complications as atmospheric inhomogeneity and reflection from a porous regolith are described briefly.     

Opacity errors in model atmospheres

Different issues involved in the numerical evaluation of continuous absorption by hydrogenlike atoms and ions have been analyzed. Usually, the calculation of the opacity coefficient is explicitly performed for a predetermined number of levels and the higher ones are treated as an integral; it is shown that there are some cases where as many as 17 discrete levels need to be added before switching to the integral approximation if an error smaller than 0.1% is wanted in the results (a condition not always fulfilled with model atmosphere codes being used). Also, approximations to Gaunt factors are analyzed. Though in some cases approximations can be used which are very good, there are other occasions when it should be advisable to switch to interpolating in original tables, or to use more elaborated expressions (such as Hummer's for the Gaunt free-free factor). A numerical procedure for solving the non linear Pg-Pe-T relation is described in an Appendix.     

Red clouds in reducing atmospheres

A dark reddish-brown high-molecular-weight polymer is produced by long wavelength ultraviolet irradiation of abundant gases in reducing planetary atmospheres. The polymer i examined by paper chromatography, mass spectrometry, and infrared, visible, and ultraviolet spectroscopy. High carbon-number straight-chain alkanes with NH₂ and, probably, OH and CO groups are identified, along with the previously reported amino acids. There are chemical similarities between this polymer and organic compounds recovered from carbonaceous chondrites and precambrian sediments. The visible and near-ultraviolet transmission spectrum of the polymer shows its absorption optical depth to be redder than λ^?2 and perhaps similar in coloration to the clouds of Jupiter, Saturn, and Titan. The near-ultraviolet absorption coefficient is ～10³ cm^?1, and typical grain sizes ～30 μm. The nitrile content is small, and the polymer should be semitransparent in the 5 μm atmospheric window. Such polymers may be a common constituent of clouds in the outer solar system and on the early Earth.     

Mean values in inhomogeneous atmospheres

A brief summary of observations of inhomogeneities in the solar atmosphere and progress in the theoretical analysis of two-dimensional model atmospheres is given. In particular, it is asserted that reliable reference models of the mean temperature, pressure, etc. may be derived only by averaging over the horizontal coordinates of a two- or three-dimensional model. In discussion of a wide variety of cases including strong chromospheric lines, weak photospheric lines, and continuum radiation, it is shown that although the derivation of mean values by first averaging over the fluctuations in the data and then applying a one-dimension analysis is an obvious first approximation, it may lead to errors of a gross qualitative nature. Thus the recent deductions by several authors of very small temperature gradients in the upper regions of sunspots are shown to be subject to considerable doubt.     

Lightning generation in planetary atmospheres

The possibilities of lightning generation on other planets are considered, and the basic conditions that exist in terrestrial clouds during lightning discharges and the various theories of charge separation are reviewed. Recent measurements of cloud structure and whistlers, as well as optical observation of lightning on Jupiter, suggest that charge separation and lightning discharges occur on other planets in ways similar to those in which they occur on Earth. Using these terrestrial ideas, it is concluded that lightning on Venus will probably be found in clouds that are located in regions of convection such as those observed downwind of the subsolar point. It is also possible that if volcanoes on Venus are erupting, they too can produce lightning discharges in their plumes although it seems unlikely that this process can account for the observed rate of discharge. Jovian lightning is most probably generated in the lower water-ice clouds. These clouds are of moderate temperatures and have strong convection and large mass loading, all important ingredients for electrical buildup. Lightning is all but ruled out for Mars, even though some electrification is possible owing to the large dust storms on that planet.     

Micro-structured magnetic atmospheres

Asymmetrical Stokes profiles are produced if the photospheric magnetic and velocity fields are structured on scales smaller than the mean-free-path of the photons. Here we put forward a compact analytical expression for the radiative transfer equation in this case. Explicitly, micro-variations of the magnetic field strength and the velocity are considered. The existence of micro-structures might have serious implications on the techniques currently used to measure solar magnetic fields. For example, we show the failure of the relationship employed to calibrate magnetographs.On leave from the Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, Largo E. Fermi 5, I-50125 Firenze, Italy     

Isothermal magnetostatic atmospheres

An investigation of a family of isothermal magneto-static atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. The distributed current in the model J is directed along the x-axis where x is the horizontal ignorable coordinate. The current J is taken proportional to the square of the magneto-static potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of solution examples are displayed depending on the four free parameters in the solutions. Three of these parameters determine the source currents for the potential field solution of the family, whereas the fourth parameter determines the magnitude of the distributed current. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and gas pressure gradient to the force balance.     

Noble gases in planetary atmospheres: Implications for the origin and evolution of atmospheres

The radiogenic and primordial noble gas content of the atmospheres of Venus, Earth, and Mars are compared with one another and with the noble gas content of other extraterrestial samples, especially meteorites. The fourfold depletion of ⁴⁰Ar for Venus relative to the Earth is attributed to the outgassing rates and associated tectonics and volcanic styles for the two planets diverging significantly within the first billion or so years of their history, with the outgassing rate for Venus becoming much less than that for the Earth at subsequent times. This early divergence in the tectonic style of the two planets may be due to a corresponding early onset of the runaway greenhouse on Venus. The 16-fold depletion of ⁴⁰Ar for Mars relative to the Earth may be due to a combination of a mild K depletion for Mars, a smaller fraction of its interior being outgassed, and to an early reduction in its outgassing rate. Venus has lost virtually all of its primordial He and some of its radiogenic He. The escape flux of He may have been quite substantial in Venus' early history, but much diminished at later times, with this time variation being perhaps strongly influenced by massive losses of H₂ resulting from efficient H₂O loss processes.Key trends in the primordial noble gas content of terrestial planetary atmospheres include (1) a several orders of magnitude decrease in ²⁰Ne and ³⁶Ar from Venus to Earth to Mars; (2) a nearly constant ²⁰Ne/³⁶Ar ratio which is comparable to that found in the more primitive carbonaceous chondrites and which is two orders of magnitude smaller than the solar ratio; (3) a sizable fractionation of Ar, Kr, and Xe from their solar ratios, although the degree of fractionation, especially for ³⁶Ar/¹³²Xe, seems to decrease systematically from carbonaceous chondrites to Mars to Earth to Venus; and (4) large differences in Ne and Xe isotopic ratios among Earth, meteorites, and the Sun. Explaining trends (2), (2) and (4), and (1) pose the biggest problems for the solar-wind implantation, primitive atmosphere, and late veneer hypotheses, respectively. It is suggested that the grain-accretion hypothesis can explain all four trends, although the assumptions needed to achieve this agreement are far from proven. In particular, trends (1), (2), (3), and (4) are attributed to large pressure but small temperature differences in various regions of the inner solar system at the times of noble gas incorporation by host phases; similar proportions of the host phases that incorporated most of the He and Ne on the one hand (X) and Ar, Kr, and Xe on the other hand (Q); a decrease in the degree of fractionation with increasing noble-gas partial pressure; and the presence of interstellar carriers containing isotopically anomalous noble gases.Our analysis also suggests that primordial noble gases were incorporated throughout the interior of the outer terrestial planets, i.e., homogeneous accretion is favored over inhomogeneous accretion. In accord with meteorite data, we propose that carbonaceous materials were key hosts for the primordial noble gases incorporated into planets and that they provided a major source of the planets' CO₂ and N₂.     

Motion in the interiors and atmospheres of Jupiter and Saturn: scale analysis,anelastic equations,barotropic stability criterion

If Jupiter's and Saturn's fluid interiors were inviscid and adiabatic, any steady zonal motion would take the form of differentially rotating cylinders concentric about the planetary axis of rotation. B. A. Smith et al. [Science215, 504–537 (1982)] showed that Saturn's observed zonal wind profile extends a significant distance below cloud base. Further extension into the interior occurs if the values of the eddy viscosity and superadiabaticity are small. We estimate these values using a scaling analysis of deep convection in the presence of differential rotation. The differential rotation inhibits the convection and reduces the effective eddy viscosity. Viscous dissipation of zonal mean kinetic energy is then within the bounds set by the internal heat source. The differential rotation increases the superadiabaticity, but not so much as to eliminate the cylindrical structure of the flow. Very large departures from adiabaticity, necessary for decoupling the atmosphere and interior, do not occur. Using our scaling analysis we develop the anelastic equations that describe motions in Jupiter's and Saturn's interiors. A simple problem is solved, that of an adiabatic fluid with a steady zonal wind varying as a function of cylindrical radius. Low zonal wavenumber perturbations are two dimensional (independent of the axial coordinate) and obey a modified barotropic stability equation. The parameter analogous to β is negative and is three to four times larger than the β for thin atmospheres. Jupiter's and Saturn's observed zonal wind profiles are close to marginal stability according to this deep sphere criterion, but are several times supercritical according to the thin atmosphere criterion.     

Abundances of isotopes in planetary atmospheres

Carbon and oxygen isotopes show no large anomalies on Venus (10–15%) or Mars (<5%); the high value of¹⁵N/¹⁴N found on Mars is explained by non-thermal escape of nitrogen. The isotopes of non-radiogenic noble gases in the atmosphere of Mars exhibit abundance patterns similar to those in the primordial component of meteoritic gases and in the Earth's atmosphere. This implies that gas fractionation took place in the inner solar nebula prior to planet formation. The relatively high value of¹²⁹Xe on Mars emphasizes its deficiency on Earth, implying a difference in accretion histories of volatiles for the two planets. In the outer solar system, we find normal isotope ratios for nitrogen and carbon on Jupiter, and for carbon on Saturn, but precision is low (±15% at best). Controversy exists about the correct value of D/H, with current estimates ranging from 2.3±1.1 to 5.1±0.7×10^–5. Planetary missions planned for the next few years should add considerably to the quantity and quality of these data.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Convective energy transport in stellar atmospheres

The motion of convective cells in an environment which changes rapidly with depth is examined. In such an environment a cell may move through regions with different levels of ionization and with associated differences in heat capacity. The energy equation is cast in a manner which is independent of the history of these cells. The convective flux at a given level of the atmosphere is written as an average over an ensemble of cells originating at a range of other levels. A procedure for correcting the temperature gradient for these non-local effects is described and results for a model solar atmosphere are given. The principal results are: (1) The rms velocity varies smoothly and is non-zero well into the photosphere (e.g.,v _rsm=1.4 km/sec at =0.2); (2) Convective overshoot reduces the radiative flux to 60% and 90% of the total at =2.5 and 0.2 respectively; and (3) The interior adiabat of the convective envelope is less sensitive to the assumed value of the average cell size than in the usual treatment of convection.Supported in part by the National Science Foundation [GP-9433, GP-9114], the Office of Naval Research [Nonr-220(47)], and Air Force Grant AG-AFOSR-171-67.     

Diffusion of radiation in planetary atmospheres

The problem of interaction of the solar radiation with the turbid Earth atmosphere, containing complicated polydispersive aerosol systems, is discussed in this paper. Equations for computing the angular functions ofn-th order scattering are derived. On the basis of these functions the spectral radiance, radiation flows and radiation balance of the atmosphere in the short-wave spectral range are calculated. The relations obtained can be used to calculate the complex index of refraction, distribution function and other characteristics of the submicron aerosol fraction, by solving the inverse problems.