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.     

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.     

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.     

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.     

Impact erosion of planetary atmospheres

The impact of a large extraterrestrial body onto a planet deposits considerable energy in the atmosphere. If the radius of the impactor is much larger than an atmospheric scale height and its velocity much larger than the planetary escape velocity, some of the planetary atmosphere may be driven off into space. The process is analyzed theoretically in this paper. The amount of gas that escapes is equal to the amount of gas intercepted by the impacting body multiplied by a factor not very different from unity. Escape occurs only if the velocity of the impacting body exceeds the planetary escape velocity. At large impact velocities the enhancement factor, which is the factor multiplying the amount of atmosphere intercepted by the impacting body, approaches a constant value approximately equal to 10¹²/V_e², where V_e is the escape velocity (in cm/sec). The enhancement factor is independent of atmospheric mass or surface pressure. Ablation of the impacting body and the planetary surface adds to the mass of gas that must be accelerated into space if escape is to occur. As a result, impact erosion of the atmosphere does not occur from a planet with an escape velocity in excess of 10 km/sec.     

Formulation of molecular diffusion in planetary atmospheres

We report on a formulation of molecular diffusion for ionized multi-component atmospheres that is valid in the diffusion and small electron mass limits. The formulation is based on the construction of successive approximations of the diffusion matrix by means of the projective iterative algorithm of Ern and Giovangigli [Projected iterative algorithms with application to multicomponent transport. Lin. Alg. and its Appl. 250, 289–315], and allows naturally for different temperatures for the neutral, ion and electron constituents of the gas. The reported expressions incorporate the effect of electric forces preventing charge separation, are explicit in the driving forces and mass conservative. Yet approximate, their accuracy can be easily tested and improved upon by going to a higher approximation of the diffusion matrix. We have illustrated the formulation with a model that solves the composition of Mars’ atmosphere. The continuity equations of the model are linearized and marched in time with an implicit numerical scheme, allowing thus for large time steps. It is found that the first and second approximations of the diffusion matrix are probably optimal trade-offs between computational cost and accuracy. Finally, the formulation is tested against more conventional approximations of the molecular diffusion velocities of neutral and ion species, showing the importance of the various assumptions that may restrict their applicability.     

Spectroscopy of planetary atmospheres in our Galaxy

About 20 years after the discovery of the first extrasolar planet, the number of planets known has grown by three orders of magnitude, and continues to increase at neck breaking pace. For most of these planets we have little information, except for the fact that they exist and possess an address in our Galaxy. For about one third of them, we know how much they weigh, their size and their orbital parameters. For less than 20, we start to have some clues about their atmospheric temperature and composition. How do we make progress from here?We are still far from the completion of a hypothetical Hertzsprung–Russell diagram for planets comparable to what we have for stars, and today we do not even know whether such classification will ever be possible or even meaningful for planetary objects. But one thing is clear: planetary parameters such as mass, radius and temperature alone do not explain the diversity revealed by current observations. The chemical composition of these planets is needed to trace back their formation history and evolution, as happened for the planets in our Solar System. As in situ measurements are and will remain off-limits for exoplanets, to study their chemical composition we will have to rely on remote sensing spectroscopic observations of their gaseous envelopes.In this paper, we critically review the key achievements accomplished in the study of exoplanet atmospheres in the past ten years. We discuss possible hurdles and the way to overcome those. Finally, we review the prospects for the future. The knowledge and the experience gained with the planets in our solar system will guide our journey among those faraway worlds.     

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.     

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.     

Effective depth of spectral line formation in planetary atmospheres

The effective level of line formation for spectroscopic absorption lines has long been regarded as a useful parameter for determining average atmospheric values of the quantities involved in line formation. The identity of this parameter has recently been disputed. Here we reestablish the dependence of this parameter on the average depth at which photons are absorbed in a semi-infinite atmosphere and show that the mean depths derived by others are similar in nature and behavior.     

Circular polarization of sunlight reflected by planetary atmospheres

Multiple scattering calculations are performed in order to investigate the nature of the circular polarization of sunlight reflected by planetary atmospheres. Contour diagrams as a function of size parameter and phase angle are made for the integrated light from a spherical but locally plane-parallel atmosphere of spherical particles. To investigate the origin of the circular polarization, results are also computed for second-order scattering and for a simpler semiquantitative model of scattering by two particles. Observations of the circular polarization of the planets are presently too meager for accurate deduction of cloud particle properties. However, certain very broad constraints can be placed on the properties of the dominant cloud particles on Jupiter and Saturn. The cloud particle size and refractive index deduced for the Jupiter clouds by Loskutov, Morozhenko, and Yanovitskii from analyses of the linear polarization are not consistent with the circular polarization. The few available circular polarization observations of Venus are also examined.     

Negative ions in the ionospheres of planetary bodies without atmospheres

Negative ions may be formed in the ionospheres of Mercury, the Moon and Jupiter's satellites with densities about a few % of the ionospheric electron density. The negative ions are produced by three mechanisms at the planetary surface: charge inversion during energetic proton scattering, with simultaneous secondary negative ion emission, and micrometeorite impacts. The density and distribution of negative ions around planetary bodies depends primarily upon the negative ion life-times determined by photodetachment by solar radiation.     

A simple expression for vertical convective fluxes in planetary atmospheres

We explore the vertical convective flux F_c in a radiative-convective grey atmosphere. An expression of the form F_c=F_sτ_o/(C+Dτ_o) appears useful, where F_s is the shortwave flux absorbed at the base of an atmosphere with longwave optical depth τ_o and C and D are constants. We find excellent agreement with an idealized grey radiative-convective model with no shortwave absorption for D=1 and C=1∼2 depending on the surface-atmosphere temperature contrast and on the imposed critical lapse rate. Where shortwave absorption is correlated with longwave opacity, as in the atmospheres of Earth and Titan, C=2, D=2 provides an excellent fit, validated against the present terrestrial situation and the results of a nongrey model of Titan's strongly antigreenhouse atmosphere under a wide range of conditions. The expression may be useful for studying the energetics of planetary climates through time where there is insufficient data to constrain more elaborate models.     

Hydrogen collisions in planetary atmospheres, ionospheres, and magnetospheres

Hydrogen is the most abundant element in the universe. Molecular hydrogen is the dominant chemical species in the atmospheres of the giant planets. Because of their low masses, neutral and ionized hydrogen atoms are the dominant species in the high atmospheres of many planets. Finally, protons are the principal heavy component of the solar wind.Here we present a critical evaluation of the current state of understanding of the chemical reaction rates and collision cross sections for several important hydrogen collision processes in planetary atmospheres, ionospheres, and magnetospheres. Accurate ab initio quantum theory will play an important role. The collision processes are grouped as follows:

(a)

H⁺+H charge transfer,

(b)

H⁺+H₂(v) charge transfer and vibrational relaxation, and

(c)

H₂(v,J)+H₂ vibrational, rotational, and ortho-para relaxation.

In each case we provide explicit representations as tabulations or compact formulas. Particularly important conclusions are that H⁺+H₂(v) collisions are more likely to result in vibrational relaxation than charge transfer and H₂ ortho-para conversion is at least an order-of-magnitude faster than previously assumed.     

Solar photo rates for planetary atmospheres and atmospheric pollutants

Unattenuated solar photo rate coefficients and excess energies for dissociation, ionization, and dissociative ionization are presented for atomic and molecular species that have been identified or are suspected to exist in the atmospheres of planets, satellites (moons), comets, or as pollutants in the Earth atmosphere. The branching ratios and cross sections with resonances have been tabulated to the greatest detail possible and the rate coefficients and excess energies have been calculated from them on a grid of small wavelength bins for the quiet and the active Sun at 1 AU heliocentric distance.     

Evaporation of ice in planetary atmospheres: Ice-covered rivers on mars

The evaporation rate of water ice on the surface of a planet with an atmosphere involves an equilibrium between solar heating and radiative and evaporative cooling of the ice layer. The thickness of the ice is governed principally by the solar flux which penetrates the ice layer and then is conducted back to the surface. These calculations differ from those of Lingenfelter et al. [(1968) Science161, 266–269] for putative lunar channels in including the effect of the atmosphere. Evaporation from the surface is governed by two physical phenomena: wind and free convection. In the former case, water vapor diffuses from the surface of the ice through a lamonar boundary layer and then is carried away by eddy diffusion above, provided by the wind. The latter case, in the absence of wind, is similar, except that the eddy diffusion is caused by the lower density of water vapor than the Martian atmosphere. For mean Martian insolations the evaporation rate above the ice is ～ 10^?8 g cm^?2 sec^?1. Thus, even under present Martian conditions a flowing channel of liquid water will be covered with ice which evaporates sufficiently slowly that the water below can flow for hundreds of kilometers even with quite modest discharges. Evaporation rates are calculated for a wide range of frictional velocities, atmospheric pressures, and insolations and it seems clear that at least some subset of observed Martian channels may have formed as ice-choked rivers. Typical equilibrium thicknesses of such ice covers are ～ 10 to 30 m; typical surface temperatures are 210 to 235°K. Ice-covered channels or lakes on Mars today may be of substantial biological interest. Ice is a sufficiently poor conductor of heat that sunlight which penetrates it can cause melting to a depth of several meters or more. Because the obliquity of Mars can vary up to some 35°, the increased polar heating at such times seems able to cause subsurface melting of the ice caps to a depth which corresponds to the observed lamina thickness and may be responsible for the morphology of these polar features.     

Thermal equilibrium and hydrostatic equilibrium for excited states in planetary atmospheres

Thermal equilibrium and hydrostatic equilibrium are mutually exclusive for any particular quantum state of an atmospheric constituent in a non-isothermal atmosphere. As a result, there is a flux of rotationally, vibrationally, and electronically excited atoms and molecules down the temperature gradient, balanced by an up-gradient transport of ground-state atoms and molecules, resulting in a net transport of excitation energy, but with no net mass transport. The energy flux is first formulated as a molecular process and applied to vibrationally excited molecular nitrogen and rotationally excited atomic oxygen in the Earth's lower thermosphere, then reformulated as a bulk process and applied to the Venusian atmosphere, where it is shown that the CO₂ vibrational flux is a significant contribution to the total eddy energy flux in the 0–60 km region.