Latitudinal profile of UV nightglow and electron precipitations

We studied experimental data on ultra-violet (UV) nightglow in the wavelength range 300-400 nm, and energetic electron fluxes measured by low-altitude polar satellite Universitetskii-Tatiana. From statistical analysis we have found three latitudinal regions of enhanced UV emission at low, middle and high latitudes. Modeling the electron precipitations to the atmosphere gave numerical estimation of the generated UV radiation. We found that the stable and quasi-stable fluxes of electrons precipitating at middle and low latitudes are too weak to explain the observed intensities of UV radiation. The high-latitude UV nightglow with intensity of several kiloRayleighs results from particle precipitation in the regions of aurora and outer radiation belt. The low-latitude UV enhancements of several hundreds Rayleighs can be related to the emission of mesospheric atomic oxygen whose concentration increases substantially at latitudes from 20° to 40°. A mechanism of the mid-latitude UV enhancements is still unknown and requires further investigations.     

Curvature effects in extended stellar atmospheres — Pure absorption

The effects of curvature in an atmosphere with pure absorption are investigated. Numerical solution of the transfer equation has been obtained in the framework of the Discrete Space Theory of Radiative Transfer. Two cases have been considered: (a) the atmosphere is irradiated at the bottom and there is no incident radiation at the top of the atmosphere; and (b) no radiation is incident on either side of the atmosphere. It is found that the thermal sources inside the atmosphere dominantly influence the emergent radiation and this is very much so, in the spherical case and for large optical thickness. The emergent luminosities increase with the geometrical thickness although the emergent specific intensities are reduced and the former seems to be because of the larger surface area and later seems to be because of the effects of curvature.     

Exact solution of a simple time-dependent integro-differential equation by the method of Laplace transform and the theory of linear singular operators

The simplest form of the equation of transfer for a time dependent radiation field in finite atmosphere is considered. This equation of transfer is an integro-differential equation, the solution of this equation is based on the theory of separation of variables, the Laplace transform and the theory of linear singular operators. The emergent intensities from the bounding faces of the finite atmosphere are determined in terms ofX-Y equations of Chandrasekhar.     

Effects of Rayleigh-scattering polarization on reflected intensity: a fast and accurate approximation method for atmospheres with aerosols

Solar radiation reflected by the atmospheres of Neptune and Uranus is dominated by Rayleigh scattering at visible wavelengths, and thus subject to the effects of polarization. Ignoring these effects can lead to errors in reflected intensity of more than 9% in a clear atmosphere. But solving the full vector equation of transfer is computationally very costly, forcing approximations with limitations that are not well understood and not generally applicable to spatially resolved observations and complex atmospheric structures. Using accurate vector radiation transfer calculations, it is here shown that differences between vector and scalar results near zero phase angle have systematic dependencies on optical depth, single scattering albedo, and angle, that provide a basis for accurate approximation of the reflected intensities. With little computational cost, it is possible to calculate corrected spatially resolved scalar intensities that closely match vector intensities, with individual errors rarely exceeding 1%, and mean and RMS errors generally within a few tenths of 1%. The correction method accounts for the attenuating effects of clouds and molecular absorption.     

Argon in the Martian atmosphere: Do the results of Mars 6 agree with the optical and radio occultation measurements?

Mars 6 discovered an inert gas (probably argon) in the Martian atmosphere. An analysis is carried out for the available spectroscopic observations, radio occultation results, and other data with the aim of determining the maximum argon content with which they are consistent. Possible seasonal variations of pressure are taken into account. It is shown that 25–30% of argon is consistent with all these data. The presence of argon slightly increases the mean pressure estimates; 25% argon increases pressures derived from radio occultation data by 0.5 mbar.     

Average photon path-length of radiation emerging from finite atmospheres

The determination of the average path-length of photons emerging from a finite planeparallel atmosphere with molecular scattering is discussed. We examine the effects of polarisation on the average path-length of the emergent radiation by comparing the results with those obtained for the atmosphere where the scattering obeys the scalar Rayleigh function. Only the axial radiation field is considered for both cases.To solve this problem we have used the integro-differential equations of Chandrasekhar for the diffuse scattering and transmission functions (or matrices). By differentiation of these equations with respect to the albedo of single scattering we obtain new equations the solution of which gives us the derivatives of the intensities of the emergent radiation at the boundaries.As in the case of scalar transfer the principles of invariance by Chandrasekhar may be used to find an adding scheme to obtain both the scattering and transmission matrices and their derivatives with respect to the albedo of single scattering. These derivatives are crucial in determining the average path length.The numerical experiments have shown that the impact of the polarisation on the average pathlength of the emergent radiation is the largest in the atmospheres with optical thickness less than, or equal to, three, reaching 6.9% in the reflected radiation.     

Polarization of the atmosphere as a foreground for cosmic microwave background polarization experiments

We quantify the level of polarization of the atmosphere due to Zeeman splitting of oxygen in the Earth’s magnetic field and compare it to the level of polarization expected from the polarization of the cosmic microwave background radiation. The analysis focuses on the effect at mid-latitudes and at large angular scales. We find that from stratospheric balloon borne platforms and for observations near 100 GHz the atmospheric linear and circular polarized intensities are about 10⁻¹² and 100 × 10⁻⁹ K, respectively, making the atmosphere a negligible source of foreground. From the ground the linear and circular polarized intensities are about 10⁻⁹ and 100 × 10⁻⁶ K, making the atmosphere a potential source of foreground for the CMB E (B) mode signal if there is even a 1% (0.01%) conversion of circular to linear polarization in the instrument.     

Time-dependent scattering and transmission function in an anisotropic two-layered atmosphere

In this paper we consider the time-dependent diffuse reflection and transmission problems for a homogeneous anisotropically-scattering atmosphere of finite optical depth and solve it by the principle of invariance. Also we consider the time-dependent diffuse reflection and transmission of parallel rays by a slab consisting of two anisotropic homogeneous layers, whose scattering and transmission properties are known. It is shown how to express the time-dependent reflected and transmitted intensities in terms of their components. In a manner similar to that given by Tsujita (1968), we assumed that the upward-directed intensities of radiation at the boundary of the two layers are expressed by the sum of products of some auxiliary functions depending on only one argument. Then, after some analytical manipulations, three groups of systems of simultaneous integral equations governing the auxiliary functions are obtained.     

Reflection effect in close binaries. IV. Limb darkening of the reflected radiation incident from an extended surface of the secondary

The law of limb darkening has been calculated when the atmosphere of the primary component is illuminated by the extended surface of the secondary component in a binary system. The specific intensities calculated at infinity show marked changes when the plane-parallel approximation is replaced by the assumption of spherical symmetry. The middle portions of the illuminated surface reflect maximum radiation while the innermost and outermost layers show lesser amount of reflected radiation.     

Twilight effects of solar ionizing radiation

The absorption of solar ionizing radiation during twilight is investigated. Ion production rates are obtained as a function of altitude and twilight intensities and altitude profiles of emissions arising from the fluorescence of solar ionizing radiation are calculated for various solar depression angles. For an atmosphere with an exospheric temperature of 750°K, the predicted overhead intensity from fluorescence of the O⁺(²P — ²D) lines at 7319–7330 diminishes from 175 R at dusk to 10 R at a solar depression angle of 10°. The predicted overhead intensities from fluorescence of the N₂⁺ Meinel and first negative systems are respectively about 175 R and 20 R at dusk diminishing to respectively 1.5 R and 0.1 R at a solar depression angle of 10°.

It is suggested that a charge transfer reaction of O⁺²D in N₂ is a significant source of N₂⁺ ions. This reaction offers a possible explanation for the high apparent rotational temperatures in the first negative system observed by Broadfoot and Hunten. Other excitation and ionization mechanisms are briefly discussed.     

Source and maintenance of the argon atmospheres of Mercury and the Moon

Abstract— We propose that argon‐40 measured in the lunar atmosphere and that in Mercury's atmosphere is due to current diffusion into connected pore space within the crust. Higher temperatures at Mercury, along with more rapid loss from the atmosphere, will lead to a similar or smaller column abundance of argon at Mercury than at the Moon, given the same crustal abundance of potassium. Because the noble gas abundance in the mercurian atmosphere represents current effusion, it is a direct measure of the crustal potassium abundance. We assume a fractal distribution of distance to a connected pore space, with the shortest distance increasing with depth. Given this “rock size” distribution, we show that the diffusive flux is not a unique function of temperature. Even though the diffusion coefficient is an exponential function of temperature, the flux to the surface is fairly insensitive to the temperature.     

A method of computing the emergent radiation by the atmosphere in the region ranging from ultraviolet to infrared

A method of computing the diffuse reflection and transmission radiation by an inhomogeneous, plane-parallel planetary atmosphere with internal emission source is discussed by use of the adding method. If the atmosphere is simulated by a number of homogeneous sub-layers, the radiation diffusely reflected or transmitted by the atmosphere can be expressed in terms of the reflection and transmission matrices of the radiation of sub-layers. The diffusely transmitted radiation due to the internal emission source can be also easily computed in the same manner. These equations for the emergent radiation are in a quite general form and are applicable to radiative transfer in the atmosphere in the region from ultraviolet to infrared radiation. With this method, the tiresome treatment due to the polarity effect of radiation is overcome.     

Auroral emission at 1084 Å

Calculations are presented of the auroral emission of a line at 1084 Å of ionized atomic nitrogen that arises from electron impact induced simultaneous ionization and dissociation of molecular nitrogen. For an aurora of IBC Class II+, we predict 330 R of 1084 Å. Estimates are also presented of the intensities of the argon lines at 1048 and 1067 Å.     

Reflection effect in close binaries. I. Distribution of radiation from a point source

The radiation field along an irradiated surface of a component in a binary system is calculated. The source of irradiation is assumed to be a point source. This is done primarily to understand easily how the incident radiation will get changed after it is being scattered by the atmosphere. It is noticed that the maximum radiation comes from intermediate points of the atmosphere, the reason being that here we have the combined radiation due to the star and incident radiation from the point source outside the star although both are diluted.     

Polarization effect on radiative transfer in planetary composite atmospheres with interacting interface

A procedure of computing the radiance and the polarization parameters of radiation diffusely reflected and transmitted by an inhomogeneous, plane-parallel terrestrial atmosphere bounded by a ruffled ocean surface is discussed with the aid of the adding method. If the atmosphere and the ocean are simulated by a number of homogeneous sublayers, the matrices of radiation reflected and transmitted diffusely by the atmosphere-ocean system can be expressed in terms of these matrices of sublayers by using only a couple of iterative equations in which the polarity effect of radiation is included. Furthermore, the upwelling radiance and the polarization degree of radiation at the top of the atmosphere can be calculated by using a single iterative equation without requiring the equation for the diffuse transmission matrix of radiation. The ruffled ocean surface can be treated as an interacting interface, where the transmitted radiation from beneath the ocean surface into the atmosphere is also taken into account into the derivation of equations. Finally, sample computations of the upwelling radiance and the polarization degree of radiation from the top of the atmosphere are carried out at the wavelength of 0.60 micron.     

Radiative Transfer in Inhomogeneous Atmospheres. I

This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres.     

Effect of continuum absorption on the polarization of resonance lines

Multiple resonance scattering of radiation in a spectrum line with absorption in the continuum is examined. It is assumed that the scattering atmosphere is semi-infinite and that there is no magnetic field or continuum emission at the frequencies of the spectrum line. The polarization characteristics of the emerging radiation are determined for unpolarized primary radiation sources distributed uniformly within an atmosphere in the case of a Voigt absorption profile. The calculations employ an iterative solution of the Ambartsumyan-Chandrasekhar matrix integral equation.     

Argon in the Martian atmosphere: Evidence from the Mars 6 descent module

In the descent of the automatic interplanetary station Mars 6, after parachute deployment, an analysis was carried out by means of a mass spectrometer, the analyzer of which was pumped out by a getter-ion pump. Unfortunately, mass spectra were not obtained. But during vehicle descent on a parachute tether, the pump discharge current was registered. The dynamics of the pump current at the end of descent operations imply that an inert gas is a basic component of the Martian atmosphere, along with CO₂. Laboratory post-experiment calibrations of other getter-ion pumps, performed with various mixtures of CO₂ and argon, result in a probable value of the argon content in the Martian atmosphere of 35 ± 10% by volume.     

Formation of the lunar atmosphere

Measurements of⁴⁰Ar and helium made by the Apollo 17 lunar surface mass-spectrometer are used in the synthesis of atmospheric supply and loss mechanisms. The argon data indicate that about 8% of the⁴⁰Ar produced in the Moon due to decay of⁴⁰K is released to the atmosphere and subsequently lost. Variability of the atmospheric abundance of argon requires that the source be localized, probably in an unfractionated, partially molten core. If so, the radiogenic helium released with the argon amounts to 10% of the atmospheric helium supply. The total rate of helium escape from the Moon accounts for only 60% of the solar windα particle influx. This seems to require a nonthermal escape mechanism for trapped solar-wind gases, probably involving weathering of exposed soil grain surfaces by solar wind protons.     

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.