Diffuse reflection of line radiation from a semi-infinite turbulent atmosphere

The diffuse reflection of line radiation from a one dimensional semi-infinite turbulent atmosphere is examined in two limiting regimes of micro-and macroturbulence. Ambartsumyan’s invariance principle is used to solve this problem. In addition to the observed spectral line profile, statistical averages describing the diffusion process in the atmosphere (mean number of scattering events, average time spent by a photon in the medium) are determined. The dependence of these quantities on the average hydrodynamic velocity and scattering coefficient is studied. It is shown that in the microturbulent regime the intensity at the line center depends only slightly on the mean nonthermal velocity. In both regimes, photons in the far wings undergo scattering more frequently than in a static atmosphere, although they spend, on average, less time in the medium. __________ Translated from Astrofizika, Vol. 50, No. 3, pp. 391–403 (August 2007).     

On the atmosphere with exponential turbulence

We present an exact calculation for the photon-average bending angle and intensity produced during occultation of a point source by an isothermal atmosphere with an exponential height dependence of turbulent power. The calculation is performed via an expansion in powers of the gradients of average refractivity and turbulent power. Conditions for the validity of the expansion are discussed. We compare results with other expressions, for the same distribution of refractivity, recently presented by V. R. Eshleman and B. S. Haugstad. Discrepancies are noted. Certain properties of photon averages, which may be of importance for the reduction of occultation data, are discussed.     

Methane in Martian atmosphere: Average spatial, diurnal, and seasonal behaviour

A large number of spectra measured by the planetary Fourier spectrometer aboard the European Mars Express mission have been studied to identify the average properties of methane in the Martian atmosphere. Using the line at 3018 cm⁻¹, we have studied the seasonal, diurnal, and spatial variations of methane through the analysis of large averages of spectra (more than 1000 measurements). Methane mixing ratio has been obtained simultaneously with water vapour mixing ratio and water ice content, by best fitting (minimising the χ²) the computed averages with synthetic spectra. These spectra were computed for different values of the three parameters (methane and water vapour mixing ratio, and water ice optical depth).The methane mixing ratio shows a slow decrease from northern spring to southern summer with an average value of 14±5 ppbv (part per billion by volume) and it does not show a particular trend with latitude. The methane mixing ratio seems not to be uniform in longitude in the Martian atmosphere, as already reported by Formisano et al. [2004. Detection of methane in the atmosphere of Mars. Science 306, 1758-1761]. Two maxima are present at −40°E and +70°E longitude. In local time, the methane mixing ratio seems to follow the water vapour diurnal cycle. The most important point for future understanding is, however, that there are special orbits in which methane mixing ratio has a very high value.     

Albedo-shifting method: Source function in a plane atmosphere

A classical problem in the theory of radiative transfer is considered: calculating the radiation field within a plane scattering atmosphere. The recently proposed albedo-shifting method is used to calculate the source function both in a semi-infinite atmosphere and in an atmophere of finite optical depth, illuminated by parallel rays. The method enables one to “suppress” scattering and obtain iterative solutions of the integral equation for the source function in only a few direct lambda iterations, even when the average number of photon scatterings in the atmosphere is very large. Translated from Astrofizika, Vol. 42, No. 4, pp. 485–500, October–December, 1999.     

Statistics of the frequency redistribution for gyroresonance radiation in the atmospheres of compact stars

We analyze in detail the statistics of the frequency redistribution of photons during the transfer of gyroresonance radiation under conditions typical of compact stars. The probabilities of photon escape from a scattering atmosphere of arbitrary optical thickness in a single scattering have been found. The effects of gyroresonance photon diffusion in space and in frequency have been simulated. We show that when photons escape from a semi-infinite atmosphere with weak absorption, the frequency redistribution effects lead to a considerable increase in the probability of photon escape from large optical depths and, consequently, modify significantly the dynamics of gyroresonance photon transfer for neutron stars and white dwarfs.     

Photon path-length distribution function (II)

The determination of the photon path-length distribution function (PLDF) in a semi-infinite plane-parallel homogeneous atmosphere is discussed while the atmosphere scatters radiation according to the 2 × 2 Rayleigh-Cabannes phase matrix. The Piessens-Huysmans method of numerically inverting the Laplace transform which proved to be successful for the non-polarized radiation works in this special case as well. To employ this method we had to define the complex H-matrix and to find a fast method to determine its numerical values. For determining the average path-lengths and the dispersion we set up a system of integral equations the solution of which gave us the H-matrix and its first two derivatives with respect to the albedo of single scattering.The influence of different parameters characterizing the interaction of the polarized radiation with the atmosphere on the PLDF and the average path-length is studied in detail and a sample of average path-lengths is given in Table I.     

Radiative Transfer in Inhomogeneous Atmospheres. II

This paper is a continuation of a study of radiative transfer in one-dimensional inhomogeneous atmospheres. Two of the most important characteristics of multiple scattering in these media are calculated: the photon escape probability and the average number of scattering events. The latter is determined separately for photons leaving the medium and for photons that have undergone thermalization in the medium. The problem of finding the radiation field in an inhomogeneous atmosphere containing energy sources is also examined. It is assumed that the power of these sources, as well as the scattering coefficient, can vary arbitrarily with depth. It is shown that knowledge of the reflection and transmission coefficients of the atmosphere makes it possible to reduce all these problems to solving some first order linear differential equations with specified initial conditions. A series of new analytic results are obtained. Numerical calculations are done for two types of atmosphere with different depth dependences for the scattering coefficient. These are interpreted physically.     

Average photon path-length in isotropically scattering finite atmospheres

The determination of the average path-length of photons in a finite isotropically scattering plane-parallel homogeneous atmosphere is discussed. To solve this problem we have used the kernel approximation method which easily allows us to find the derivatives of the intensity with respect to optical depth, optical thickness and albedo of single scattering.In order to check the results we have used another approach by exploiting the set of integrodifferential equations of Chandrasekhar for theX- andY-functions. This approach allows us to find the average path length only at the boundaries of the atmosphere but on the other hand it gives also the dispersion of the path-length distribution function, thus generating the input parameters for determining the approximate path-length distribution function. It occurred that the set so obtained is stable and the results are highly accurate.As a by-product we obtain the first two derivatives of theX- andY-functions with respect to the albedo of single scattering and optical thickness, and the mixed derivative.     

Laser guide stars for extremely large telescopes: efficient Shack–Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm

Over the last few years increasing consideration has been given to the study of laser guide stars (LGS) for the measurement of the disturbance introduced by the atmosphere in optical and near-infrared (near-IR) astronomical observations from the ground. A possible method for the generation of a LGS is the excitation of the sodium layer in the upper atmosphere at approximately 90 km of altitude. Since the sodium layer is approximately 10 km thick, the artificial reference source looks elongated, especially when observed from the edge of a large aperture. The spot elongation strongly limits the performance of the most common wavefront sensors. The centroiding accuracy in a Shack–Hartmann wavefront sensor, for instance, decreases proportionally to the elongation (in a photon noise dominated regime). To compensate for this effect, a straightforward solution is to increase the laser power, i.e. to increase the number of detected photons per subaperture. The scope of the work presented in this paper is twofold: an analysis of the performance of the weighted centre of gravity algorithm for centroiding with elongated spots and the determination of the required number of photons to achieve a certain average wavefront error over the telescope aperture.     

Nonlinear equations for statistical averages describing processes of multiple scattering

The Lagrangian formalism is used to obtain nonlinear equations for frequently encountered statistical characteristics of radiative transfer. Under the assumption of complete frequency redistribution, the average number of scatterings and the average time of stay of a photon in a one-dimensional, semi-infinite atmosphere are analyzed. Two typical problems of multiple scattering are solved to illustrate the possible applications of the equations obtained. Translated from Astrofizika, Vol. 43, No. 3, pp. 463-471, July– September, 2000.     

The transmission to space of the light produced by lightning in the clouds of Venus

A Monte Carlo program by Thomason and Krider has been adapted to the Venus cloud geometry and optical properties. If lightning flashes occur within or just below the clouds, the fraction of photons of visible light escaping to space is 0.1–0.4, depending on the location of the flash. For flashes near the surface, only one blue photon in 10⁴ was found to escape; about 5% of the red ones are transmitted. Failure of the Pioneer Venus Orbiter to unambiguously detect optical lightning signals from space is not due to attenuation by the atmosphere and clouds. In any case, lightning is not acceptable as an explanation for ashen light.     

Photon path-length distribution function (I)

The determination of the photon path-length distribution function (PLDF) for the case of linearly anisotropic (Rocard) scattering in a semi-infinite plane-parallel homogeneous atmosphere using the Piessens-Huysmans method is described in detail. It has been shown that in this case the PLDF may have a minimum at small path-lengths — a feature which is never encountered in isotropic scattering. The respective regions with minima in the (µ, )-plane have been sorted out. As a rule, the average path-length in the case of the forward/backward Rocard scattering is larger/smaller than that in the isotropic case. The precise average path-lengths for a number of parameters are shown in Table I.     

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.     

Atmospheres and spectra of strongly magnetized neutron stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields     and effective temperatures     . The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free–free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron–ion plasma. Since the radiation emerges from deep layers in the atmosphere with     , plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature     around the ion cyclotron resonance     , where Z and A are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when     . Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.     

Elemental abundance analyses with DAO spectrograms — XVIII. The double-lined spectroscopic binary 46 Draconis

Equipartition magnetic fields can dramatically affect the polarization of radiation emerging from accretion disc atmospheres in active galactic nuclei. We extend our previous work on this subject by exploring the interaction between Faraday rotation and absorption opacity in local, plane-parallel atmospheres with parameters appropriate for accretion discs. Faraday rotation in pure scattering atmospheres acts to depolarize the radiation field by rotating the polarization planes of photons after last scattering. Absorption opacity in an unmagnetized atmosphere can increase or decrease the polarization compared to the pure scattering case, depending on the thermal source function gradient. Combining both Faraday rotation and absorption opacity, we find the following results. If absorption opacity is much larger than scattering opacity throughout the atmosphere, then Faraday rotation generally has only a small effect on the emerging polarization because of the small electron column density along a photon mean free path. However, if the absorption opacity is not too large and it acts alone to increase the polarization, then the effects of Faraday rotation can be enhanced over those in a pure scattering atmosphere. Finally, while Faraday rotation often depolarizes the radiation field, it can in some cases increase the polarization when the thermal source function does not rise too steeply with optical depth. We confirm the correctness of the analytic calculation by Silant'ev of the high magnetic field limit of the pure scattering atmosphere, which we incorrectly disputed in our previous paper.     

Turbulence in planetary occultations: III. Effects on atmospheric profiles derived from intensity measurements

The intensities of radio and optical signals observed during spacecraft and stellar occultations by planets scintillate due to atmospheric turbulence. The combined effect of turbulent fluctuations in refractivity and the average atmospheric gradient are found to produce slightly smaller signal intensity scintillations than the homogeneous case when there is no gradient, in contrast to a prediction that the scintillations would be markedly increased. Profiles of atmospheric temperature and pressure derived from intensity measurements are found to have much larger errors due to turbulence than do the corresponding profiles derived from radio Doppler frequency measurements. However, such errors are still small in the limit of weak scattering, which is assumed here. Radio and optical occultation experiments tend to be complementary since the generally shorter distances involved in the former mean that the radio experiments can probe relatively deeply into the atmosphere, while the optical experiments are limited to tenuous atmospheric regions. Because the radio experiments generally have a much greater dynamic measurement range, they are more likely to encounter conditions where strong scattering occurs than will the optical occultation experiments, provided the rms turbulent refractivity increases with depth approximately as the refractivity of the quiescent atmosphere.     

Mars' water isotope (D/H) history in the strata of the North Polar Cap: Inferences about the water cycle

A time varying stable isotope model for the D/H history of Mars water cycle is developed with variable atmosphere, space loss rate, ground and ice cap flux rates. It considers coupled ground reservoirs and traces D/H in the air and reservoirs secularly and over obliquity cycles. The various flux rates are prescribed time variables that simulate surface flux, and solar driven space loss rates. Predicted bulk averages for the ice cap, ground ice reservoirs and atmosphere span the observed ranges reported by Mumma et al. [Mumma, M.J., Novak, R.E., DiSanti, M.A., Bonev, B., Dello Russo, N., Magee-Sauer, K., 2003. The Martian Atmosphere. Conference Reports of “Sixth International Conference on Mars Atmosphere,” No. 3186]. When the dominant obliquity cycle variations are scaled so that the model delivers present seasonal variations, the present long term bulk D/H average for the ice cap is ∼+2.7 (equivalent to +1700‰ in δ(D) wrt SMOW). The obliquity driven D/H cycle in the ice cap's layers varies between 3 and 6. The smaller more accessible reservoirs have larger bulk averages with the smallest being able to reach D/H values over 9 within ∼¹⁰⁵ years. Small hypothetical solar activity driven variations in the escape rate to space and in the fractionation constant [Krasnopolsky, V.A., Feldman, P.D., 2001. Science 294, 1914-1917] for the escape process can produce a “solar wiggle” whose D/H amplitude can reach 0.1 (δ(D) amplitude of 100‰). Because of the temporal variability, a single modern measured atmospheric D/H ratio at a particular Ls cannot tell very much about the total water inventory of Mars. A bulk average for the Northern Ice Cap and better still a dated vertical profile of D/H from the ice cap would, however, go a long way towards illuminating the “modern” water history of Mars. The age and stability of the Northern Ice Cap and the D/H history locked in the layering is discussed. An ice cap that is very young and exchanges its mass through the atmosphere often will necessarily have a large D/H.     

On the efficiency of polarization measurements while studying aerosols in the terrestrial atmosphere

It has been shown that the orbital polarization measurements of the Earth in the spectral range λ > 300 nm do not allow the sets of the Stokes parameters satisfying the homogeneity requirement for the optical properties of the “atmosphere + surface” system to be retrieved. Due to this, the atmospheric and surface contributions cannot be correctly separated and the physical properties of the atmospheric aerosol cannot be determined. This is caused by the optical heterogeneity of the system, the different nature of aerosol above different relief features, and the poorly predictable temporal changes of the optical properties of the “atmosphere + surface” system. Observations at λ < 300 nm are more acceptable, since not only the surface but also the tropospheric layer of the atmosphere, which are both mostly subjected to the effects of horizontal inhomogeneity and temporal variations, become practically invisible due to a high absorption by the ozone layer. Because of this, from the scans along specified latitude zones, one may obtain the quasi-homogeneous dependences of the second Stokes parameter Q(α) (U(α) = 0) suitable for estimating the physical characteristics of the stratospheric aerosol and revealing their horizontal and temporal variations.