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1.
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.  相似文献   

2.
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.  相似文献   

3.
A generalized principle of invariance is derived for a plane-parallel atmosphere. On the basis of this principle a method for determining the radiation field in a multilayer atmosphere is proposed. This method, the first part of which is the well-known adding method, permits the application to problems involving optically finite as well as semi-infinite atmospheres. The reflecting boundaries may be incorporated, though in that case it is not possible to use the adding method.Some numerical results are given for the standard and Milne problems and for the problem with internal sources.  相似文献   

4.
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.  相似文献   

5.
An efficient methodical approach is proposed to the study of pulsation-type motions in the atmospheres of hot stars. Several well-studied stars are used as examples to demonstrate the appropriateness of the method, which allows to study in detail the kinematics of the atmosphere and do asteroseismological forecasts. This approach makes it possible to separately analyze different kinematics of the rising and falling layers of the stellar atmosphere, and to spectroscopically reveal different rotation of the star if such is the case. The differential rotation of atmospheric layers of HD 93521 is confirmed by the model computations.  相似文献   

6.
A numerical solution to the integral equation for radiative transfer by resonance reradiation in an isothermal spherical atmosphere is described. The method presented is 100 times more efficient than earlier spherical radiative transfer models. The new model can accommodate density variations in the full three dimensional space and includes effects due to the presence of pure absorbers. Complete frequency redistribution is assumed for photon scattering. Applications of this model to the problem of solar photons scattered by atomic hydrogen in the atmospheres of Venus, Earth and Mars are described, and limb and disk profiles, as well as equivalent mean disk intensities for Venus, Earth and Mars, are presented.  相似文献   

7.
The formation of spectral lines in a turbulent atmosphere with a spatially correlated velocity field is examined. A new approach for solving this problem is proposed which is not based on the Fokker-Planck formalism. The invariant imbedding method makes it possible to reduce the problem of finding the mean radiant intensity observed in a line to solving a system of differential equations. This possibility is based on determining the mean intensity of the radiation emerging from the medium for a fixed value of the turbulent velocity at its boundary. A separate integral equation is derived for this quantity. The dependence of the line profile, integrated intensity, and width on the mean correlation length and the average value of the hydrodynamic velocity is studied. It is shown that the transition from a microturbulent regime to a macroturbulent regime occurs within a comparatively narrow range of variation in the correlation length. The proposed method yields a solution to the problem for a family of inhomogeneous atmospheres with different optical thicknesses, which makes it easy to determine the radiation field inside the turbulent medium. This approach can be generalized in various ways, in particular, it can be applied without significant changes to the case where the correlation length depends on position within the atmosphere. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 219–232 (May 2007).  相似文献   

8.
Shved  G. M.  Semenov  A. O. 《Solar System Research》2001,35(3):212-226
The standard problem of radiative transfer in a rovibrational band is formulated for an optically semi-infinite plane-parallel planetary atmosphere using a model of a linear molecule with two vibrational states. The solution of the problem describes the variation with height of the population of the excited vibrational state due to the existence of the upper boundary of the atmosphere. We seek this solution as a function of the specially introduced dimensionless parameters—the atmosphere depth and four similarity parameters—and study it for the parameter values that can be realized in the planetary atmospheres, including the atmospheres of extrasolar planets. It is shown that an increase in the optical density of the atmosphere can reduce the population of an excited vibrational state in the band at the upper boundary of the atmosphere by as much as several orders of magnitude as compared to the population corresponding to the optically thin band limit. The anomalous decrease in the opacity of the atmosphere, when only several lines of the band are involved in radiative transfer, is predicted. We also determined the accuracy of calculating the population in the approximation of the Doppler line profile. An approximate formula is obtained for the dimensionless height of the boundary of the layer in which the local thermodynamic equilibrium exists for vibrational states. We propose a model and the formula following from this model to roughly evaluate the decrease in this height due to the impact on the population of additional radiative transitions between the state being considered and the underlying state belonging to another vibrational mode of the molecule.  相似文献   

9.
In this paper we have endeavored to critically evaluate our present understanding of cometary atmospheres. Following a brief introduction of the significance of the study of cometary atmospheres (Section 1), the relevant photometric and spectroscopic observations are summarized in Section 2.The interaction with the solar radiation, with regard to both the excitation of the observed species as well as the dissociation of stable molecules evaporating from the nucleus, is considered in Sections 3 and 4. The gas phase chemistry likely to take place in the dense inner coma is next considered in Section 5.The exospheric and hydrodynamic models of the expanding cometary atmosphere are considered in detail in Section 6, and both their limitations as well as possible improvements are discussed.The observed chemical composition of the neutral atmosphere and the inferred chemical composition of the volatile component of the nucleus, together with possible variations between different classes of comets is next considered in Section 7, and their possible cosmogonic significance is discussed.In conclusion, some of the important directions in which future research should progress, in order to provide more complete and secure knowledge of cometary atmospheres, are stressed (Section 8).Astrophysics and Space Science Review Paper.  相似文献   

10.
Data on the low-temperature (< 200 K) dependence of the kinetics of chemical reactions are of great importance for understanding the composition of planetary atmospheres (as well as interstellar clouds). To date such studies have been relatively rare but the situation is beginning to change. During the past 10 years a number of experimental instruments have been designed to address this problem. These instruments rely on either cryogenic or supersonic cooling, and both methods have been applied to the study of neutral-neutral or ion-neutral reactions. We briefly review these different techniques, with an emphasis on the CRESU method, and provide examples of the types of reactive systems that have been studied, with particular attention to those relevant to the atmosphere of Titan. The perspectives for future work are also evoked.  相似文献   

11.
Despite recent progress in the modeling of alkali atmospheres like those around the Moon and Mercury, many problems still exist. It is proposed that Rydberg Matter (RM) clusters containing Na and K atoms are the main part of the alkali atmospheres of the Moon and Mercury, forming large clouds. RM clusters are studied in the laboratory with laser fragmentation and laser spectroscopy methods. Due to the very large collision cross sections of Rydberg atoms and RM clusters, the atmospheres are not collision free, as normally assumed based on the low densities of free alkali atoms. The non-escaping radial density variation for the Na atoms, observed, e.g., on the Moon, and the Maxwellian velocity distributions observed on Mercury are caused by a true atmosphere with collisional equilibration; this process is not possible in an exosphere. Fast alkali atoms are released from the RM clusters already at large heights by solar photons and charged particle impact. The kinetic temperatures derived for the atmospheres agree with the quantized energy release. The cluster model predicts that the rate of loss from the surface is much smaller than for a purely atomic model, since the transient storage is in the RM cluster form in the atmosphere and not at the surface. The conductance of the atmosphere is of the order of 100 S due to the facile collisional ionization of the RM clusters. The apparent depletion of K in the atmosphere of Mercury is explained.  相似文献   

12.
T L Schindler  J F Kasting 《Icarus》2000,145(1):262-271
NASA's proposed Terrestrial Planet Finder, a space-based interferometer, will eventually allow spectroscopic analyses of the atmospheres of extrasolar planets. Such analyses would provide information about the existence of life on these planets. One strategy in the search for life is to look for evidence of O3 (and hence O2) in a planet's atmosphere; another is to look for gases that might be present in an atmosphere analogous to that of the inhabited early Earth. In order to investigate these possibilities, we have calculated synthetic spectra for several hypothetical terrestrial-type atmospheres. The model atmospheres represent four different scenarios. The first two, representing inhabited terrestrial planets, are an Earth-like atmosphere containing variable amounts of oxygen and an early Earth-type atmosphere containing methane. In addition, two cases representing Mars-like and early Venus-like atmospheres were evaluated, to provide possible "false positive" spectra. The calculated spectra suggest that ozone could be detected by an instrument like Terrestrial Planet Finder if the O2 concentration in the planet's atmosphere is > or = 200 ppm, or 10(-3) times the present atmospheric level. Methane should be observable on an early-Earth type planet if it is present in concentrations of 100 ppm or more. Methane has both biogenic and abiogenic sources, but concentrations exceeding 1000 ppm, or 0.1% by volume, would be difficult to produce from abiogenic sources alone. High methane concentrations in a planet's atmosphere are therefore another potential indicator for extraterrestrial life.  相似文献   

13.
A review of non-local, deep transport mechanisms in the atmosphere of Earth provides a good foundation for examining whether similar mechanisms are operating in the atmospheres of Mars and Titan. On Earth, deep convective clouds in the tropics constitute the upward branch of the Hadley Cell and provide a conduit through which energy, moisture, momentum, aerosols, and chemical species are moved from the boundary layer to the upper troposphere and lower stratosphere. This transport produces mid-tropospheric minima in quantities such as water vapor and moist static energy and maxima where the clouds detrain. Analogs to this terrestrial transport are found in the strong and deep thermal circulations associated with topography on Mars and with Mars dust storms. Observations of elevated dust layers on Mars further support the notion that non-local deep transport is an important mechanism in the atmosphere of Mars. On Titan, the presence of deep convective clouds almost assures that non-local, deep transport is occurring and these clouds may play a role in global cycling of energy, momentum, and methane. Based on the potential importance of non-local deep transport in Earth's atmosphere and supported by evidence for such transport in the atmospheres of Mars and Titan, greater attention to this mechanism in extraterrestrial atmospheres is warranted.  相似文献   

14.
We present radiation transfer models that demonstrate that reflected light levels from 3D exoplanetary atmospheres can be more than 50 per cent lower than those predicted by models of homogeneous or smooth atmospheres. Compared to smooth models, 3D atmospheres enable starlight to penetrate to larger depths resulting in a decreased probability for the photons to scatter back out of the atmosphere before being absorbed. The increased depth of penetration of starlight in a 3D medium is a well-known result from theoretical studies of molecular clouds and planetary atmospheres. For the first time we study the reflectivity of 3D atmospheres as a possible explanation for the apparent low geometric albedos inferred for extrasolar planetary atmospheres. Our models indicate that 3D atmospheric structure may be an important contributing factor to the non-detections of scattered light from exoplanetary atmospheres. We investigate the self-shadowing radiation transfer effects of patchy cloud cover in 3D scattered light simulations of the atmosphere of HD 209458b. We find that, for a generic planet, geometric albedos can be as high as 0.45 in some limited situations, but that in general the geometric albedo is much lower. We conclude with some explanations on why extrasolar planets are likely dark at optical wavelengths.  相似文献   

15.
《Planetary and Space Science》2007,55(10):1470-1489
Uncertainties carried by the different kinetic parameters included in photochemical models of planetary atmospheres have rarely been considered even if they are supposed to be contributing mostly to the inconsistencies between observations and computed predictions. In this paper, we report the first detailed analysis of the propagation of uncertainties carried by the reaction rate coefficients included in an up-to-date photochemical model of Titan's atmosphere. Monte Carlo calculations performed on these reaction rate coefficients have been used to introduce their uncertainties and to investigate their significance on the photochemical modeling of Titan's atmosphere. Crude approximations in the implemented physical processes have been adopted to limit the number of free parameters. This allows us to pinpoint specifically the importance of chemical processes uncertainties in Titan's photochemical models and to evaluate their chemical robustness. First implications of this preliminary study related to purely chemical rate coefficient uncertainties are discussed. They are important enough to question indeed any comparisons between theoretical models with observations as well as any potential conclusions subsequently inferred. Since the latest missions, such as Cassini–Huygens, are likely to induce an ever-increasing interest for such kind of comparing studies, our conclusions show that it is crucial to reform the way we think of, and use, current photochemical models to understand the processes occurring in the atmospheres of the outer Solar System.  相似文献   

16.
The model of the standard problem of radiative transfer in a vibrational–rotational band that we suggested previously (Shved and Semenov, 2001) for a nonlocal thermodynamic equilibrium (non-LTE) in vibrational molecular states is used to study the populations of these states in a nonisothermal planetary atmosphere. The temperature profile in the atmosphere is specified as a temperature perturbation in the form of a Gaussian function that is superimposed on an isothermal atmosphere. We show that the temperature profile has a complex effect on the state populations, which makes it difficult to analytically represent this effect. We investigate the influence of the peculiar features of the temperature profile in an LTE layer on the non-LTE height and suggest a criterion for determining those features that weakly affect this height. Using the populations of the CO2 0110 and 0001 states in the atmospheres of the Earth and Mars as examples, we show that the formulas suggested for estimating the non-LTE height are efficient.  相似文献   

17.
By using a non-local convection theory, both the local and nonlocal convective envelope models of evolutionary series of stars with masses from 1 to 30 solar masses are calculated. The problem of supersonic convection is reviewed. The results show that the convective velocities in the stellar atmosphere are seriously overestimated by the local mixing-length theory. Convection is strongly supersonic in the atmospheres of yellow giant and super-giants, while the local mixing-length theory is used. However, it becomes subsonic for most stars when convection returns to the normal nonlocal treatment. Convection velocities increase with increase of luminosities of stars. There is still weak supersonic convection in few red and yellow giant and super-giants. It is suspected whether this supersonic convection in stellar atmospheres is true.  相似文献   

18.
A simple steady-state photochemical model is developed in order to determine typical molecular oxygen concentrations for a comprehensive range of primitive abiotic atmospheres. Carbon dioxide is assumed to be the dominant constituent in these atmospheres since CO2 photodissociation may potentially result in the enhancement of the O2 partial pressure. The respective effects of the H2O content, temperature, eddy diffusion coefficient and UV flux on the results are investigated. It is shown that for any pressure at the surface, the partial pressure of molecular oxygen does not exceed 10 mbar. The peculiar case of a runaway greenhouse which has possibly taken place on Venus is qualitatively envisaged. Although O2 is basically absent in the present Venus atmosphere, a transient presence in a primitive stage cannot be ruled out. Possible mechanisms for O2 removal in such an atmosphere are reviewed. At the present stage, we think that the detection of large O2 amounts would be at least a good clue for the presence of life on an extrasolar planet.  相似文献   

19.
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.  相似文献   

20.
R.J. de Kok  D.M. Stam 《Icarus》2012,221(2):517-524
The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scattering particles. Here, we present results of calculations with a three-dimensional Monte Carlo code that simulates the transmitted flux during occultations or transits. For isotropically scattering particles, like gas molecules, the transmitted flux appears to be well-described by the total atmospheric optical thickness. Strongly forward-scattering particles, however, such as commonly found in atmospheres of Solar System planets, can increase the transmitted flux significantly. For exoplanets, such added flux can decrease the apparent radius of the planet by several scale heights, which is comparable to predicted and measured features in exoplanet transit spectra. We performed detailed calculations for Titan’s atmosphere between 2.0 and 2.8 μm and show that haze and gas abundances will be underestimated by about 8% if forward-scattering is ignored in the retrievals. At shorter wavelengths, errors in the gas and haze abundances and in the spectral slope of the haze particles can be several tens of percent, also for other Solar System planetary atmospheres. We also find that the contribution of forward-scattering can be fairly well described by modelling the atmosphere as a plane-parallel slab. This potentially reduces the need for a full three-dimensional Monte Carlo code for calculating transmission spectra of atmospheres that contain forward-scattering particles.  相似文献   

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