Characteristics of the radiation emerging from the top of a Rayleigh atmosphere—II Total upward flux and albedo

The solution of the equation of radiative transfer in a medium exhibiting Rayleigh scattering, as developed by S. Chandrasekhar, has been used for an extensive series of computations(³) of the characteristics of the scattered and diffusely reflected radiation emerging from the top of an atmospheric model which corresponds in many respects to the sunlit portion of the earth's atmosphere. The first part of this two-part discussion dealt with the intensity, degree of polarization, plane of polarization and the neutral points of the emergent light as functions of sun elevation, direction in the downward hemisphere, optical thickness of the model atmosphere and reflectivity of the underlying surface. This second part is concerned with the upward flux obtained by an integration of the intensity over the entire hemisphere, for the incident radiation (a) being independent of wavelength or (b) having the spectral distribution of the extra-terrestrial solar radiation. Integration with respect to wavelength in the latter case, together with an approximation for the sphericity of the atmosphere, yields a value of 7.6 per cent for the earth's planetary albedo due to scattering by the clear atmosphere. An approximation for ozone absorption decreases the computed albedo to 6.9 per cent.     

Intensity and polarization of radiation reflected from accretion disc

We consider the reflection of non-polarized radiation from the point-like sources above the accretion discs both the optically thick and optically thin. We investigate the dependence of the polarization of reflected radiation on the aperture angle of incident radiation. The aperture angle is determined by the radius of accretion disc and the height of the source above the disc. For optically thick accretion discs we show that, if the aperture angle is smaller 70 grad, then the wave electric field oscillations of reflected radiation are parallel to the accretion disc plane. For aperture angle greater than 70 grad the electric field oscillations are parallel to the plane “normal to accretion disc—the line of sight”. The latter also holds for reflection from the optically thin accretion disc independent of the aperture angle value.     

Determination of the single-scattering albedo from polarization measurements of a rayleigh atmosphere

Exact analysis of a Rayleigh-scattering half space is used to solve the inverse problem whereby the single-scattering albedo can be determined from measurements of the polarized radiation emerging from the atmosphere.     

Intensity and polarization line profiles in a semi-infinite Rayleigh-scattering planetary atmosphere. I. Integrated flux

Absorption and polarization line profiles as well as the curves of growth in the integrated light of a planet over the whole range of phase angles have been computed assuming a semi-infinite atmosphere scattering according to Rayleigh’s phase-matrix which takes polarization into account. The relative change in line depth and equivalent widths qualitatively agree with the observations of the CO₂ bands in Venus reported by Young, Schorn and Young (1980). It is pointed out that the bands might be formed in a part of the atmosphere which is different from that where continuum polarization originates.     

Circular polarization of the 1.4 GHz emission from Jupiter's radiation belts

Measurements of the 1.4 GHz emission from Jupiter made when D_E was 3°·1 show the circular polarization to vary from +0.8 to ?1.1% as the planet rotates. The rms scatter of the points about the mean curve is only 0.09%. Expressed as a function of Jovian magnetic latitude the polarization at first increases linearly but beyond latitudes ～7° the curve flattens. This shape requires that the radiating electrons have a pitch angle distribution similar to that inferred earlier from the beaming and linear polarization. The magnitude of the circular polarization requires an equatorial magnetic flux density in the belt of about 0.3G, consistent with the Pioneer results.Compared with measurements made one orbital period earlier, the total flux density has decreased by 15%, but the beaming has not changed appreciably.     

The polarization of optical radiation from the magnetic white dwarfs

It is pointed out that, because of the large Faraday rotation an outlet of linear polarization from the photosphere of a white dwarf is hampered. In accordance with this fact it is proposed to distinguish two types of magnetic white dwarfs. The first type (its representative is Grw 70°8247) has a linear polarization which is comparable in magnitude with the circular one. Polarization of radiation from the white dwarfs of the first type cannot arise in the photosphere. It arises in the corona of the star either as a result of cyclotron emission of hot electrons (T～10⁶ K) or as a result of scattering of slightly polarized emission from the photosphere in the corona. For the first type dwarfs such magnetic fields are required thatω _B ω_opt, i.e.B(1?3)×10⁸G. The white dwarfs of the second type (its representative is G 99-37) have their linear polarization much smaller than the circular one. Polarization of these white dwarfs can arise as a result of the transfer of radiation in the nonisothermal photosphere. Magnetic fields required for the second type can be much smaller:B cos γ=(1?10)×10⁶ G. It is shown that the photospheric model allows to obtain the quantitative accordance of the theory with all the observational data for G 99-37 and is not in accordance with the data for Grw 70°8247, at the same time the model with cyclotron emission from the corona explains the magnitude of both linear and circular polarization and their wavelength dependence for Grw 70°8247.     

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.     

Intensity of the infrared radiation from interstellar grains in the solar neighborhood

The expected intensity distribution of the infrared radiation in the solar neighborhood from the grain models of dirty ice, graphite and graphite core-dirty ice mantle has been calculated. It is found that the expected intensity from grain models at 100 agrees reasonably well with the observations of Hoffmann and Frederick.     

Intensity Fluctuations of Radiation Escaping from a Multicomponent Stochastic Atmosphere. I

This is the first part of a paper devoted to a theoretical investigation of intensity fluctuations of radiation at the frequencies of a spectral line formed in a multicomponent stochastic atmosphere. It is assumed that the optical depth of structural elements and the power of the energy sources contained in them undergo random variations. The frequency dependence of the relative mean-square deviation of the intensity of radiation escaping from the atmosphere is determined. Two special cases are considered and it is shown that the behavior of this quantity is different, depending on which of the indicated characteristics of the medium undergoes random variations. The results make it possible to judge the character of random variations in the fine structure of a radiating medium from observations of it in the cores and wings of spectral lines. Recent observations of prominences made using the SUMER spectrometer in the SOHO international project served as the specific motivation for the work.     

Thermal cyclotron radiation from hot coronal loops and peculiarities of the polarization structure of solar microwave emission sources: I. Brightness temperature

We discuss the possible contribution of the thermal cyclotron radiation from hot coronal magnetic loops to the observed characteristics of the microwave emission from solar active regions. Based on the simplest three-dimensional model of a loop in the shape of a hot torus, we have calculated the expected peculiarities of the frequency and polarization structures of microwave emission sources associated with sunspots and containing coronal loops. Our model calculations of the two-dimensional brightness temperature distributions at various wavelengths for the ordinary and extraordinary modes and the wavelength dependences of the brightness temperatures are presented in the first part of the work. The loop size, the electron density, and the source position on the disk have been found to affect these characteristics. Our numerical calculations of the brightness temperature distributions and spectra have confirmed the well-known assumption that under certain conditions the spectrum of a hot filament can contain cyclotron lines and the sense of the polarization can change over the range. The results obtained here refer to the brightness temperature along the line of sight that crosses the photosphere at a point with given coordinates, i.e., these are the emission characteristics at a fixed point of the source. Integrated characteristics (the flux from the entire source and its polarization) and a discussion of the hot loop model will be given in the second part of the work.     

Electro-hydromagnetic waves in a fully ionized gas—I

Transport equations are used to determine coefficients which are generalizations for any frequency of electric field of the parallel, Pedersen and Hall conductivities in a fully ionized gas.

These coefficients are used in an investigation of the propagation of weak electromagnetic and hydromagnetic waves of all frequencies across a homogeneous and constant magnetic field in a rarefied fully ionized gas. For propagation perpendicular to the magnetic field it is found for all frequencies

(i)

(ii)

where V² = H²/4π and v, h are the perturbations of the velocity, magnetic field. Similar relationships are deduced for propagation at any angle to the field for frequencies greater than about 10 times the gyrofrequency of electrons.

The theory is applied to discuss transmission of disturbance across the interplanetary medium, the temperature of the solar corona and the earth's outer atmosphere, the emission of non-thermal solar radio noise, cosmic radio noise and the anomalous emission of light from shock fronts.     

The polarization of scattered Lyα radiation around high-redshift galaxies

The high-redshift Universe contains luminous Lyα emitting sources such as galaxies and quasars. The emitted Lyα radiation is often scattered by surrounding neutral hydrogen atoms. We show that the scattered Lyα radiation obtains a high level of polarization for a wide range of likely environments of high-redshift galaxies. For example, the backscattered Lyα flux observed from galaxies surrounded by a superwind-driven outflow may reach a fractional polarization as high as ∼40 per cent. Equal levels of polarization may be observed from neutral collapsing protogalaxies. Resonant scattering in the diffuse intergalactic medium typically results in a lower polarization amplitude (≲7 per cent), which depends on the flux of the ionizing background. Spectral polarimetry can differentiate between Lyα scattering off infalling gas and outflowing gas; for an outflow, the polarization should increase towards longer wavelengths while for infall the opposite is true. Our numerical results suggest that Lyα polarimetry is feasible with existing instruments, and may provide a new diagnostic of the distribution and kinematics of neutral hydrogen around high-redshift galaxies. Moreover, polarimetry may help suppress infrared lines originating in the Earth's atmosphere, and thus improve the sensitivity of ground-based observations to high-redshift Lyα emitting galaxies outside the currently available redshift windows.     

Climatic and biological simulations in a two-way coupled atmosphere–biosphere model (CABM)

Today, most land surface process models have prescribed seasonal change of vegetation with regard to the exchange processes between land and the atmosphere. However, in order to consider the real interaction between vegetation and atmosphere and represent it best in a climate model, the vegetation growth process should be included. In other words, “life” should be brought into climate models. In this study, we have coupled the physical and biological components of AVIM (Atmosphere–Vegetation Interaction Model), a land surface model including plant ecophysiological processes, into the IAP/LASG L9 R15 GOALS GCM. To exhibit terrestrial vegetation information, the vegetation is given a high resolution of 1.5° by 1.5° to nest and couple the fine grid cells of land with the coarse grid cells of atmosphere, which is 7.5° longitude and 4.5° latitude. The simulated monthly mean surface air temperature and precipitation is close to the observations. The monthly mean Leaf Area Index (LAI) is consistent with the observed data. The global annual mean net primary production (NPP) simulation is also reasonable. The coupled model is stable, providing a good platform for research on two-way interaction between land and atmosphere, and the global terrestrial ecosystem carbon cycle.     

Reversal of the polarization of cyclotron radiation in a hot coronal loop

Spectropolarimetric features of thermal cyclotron radiation of solar coronal loops and the possibility of interpretation of the observed reversal of the sense of polarization of centimeter and decimeter waves are discussed. To this end, thermal cyclotron radiation is computed in terms of the simplest model of a three-dimensional hot loop (a half-torus). Such a loop is shown to be capable of changing appreciably the properties of the radiation of a solar active region at centimeter and decimeter wavelengths. A detailed analysis is performed to determine the conditions under which the radiation spectrum of an active region containing a coronal loop may have a complex pattern with several maxima or relatively narrow-band cyclotron lines, and the sense of polarization may change several times in the wavelength interval considered. These conditions are modelled by such parameters as the structure of the magnetic field, electron density, and size of the loop. The results of the computations of two-dimensional brightness temperature distributions at different wavelengths for ordinary and extraordinary waves at fixed points of the loop and the integrated parameters of the flux and polarization of radiation in terms of the model discussed are reported. Cases are considered where the line of sight is crossed by one or two loops. The expected distribution of polarization across the source in the model considered is compared to the results of RATAN-600 observations of the solar active region AR 7962 made on May 12–14, 1996.     

Transfer of polarization of radiation in a magnetoactive cosmic plasma

The variation in the polarization of radiation propagating in a magnetoactive plasma due to the Faraday effect and differential absorption of ordinary and extraordinary waves is considered. This problem is especially important for polarization studies of the distributed cosmic emission, the radiation of discrete sources, etc. An Equation (1.10) describing the variation of the polarization tensor (1.2) (or (1.2a)) along the direction of propagation is formulated. This equation correctly accounts for the effect of absorption in distinction to the corresponding equation ofKawabata (1964). Equation (1.10), which was obtained for a homogeneous medium, is also true for an inhomogeneous plasma when the geometrical optics approximation is valid for the radiation, the difference between the refractions of ordinary and extraordinary waves is negligible, and inequalities (1.13) are satisfied. In this case, however, the tensorsS _iq ,R _iqlm , andK _iqlm in (1.10) will depend on the coordinate.The case of quasi-longitudinal propagation for circularly polarized ordinary and extraordinary waves is treated in detail by means of (1.10). In this case, which is frequently realized in a cosmic plasma, the equations of transfer written in terms of the Stokes parameters (1.3) take the form of (2.3). Their solution for the case of a uniform plasma is obtained as (2.8)–(2.10). From the analysis of these solutions it follows that, if absorption is neglected, the orientation of the polarization ellipse of the radiation emitted in a layer of thicknessz of a magnetoactive plasma varies according to (2.20), i.e. twice as slowly as the angle of radiation incident on the layer (see (2.15)). In the presence of absorption the polarization ellipse ceases to rotate at a distance from the beginning of the layer (K _{e, 0} is the amplitude of the absorption coefficient of the extraordinary wave). If the Faraday effect is not important (see (2.24)), the angle is close to the ellipse orientation of sources in the plasma ^S . For a strong Faraday effect (2.24a) the angle is displaced relative to ^S by ±/4.The character of polarization of radiation in a plasma changes abruptly if the conditions for negative re-absorption are satisfied (K _{e, o}<0). For strong amplification within a source of dimensionsL and a marked difference in re-absorption of ordinary and extraordinary waves , the radiation emitted by the source belongs entirely to one type of wave; the polarization of this radiation is completely defined by the polarization of waves of this type in a cosmic plasma and does not depend directly on the polarization of radiation emitted by individual electrons of this source. The latter circumstance is of great importance for a treatment of the polarization characteristics of radio emission from cosmic sources with negative re-absorption.Translated from the Russian by Dean F. Smith.     

Atmospheric effect on the upwelling radiation at the top of the atmosphere over a stream

A new version is adopted for the evaluation of the upwelling radiation from atmosphere bounded by the surface, where the surface is composed of two half semi-infinite Lambert surfaces and a stream is inserted between them. The contrast of the stream is discussed with respect to the atmospheric effect. The width of the stream is considered to be 0.5, 1, and 3km; The solar and observational direction is located in the normal plane to the stream. The observational site is located at altitude 30km. The horizontal distance of observational site to the stream is fixed to 6.28 . The atmosphere is assumed to be homogeneous, which is composed of aerosol and molecules, where the model aerosol is of the oceanic type.In the computational procedure, a probability of radiation interacting with respective half surfaces and the stream are calculated based on the assumption of single scattering in the atmosphere, where isotropic scattering is undertaken. By use of this probability, the emergent radiation at the top of the atmosphere is calculated approximately by considering the radiative interactions between atmosphere and surfaces up to twice. The numerical simulation exhibits the extraordinary effect near the stream. The contrast of the stream depends upon the albedo of the surrounding surfaces. It increases with the increase of the stream width and decreases with the optical thickness.     

Intensity and polarization line profiles in a semi-infinite Rayleigh-scattering planetary atmosphere. III. Variation of polarization profiles and the Stokes parameter Q over the disk

The variation of the polarization profiles, the Stokes parameters Q andU, and the angle defining the plane of polarization along the intensity equator and along the mirror meridian, on whichμ = μ ₀, in a Rayleighscattering atmosphere is studied. It is found that these variations are more complex than thought hitherto, particularly at large phase angles.