Radiative transfer in an infinite cylinder

The problem of radiation transfer in a cylinder with diffuse reflectivity and containing an energy source is connected with the source-free radiation transfer problem with isotropic boundary condition. Equation for the radiation heat flux is obtained for a polynomial source. In the special case of isotropic scattering, the radiation heat flux is given in terms of the albedo of the second problem. An expression is also given for the net radiation heat flux.     

Radiation transfer for an inhomogeneous half-space with an internal source

The emergent flux for radiation transfer in an inhomogeneous half-space with internal source is obtained in terms of the source-function of the diffuse reflection problem. Modified Eddington method is used to calculate the diffuse problem and, hence, the emergent flux. Numerical result are given and compared with previous work.On leave of absence from the Nuclear Research Centre, Cairo, Egypt.     

Radiation transfer in a diffuse and specular reflecting slab with Rayleigh scattering

A method of analysis is presented for solving the radiative transfer problem in an absorbing, emitting, inhomogeneous, and anisotropically scattering plane-parallel medium with specular and diffuse reflecting boundaries and internal source (problem 1). Exact relations for the radiation heat flux at the boundaries of problem 1 are obtained in terms of the radiation density and albedos of the corresponding source-free medium with specular reflecting boundaries (problem 2). Two coupled integral equations for the radiation density and the second moment of the radiation intensity for problem 2 with Rayleigh phase functions are obtained. The Galerkin method is used to solve these equations. Albedos of problem 2 are compared with theF _n method. Numerical results for radiation heat fluxes at the boundaries of problem 1 are tabulated for different forms of the internal source.     

The energy-dependent radiation transfer in a homogeneous finite cylinder

Radiation transfer problem in the slowing-down region for cylindrical geometry with diffuse reflectivity and internal source is connected with source-free problem with isotropic boundary condition. Modelled kernels are used to represent the slowing-down kernel. Calculations are performed for the radiation flux at the boundary of the cylinder. Numerical results are obtained using the bi-variation technique.     

Padé approximant calculations for dispersive,isotropic scattering,homogeneous media

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.     

The energy-dependent radiation transfer in a homogeneous finite sphere

Radiation transfer problem in the slowing-down region is solved for a spherical geometry. Modelled kernels are used to represent the slowing-down kernel. Calculations are performed for the radiation flux at the boundary of the sphere for two cases: (i) in the presence of internal source, (ii) if the radiation is incident on the sphere. Numerical results are obtained by using the Padé approximant technique.     

The spectra of radiation and relativistic electrons formed by Compton scattering at non-zero particle fluxes

The formation of steady-state spectra of radiation or particles by Compton scattering is discussed for the case when the flux from the source is present. Power-law distributions, or those characterized by a power-law asymptotic behaviour, can appear under these conditions.The power indices and normalizations have been found as well as the flux directions for the electron and photon distributions in two cases. The first case is that of differential energy transfer over the electron spectrum (interaction with soft radiation). For the case of integrated transfer, relations have been found between the indices.The possibility of a power-law electron spectrum (with an index =2) has been shown for scattering by equilibrium radiation (the black-body background included).     

Surface heat current in an inhomogeneous slab with reflecting walls

The problem of radiative transfer in an inhomogeneous finite medium with boundary surfaces which reflects both diffusely and specularly is connected with a source-free specular boundary condition radiation tramsfer. Numerical results are obtained for the partial heat flux using the bi-variational technique.     

Reflection effect in close binaries: effects of reflection on spectral lines

Reflection effect phenomenon is studied on the formation of spectral lines in a close binary system when primary component has an extended atmosphere and the secondary component is a point source. Irradiation effect is calculated using one dimensional rod model and self radiation is calculated using continuum radiative transfer equation in spherically symmetric atmosphere. The total radiation is the sum of the radiation of the individual components and the mutually reflected light. Line profiles are also computed along the line of sight observer at infinity for irradiation, self radiation and total radiation and compared in order to study the reflection effect on spectral lines. It is found that the radiation field varies on the primary component when angle of incidence changes from the secondary component. The contour maps show that the radiative interaction makes the outer surface of the primary star warm when its companion illuminates the radiation. The effect of reflection on spectral lines is studied and noticed that the flux in the lines increases at all frequency points and the cores of the lines received more flux than the wings and equivalent width changes accordingly.     

Polarized radiation transfer in finite atmospheric media

The problem of monoenergetic polarized radiation transfer in a plane-parallel finite atmospheric medium is proposed. Pomraning–Eddington approximation is used to obtain the analytical solution for both the total intensity and the difference function of the polarized radiation. The medium is assumed to have specular reflecting boundaries with angular-dependent externally incident flux. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the reflectivity and transmissivity are obtained for the different degrees of polarization.     

Reassessment of net radiation measurements in the atmosphere of Venus

Net radiative flux measurements by instruments on the Pioneer Venus Day, North, and Night probes are too large below 30 km to be consistent with present estimates of atmospheric opacity. We evaluate the only known mechanisms which could potentially have caused significant errors in the deep atmosphere, namely, (1) radiation field perturbations behind each probe due to its thermal wake, (2) cloud particle deposition on the sensor windows, and (3) thermal perturbations within the radiation sensor produced by gas flow through the sensor window retainers. Thermal analysis of the wake effect shows that temperature perturbations are not large enough to produce significant flux perturbations when gas opacity and sensor field-of-view characteristics are taken into account. The particle deposition effect is rejected because it requires a signature in the measured radiation profile which is not observed. The absence of such a feature also implies that mode 3 cloud particles are either not sulfuric acid or are far less numerous than previously reported. We find that the third mechanism is the most likely source of the large net flux measurements. However, this error is not sufficiently constrained by laboratory data to allow rigorous corrections to the measured flux profiles. If we use radiative transfer calculations to constrain the fluxes at 14 km and limited laboratory data to estimate the altitude dependence of the error, then we obtain a plausible set of corrected flux profiles which are roughly consistent with reasonable H₂O mixing ratios below the clouds.     

One-photon and two-photon annihilation lines in gamma-bursts,II

This paper, which is a continuation of Paper I (Zheleznyakov and Litvinchuk, 1985), studies the formation of a one-quantum annihilation line in the spectrum of gamma-ray bursts. The radiative transfer equation together with the positron density balance relation is solved, and the expected photon fluxes in the one- and two-quantum annihilation lines are calculated. The fractional luminosities of these lines versus source parameters are investigated. For a gamma-burst one-photon annihilation line, the luminosity is always much less than that for the two-photon line-i.e., the positron source power transforms almost entirely into radiation in the two-quantum annihilation line and the positron density depends solely on the specific source power and two-quantum annihilation probability. The flux of one-quantum annihilation quanta 1 MeV is estimated to be less than what modern detectors can resolve. This explains failure to detect the one-photon annihilation lines in gamma-bursts so far.     

Volterra equation for the matrix source function at resonance scattering

A matrix transfer equation for multiple resonance scattering of radiation in a spectral line in a semiinfinite atmosphere with a uniform distribution of primary radiation sources is examined. A nonlinear matrix integral is obtained for this equation as a generalization of the Rybicki two-point Q-integral. One special case of the matrix [^(Q)] {\mathbf{\hat{Q}}} -integral is the Volterra equation for the matrix source function of the problem discussed here. The Volterra equation is solved numerically for a Doppler profile of the absorption coefficient. Several polarization characteristics of the emerging radiation are obtained.     

A fourier transform solution of radiation transfer in a spherical-inhomogeneous medium

The radiative heat flux at the boundary of a sphere containing an internal energy source and subject to general boundary conditions (problem 1) is obtained in terms of the albedo of the corresponding source-free problem with isotropic boundary condition (problem 2). The solution of problem 2 is performed on the basis of the integral Fourier transforms method. Numerical results for the partial heat flux and emissivity for a given internal energy source and inhomogeneous medium, isotropic scattering are obtained.     

Radiation transfer through atmospheric aerosol media with anisotropic scattering

Radiation transfer in atmospheric aerosol media with general boundary conditions has been studied for anisotropic scattering. The considered aerosol medium assumed to have specular and diffused reflecting boundary surfaces and in the presence of internal source. The radiation transfer scattering parameters as single scattering albedo, asymmetry factor, scattering, absorption, extinction efficiencies and anisotropic scattering coefficient have been calculated using the Mie theory. The problem with general boundary conditions is solved in terms of the solution of source-free problem with simply boundary conditions. Pomraning-Eddington approximation is used to solve the source-free problem. For the sake of comparison, a weight function is introduced and used in two special forms. The calculated partial heat fluxes with the two methods are compared and showed good agreement. Some of our results are found in a good agreement with published data.     

Radiation transfer for linearly anisotropic phase functions

Radiative transfer equation in a plane-parallel medium with isotropic boundary conditions for linearly anisotropic scattering phase function is considered. Two coupled integral equations for total density of radiation and total radiation flux are obtained. The Galerkin method is used to solve these equations. Numerical results for the radiative fluxes at the boundaries show that the Galerkin method yields accurate results compared well with other exact methods.     

ART-P/GRANAT observations of the X-ray source KS 1731-260

The results of observations of the transient X-ray burster KS 1731-260 with the ART-P telescope onboard the GRANAT observatory are presented. The observations were performed in 1990–1991 at the initial stage of the source’s 12-yr activity period when no studies were conducted by other X-ray observatories. The flux from KS 1731-260 is shown to have systematically decreased, forming a separate initial “minioutburst” of the source with a duration of ～2.5 yr. The decrease in flux was accompanied by an increase in the spectral hardness of KS 1731-260 and an enhancement of its burst activity; two X-ray bursts were detected in the last observing sessions when the flux decreased by 40–60%. Their analysis showed that they occurred in a medium with an appreciable hydrogen abundance; i.e., the enrichment efficiency of the material in the lower atmospheric layers of the neutron star during quasi-steady hydrogen burning was low. The BDLE model that was suggested by Grebenev et al. (2006) to describe the radiation spectra of weakly magnetized accreting neutron stars has been used for the first time to analyze the continuum radiation spectrum of the source. This model incorporates two spectral components associated with the radiation from the boundary layer formed at the place of contact between the accretion disk and the neutron star surface and with the radiation from the accretion disk proper. The model satisfactorily fits the observed radiation spectra of the source and allow such parameters of the binary system as the accretion disk inclination, the bolometric luminosity (accretion rate), and the temperature of the outer boundary layer to be estimated. The boundary layer radiation for KS 1731-260 is shown to have originated in an exponential atmosphere of moderate optical depth for Thomson scattering under conditions where comptonization had no time to form the Wien spectrum, but only modified the thermal plasma radiation spectrum.     

Source vector in Rayleigh-Cabannes scattering atmosphere: the nonconservative milne problem

We consider the radiative transfer in a nonconservative homogeneous plane-parallel semi-infinite planetary atmosphere where the scattering processes are described by the Rayleigh-Cabannes phase matrix and where the primary sources are in infinitely deep layers. If we use the superposition principle we derive the Cauchy problem for the source vector.As a by-product the external field of radiation for the problem described is obtained using the principle of invariance by Chandrasekhar. The respective formulae for the radiation field in the deep layers and for the extrapolation distance are given. It is shown that the Rubenson degree of polarization even in the case of near-conservative atmospheres reaches the asymptotic regime at rather small values of the optical depth. The-plane reliefs of the characteristic equation, extrapolation distance and the normalized components of the source vector at the boundary are given along with a sample of zeros of the characteristic equation.     

Infrared studies of X-ray sources

A detailed study of the infrared radiation from galactic X-ray sources indicates that the galactic bulge sources and X-ray binary sources have different infrared emission characteristics. The galactic bulge sources seem to show a power law dependence between the X-ray flux and the infrared flux emitted by the X-ray source. The results presented suggests that the infrared radiation in the galactic bulge sources is dominated by free-free radiation and, in the case of eclipsing binary sources, the black-body emission from the early-type companion star contributes significantly to the infrared radiation.     

The generation of ionization-shock front oscillations by a variable radiation flux

The effect of a time-varying radiation flux incident on an ionization front on the generation of ionization-shock front oscillations in the interstellar medium is analyzed analytically and numerically. We take into account both variations in the flux of ionizing radiation directly from the source that produces the ionization front and the absorption of energetic photons by the post-front plasma. Based on our calculations, we show that the time dependence of the radiation flux can be an additional factor (apart from small inhomogeneities in the interstellar medium) that contributes to the amplification of oscillations and to the kinetic energy input to the observed turbulent motions in H II regions.