首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
A formal derivation is presented of the energy transfer rate between radiation and matter due to the scattering of an isotropic distribution of resonance line photons. The derivation is developed in the context of the two-level atom in the absence of collisions and radiative transitions to and from the continuum, but includes the full angle-averaged redistribution function for photon scattering. The result is compared with previous derivations, all of which have been based on a Fokker–Planck approximation (FPA) to the radiative transfer equation. A new FPA, including a Kramers–Moyal extension to higher (post-diffusive) orders, is derived to solve the radiative transfer equation, and time-dependent numerical solutions are found. The relaxation of the colour temperature to the matter temperature is computed as the radiation field approaches statistical equilibrium through scattering. The results are discussed in the context of the Wouthuysen–Field mechanism for coupling the 21-cm spin temperature of neutral hydrogen to the kinetic temperature of the gas through Lyα scattering. The evolution of the heating rate is also computed, and shown to diminish as the gas approaches statistical equilibrium.  相似文献   

2.
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.  相似文献   

3.
A unifying theoretical approach is presented to derive from the general principles of Quantum Electrodynamics both the radiative transfer equations for polarized radiation and the statistical equilibrium equations for an atomic system interacting with a polarized radiation field. The radiation field is described by means of Stokes parameters while the atomic system is described in terms of its density-matrix operator. The non-diagonal terms of the density matrix are fully accounted for so that this formalism can be suitably employed to describe a wide variety of physical phenomena like resonance scattering, the Hanle effect and the Zeeman effect, either in optically thin or optically thick atmospheres, together with all the possible intermediate situations.The general formulae derived in the first sections of the paper are subsequently particularized introducing the dipole approximation in the relevant matrix elements describing the interaction between the atomic system and the radiation field. The final equations assume a quite compact expression by the introduction of suitable spherical tensors connected with the components of the polarization unit vectors associated with each direction of the radiation field. The general expressions and the main properties of these tensors are discussed in the Appendix.  相似文献   

4.
A general Monte Carlo relaxation method has been formulated for the computation of physically self-consistent model stellar atmospheres. The local physical state is obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer. Anisotropic Thomson scattering is included in the equation of transfer and radiation pressure effects are included in the hydrostatic equation. The constraints of hydrostatic and radiative equilibrium are enforced. Local thermodynamic equilibrium (L.T.E.) is assumed as a boundary condition deep in the atmosphere. Elsewhere in the atmosphere L.T.E. is not assumed.The statistical equilibrium equations are solved with no assumptions made concerning detailed balance for the bound-bound radiative processes. The source function is formulated in microscopic detail. All atomic processes contributing to the absorption and emission of radiation are included. The kinetic energy balance equation for the electron gas is formulated in detail. All atomic processes by which kinetic energy is gained and lost by the electron gas are included.The method has been applied to the computation of a model atmosphere for a pure hydrogen early-type star. An idealized model of the hydrogen atom with five bound levels and the continuum was adopted. The results of the trial calculation are discussed with reference to stability, accuracy, and convergence of the solution.Contribution No. 385 from the Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.  相似文献   

5.
A. I. Shapiro 《Astrophysics》2002,45(2):215-222
A model problem in the theory of line formation in an optically thick, purely scattering, stellar atmosphere is considered. The integral equation of radiation transfer at line frequencies is solved numerically for a two-level atom in the approximation of complete frequency redistribution in scattering. The numerical results are compared with those calculated from equations of the asymptotic theory. On the basis of the asymptotic theory, the positions of intensity maxima in a line are found for different absorption profiles.  相似文献   

6.
Linear FREDHOLM integral equations are derived for the STOKES vector of the radiation emerging from a scattering plane parallel medium of finite optical thickness. The integral equations are obtained by means of imbedding the slab in an infinite medium. They are formulated in terms of GREEN 's function matrices and renormalized for the asymptotic eigenmode. Explicitly, linear integral equations are given for the reflection and transmission matrices. The reciprocity principle is employed to obtain integral equations also for the mean intensity of the inner radiation field in the case of the slab albedo problem.  相似文献   

7.
Once the need for an iterative procedure in order to solve the problem of the formation of spectral lines in the case of a model atom with many energy levels, the sequel is to seek for the most effective form of such an iterative scheme. It is an almost universal is assumed within all the iterative methods for the solution of those radiative transfer problems, in which the transfer equations are coupled to the state of the matter, to take as the input of each step of iterations the values of the opacity coefficients obtained as a result of the previous one. This is, for instance, the procedure used to correct the temperature in the computation of stellar atmosphere models, or that to build the -operator (either the exact or the approximated one) within the Accelerated Lambda Iteration methods. Yet, if we assume, in order to solve the multilevel line transfer problem, that at each step of iterations the line opacities are known, we can express via the statistical equilibrium equations the populations of the energy levels - and consequently the source functions of the relevant spectral lines - as a linear function of the full set of the corresponding mean intensities of the radiation field. Once such linear forms for the source functions, we are able to solve without the need of any further approximation the radiative transfer equations for are obtained lines, now linearly coupled through the above linear forms of the statistical equilibrium equations. This is achieved by means of the Implicit Integral Method that we already presented in a series of previous papers.  相似文献   

8.
A method for rapid calculation of the multiply-scattered solar induced radiation field in the troposphere and stratosphere is presented. The method is described in sufficient detail so that the mathematical model can be incorporated in a straightforward manner into photochemical models of the troposphere and stratosphere. Results are described which show that multiple scattering and ground albedo can result in large amplifications of the radiation field in the photochemically active region 240–1000 nm.  相似文献   

9.
Interaction between planetary atmospheres and small bodies is connected with radiation effects. Submicron particles in the Earth's upper atmosphere strongly influence the scattering of the shortwave solar radiation. Based on the mutual connection between the environmental and radiation field structures it is possible to determine the physical characteristics of the particle set in this environment. Generaly, the diffused radiation field in the real atmosphere is given by a sum of elementary and multiple scattering components. Solving the inverse problems always leads to complicated integral equations. A major part of the diffused radiation field in the upper atmosphere is due to the first order scattering. The paper presents a new method for determination of the effective complex refractive index and size distribution of the particles based on the radiance data. The solution of integral equations is to be found in the space of quadratically integrable and continuous functionsf L 2.  相似文献   

10.
We present an exact low-energy expansion redward of Lyα of the Rayleigh scattering cross-section by atomic hydrogen, which is given by the Kramers–Heisenberg formula. The expansion is expressed as a power series of  (ω/ωl)  , where ωl and ω are the angular frequencies corresponding to the Lyman limit and the incident radiation, respectively. The expansion coefficients are represented as infinite sums over all the intermediate states and they can also be expressed as the regular particular solutions of inhomogeneous differential equations, which is known as the Dalgarno and Lewis method. In this paper, using a software capable of symbolic calculations, we obtain the exact values of these coefficients. We provide brief discussions on the accuracies of approximate expressions for Rayleigh scattering by a hydrogen atom found in the literature.  相似文献   

11.
We have calculated the distortions of the cosmic microwave background (CMB) spectrum in the wavelength range 2–50 cm due to the superposition of the CMB hydrogen recombination radiation in subordinate lines. The level populations were determined by numerically solving the equation of recombination kinetics together with the statistical equilibrium equations for a 60-level model hydrogen atom. The relative distortions are ≈10?7–10?6, with their wavelength dependence having a low-contrast, wavy pattern. However, the contrast increases severalfold and becomes pronounced when passing to the differential distortion spectrum. We study the dependence of the distortions on cosmological parameters.  相似文献   

12.
Chultem  Ts.  Yakovkin  N. A. 《Solar physics》1974,34(1):133-150
The statistical equilibrium equations for the continuum and first 10 levels of a hydrogen atom show that the radiation of a bright prominence (the brightness of the H line has attained 56 mÅ of the disc centre spectrum) is completely due to scattering of the Sun radiation. The basic unknowns are separated with certainty: electron concentration (n e = 3.0 × 1010 cm–3), effective thickness (l = 4.2 × 108 cm) and electron temperature (T e = 5000 K).Radiation of a very bright prominence (A (H) = 213 mÅ; T e = 7300 K; n e = 5.0 × 1011 cm–3; l = 1.3 × 107 cm) is on account of electron impacts (40%) and the Sun radiation scattering (60%).The parameters are shown to depend greatly on the prominence optical thickness in the lines of the first subordinate series of a hydrogen atom. In the course of determination all the parameters and 100 interconnected integral equations of the radiation diffusion have been thickness-averaged; the population of levels has been calculated by observations using the self-absorption factors.  相似文献   

13.
The method of computing the radiation field in an infinite circular cylinder proposed in Part I is now applied to the case of isotropic scattering with sources on the boundary and axis of the cylinder, as well as for a uniform distribution of sources inside the cylinder. For the simplest kernel we obtain exact solutions of the basic integral equation in explicit form. For scattering in a spectral line with complete frequency redistribution and a power absorption profile we develop an asymptotic theory for the case when the optical radius of the cylinder is large. We solve the asymptotic equations for the basic characteristics of the scattering in closed form for conservative scattering and find its asymptotics. We obtain estimates of the mean number of scatterings with a layered source, and also the mean and variance of the number of scatterings with a uniform source distribution.Translated fromAstrofizika, Vol. 37, No. 4, 1994.This work was carried out with the financial support of the Russian Basic Research Fund (grant 93-02-2957).  相似文献   

14.
An approximate solution has been obtained for the problem of multiple scattering of light in an optically thin, inhomogeneous spherically symmetric planetary atmosphere illuminated by parallel solar radiation. A three-stream division of the radiation field has been made and a generalized Eddington approximation developed to solve the moment equations of the problem.  相似文献   

15.
In this paper we develop a new method, combined with Laplace transformation and Wiener-Hopf technique, to obtain unique solutions of transport equations in finite media. For this purpose we consider the simple transfer equation for diffuse reflection by a plane-parallel finite atmosphere scattering radiation with moderate anisotropy. It is transformed, by Laplace transformation, into two coupled linear integral equations which are then reduced to two uncoupled Fredholm integral equations admitting of unique solutions by the method of iteration for values of the breadth of the atmosphere greater than that specified, depending on the scattering process.  相似文献   

16.
In this paper we develop a new exact method combined with finite Laplace transform and theory of linear singular operators to obtain a solution of transport equation in finite plane-parallel steady-state scattering atmosphere both for angular distribution of radiation from the bounding faces of the atmosphere and for intensity of radiation at any depth of the atmosphere. The emergent intensity of radiation from the bounding faces are determined from simultaneous linear integral equations of the emergent intensity of radiation in terms ofX andY equations of Chandrasekhar. The intensity of radiation at any optical depth for a positive and negative direction parameter is derived by inversion of the Laplace transform in terms of intergrals of the emergent intensity of radiation. A new expression of theX andY equation is also derived for easy numerical computation. This is a new and exact method applicable to all problems in finite plane parallel steady scattering atmosphere.  相似文献   

17.
An analysis has been made of temperature fluctuations expected for various grain materials exposed to the interstellar radiation field. It is shown that in all but the densest clouds average grain temperatures in the 5–10 K range are of little statistical significance because of large fluctuations produced by absorbed photons from the interstellar radiation field. At higher average temperatures large fluctuations may still be present for certain grain materials and grain radii. The effect of these fluctuations on the simple problem of H atom recombination on grain surfaces is discussed.  相似文献   

18.
Assuming some hydrogen atoms are distributed in the magnetosphere of a pulsar, the gas we are dealing with is a mixture of plasma and hydrogen atoms. Because the induced electrical field in the plasma surrounding the pulsar is very strong, due to the rotation of the pulsar associated with a strong magnetic field, the electric polarization of an atom will include the nonlinear term of the electric field. We obtain the nonlinear dispersion relation for the mixed gas from the Maxwell equations and derive the nonlinear Schrödinger equation, which has solitons as its solution under a certain condition. The curvature radiation of solitons moving along the magnetic field lines is a plausible way to explain the strong radio emission which comes from a pulsar, particularly some field lines existing near the light cylinder with radii of curvature smaller than the radius of the pulsar.  相似文献   

19.
On the ground of the proper wave representation the general theory is developed of radiative transfer in a homogeneous plasma with the strong magnetic field ( B /1). The linear and nonlinear equations are derived which generalize the corresponding equations of scalar radiative transfer theory in isotropic media. The solutions of some problems are given for the cases when the magnetic field is perpendicular to the surface: diffuse reflection of radiation from a semiinfinite medium, provided the sources are placed far from the surface (Milne's problem) and have constant intensity, increase linearly or quadratically with the optical depths, or decrease exponentially from the surface.  相似文献   

20.
本文认为强磁场中的逆Compton散射可能是γ射线爆的主要辐射机制.其能谱是由源区质子产生的低频光子经强磁场中非热电子的Compton散射形成的.我们利用非相对论情形(B/B_(cr)≤1,hv_i/m_ec~2≤1)下强磁场中的Compton散射微分截面,导出了上述Compton散射的辐射谱公式,由此很好地拟合了典型γ射线爆GB811016的观测能谱.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号