Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- Chapter 1 Definitions of fundamental quantities of the radiation field -- 1.1 Specific intensity -- 1.2 Net flux -- 1.2.1 Specific luminosity -- 1.3 Density of radiation and mean intensity -- 1.4 Radiation pressure -- 1.5 Moments of the radiation field -- 1.6 Pressure tensor -- 1.7 Extinction coefficient: true absorption and scattering -- 1.8 Emission coefficient -- 1.9 The source function -- 1.10 Local thermodynamic equilibrium -- 1.11 Non-LTE conditions in stellar atmospheres -- 1.12 Line source function for a two-level atom -- 1.13 Redistribution functions -- 1.14 Variable Eddington factor -- REFERENCES -- Chapter 2 The equation of radiative transfer -- 2.1 General derivation of the radiative transfer equation -- 2.2 The time-independent transfer equation in spherical symmetry -- 2.3 Cylindrical symmetry -- 2.4 The transfer equation in three-dimensional geometries -- 2.5 Optical depth -- 2.6 Source function in the transfer equation -- 2.7 Boundary conditions -- 2.8 Media with only either absorption or emission -- 2.9 Formal solution of the transfer equation -- 2.10 Scattering atmospheres -- 2.11 The K -integral -- 2.12 Schwarzschild-Milne equations and Lambda, Phi, Chi operators -- 2.13 Eddington-Barbier relation -- 2.14 Moments of the transfer equation -- 2.15 Condition of radiative equilibrium -- 2.16 The diffusion approximations -- 2.17 The grey approximation -- 2.18 Eddington's approximation -- REFERENCES -- Chapter 3 Methods of solution of the transfer equation -- 3.1 Chandrasekhar's solution -- 3.2 The H-function -- 3.2.1 The first approximation -- 3.2.2 The second approximation -- 3.3 Radiative equilibrium of a planetary nebula -- 3.4 Incident radiation from an outside source -- 3.5 Diffuse reflection when omega = 1 (conservative case).

3.6 Iteration of the integral equation -- 3.7 Integral equation method. Solution by linear equations -- REFERENCES -- Chapter 4 Two-point boundary problems -- 4.1 Boundary conditions -- 4.2 Differential equation method. Riccati transformation -- 4.3 Feautrier method for plane parallel and stationary media -- 4.4 Boundary conditions -- 4.5 The difference equation -- 4.6 Rybicki method -- 4.7 Solution in spherically symmetric media -- 4.8 Ray-by-ray treatment of Schmid-Burgk -- 4.9 Discrete space representation -- REFERENCES -- Chapter 5 Principle of invariance -- 5.1 Glass plates theory -- 5.2 The principle of inariance -- 5.3 Diffuse reflection and transmission -- 5.4 The invariance of the law of diffuse reflection -- 5.5 Evaluation of the scattering function -- 5.6 An equation connecting I (0, Mu) and S(Mu, Mu') -- 5.7 The integral for S with p(cos Theta = Omega(1 + x cos Theta) -- 5.8 The principle of invariance in a finite medium -- 5.9 Integral equations for the scattering and transmission functions -- 5.10 The X - and the Y -functions -- 5.11 Non-uniqueness of the solution in the conservative case -- 5.12 Particle counting method -- 5.13 The exit function -- REFERENCES -- Chapter 6 Discrete space theory -- 6.1 Introduction -- 6.2 The rod model -- 6.3 The interaction principle for the rod -- 6.4 Multiple rods: star products -- 6.5 The interaction principle for a slab -- 6.6 The star product for the slab -- 6.7 Emergent radiation -- 6.8 The internal radiation field -- 6.9 Reflecting surface -- 6.10 Monochromatic equation of transfer -- 6.12 Solution of the spherically symmetric equation -- 6.13 Solution of line transfer in spherical symmetry -- 6.14 Integral operator method -- REFERENCES -- Chapter 7 Transfer equation in moving media: the observer frame -- 7.1 Introduction -- 7.2 Observer's frame in plane parallel geometry.

7.3 Wave motion in the observer's frame -- 7.4 Observer's frame and spherical symmetry -- 7.4.1 Ray-by-ray method -- 7.4.2 Observer's frame and discrete space theory -- 7.4.3 Integral form due to Averett and Loeser -- REFERENCES -- Chapter 8 Radiative transfer equation in the comoving frame -- 8.1 Introduction -- 8.2 Transfer equation in the comoving frame -- 8.3 Impact parameter method -- 8.4 Application of discrete space theory to the comoving frame -- 8.5 Lorentz transformation and aberration and advection -- 8.6 The equation of transfer in the comoving frame -- 8.7 Aberration and advection with monochromatic radiation -- 8.8 Line formation with aberration and advection -- 8.9 Method of adaptive mesh -- REFERENCES -- Chapter 9 Escape probability methods -- 9.1 Surfaces of constant radial velocity -- 9.2 Sobole method of escape probability -- 9.3 Generalized Sobolev method -- 9.4 Core-saturation method of Rybicki (1972) -- 9.5 Scharmer's method -- 9.6 Probabilistic equations for line source function -- 9.6.1 Empirical basis for probabilistic formulations -- 9.6.2 Exact equation for S / B -- 9.6.3 Approximate probabilistic equations -- 9.7 Probabilistic radiative transfer -- 9.8 Mean escape probability for resonance lines -- 9.9 Probability of quantum exit -- 9.9.1 The resolvents and Milne equations -- REFERENCES -- Chapter 10 Operator perturbation methods -- 10.1 Introduction -- 10.2 Non-local perturbation technique of Cannon -- 10.3 Multi-level calculations using the approximate lambda operator -- 10.4 Complete linearization method -- 10.5 Approximate lambda operator (ALO) -- 10.6 Characteristic rays and ALO-ALI techniques -- REFERENCES -- Chapter 11 Polarization -- 11.1 Elliptically polarized beam -- 11.2 Rayleigh scattering -- 11.3 Rotation of the axes and Stokes parameters -- 11.4 Transfer equation for I(Theta, Phi).

11.5 Polarization under the assumption of axial symmetry -- 11.6 Polarization in spherically symmetric media -- 11.7 Rayleigh scattering and scattering using planetary atmospheres -- 11.8 Resonance line polarization -- REFERENCES -- Chapter 12 Polarization in magnetic media -- 12.1 Polarized light in terms of I, Q, U, V -- 12.2 Transfer equation for the Stokes vector -- 12.3 Solution of the vector transfer equation with the Milne-Eddington approximation -- 12.4 Zeeman line transfer: the Feautrier method -- 12.5 Lambda operator method for Zeeman line transfer -- 12.6 Solution of the transfer equation for polarized radiation -- 12.7 Polarization approximate lambda iteration (PALI) methods -- REFERENCES -- Chapter 13 Multi-dimensional radiative transfer -- 13.1 Introduction -- 13.2 Reflection effect in binary stars -- 13.3 Two-dimensional transfer and discrete space theory -- 13.4 Three-dimensional radiative transfer -- 13.5 Time dependent radiative transfer -- 13.6 Radiative transfer, entropy and local potentials -- 13.7 Radiative transfer in masers -- REFERENCES -- Symbol index -- Index.