An Introduction to Radiative Transfer : Methods and Applications in Astrophysics

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An Introduction to Radiative Transfer : Methods and Applications in Astrophysics

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 480 p.
  • 言語 ENG
  • 商品コード 9780521779890
  • DDC分類 523.82

Full Description


Astrophysicists have developed several very different methodologies for solving the radiative transfer equation. An Introduction to Radiative Transfer presents these techniques as applied to stellar atmospheres, planetary nebulae, supernovae, and other objects with similar geometrical and physical conditions. Accurate methods, fast methods, probabilistic methods and approximate methods are all explained, including the latest and most advanced techniques. The book includes the different techniques used for computing line profiles, polarization due to resonance line scattering, polarization in magnetic media and similar phenomena. Exercises at the end of each chapter enable these methods to be put into practice, and enhance understanding of the subject. This 2001 book will be valuable to graduates, postgraduates and researchers in astrophysics.

Table of Contents

Preface                                            xi
Definitions of fundamental quantities of 1 (28)
the radiation field
Specific intensity 1 (1)
Net flux 2 (3)
Specific luminosity 4 (1)
Density of radiation and mean intensity 5 (2)
Radiation pressure 7 (1)
Moments of the radiation field 8 (1)
Pressure tensor 8 (1)
Extinction coefficient: true absorption 9 (1)
and scattering
Emission coefficient 10 (2)
The source function 12 (1)
Local thermodynamic equilibrium 12 (1)
Non-LTE conditions in stellar atmospheres 13 (2)
Line source function for a two-level atom 15 (1)
Redistribution functions 16 (9)
Variable Eddington factor 25 (4)
Exercises 25 (2)
References 27 (2)
The equation of radiative transfer 29 (35)
General derivation of the radiative 29 (1)
transfer equation
The time-independent transfer equation in 30 (2)
spherical symmetry
Cylindrical symmetry 32 (1)
The transfer equation in 33 (5)
three-dimensional geometries
Optical depth 38 (1)
Source function in the transfer equation 39 (1)
Boundary conditions 40 (1)
Media with only either absorption or 41 (1)
emission
Formal solution of the transfer equation 42 (2)
Scattering atmospheres 44 (2)
The K-integral 46 (1)
Schwarzschild-Milne equations and 47 (4)
Λ, Φ, X operators
Eddington-Barbier relation 51 (1)
Moments of the transfer equation 52 (1)
Condition of radiative equilibrium 53 (1)
The diffusion approximations 53 (2)
The grey approximation 55 (1)
Eddington's approximation 56 (8)
Exercises 58 (5)
References 63 (1)
Methods of solution of the transfer equation 64 (24)
Chandrasekhar's solution 64 (6)
The H-function 70 (4)
The first approximation 72 (1)
The second approximation 73 (1)
Radiative equilibrium of a planetary 74 (1)
nebula
Incident radiation from an outside source 75 (3)
Diffuse reflection when ω = 1 78 (1)
(conservative case)
Iteration of the integral equation 79 (3)
Integral equation method. Solution by 82 (6)
linear equations
Exercises 83 (3)
References 86 (2)
Two-point boundary problems 88 (24)
Boundary conditions 88 (2)
Differential equation method. Riccati 90 (2)
transformation
Feautrier method for plane parallel and 92 (1)
stationary media
Boundary conditions 93 (1)
The difference equation 94 (5)
Rybicki method 99 (2)
Solution in spherically symmetric media 101(5)
Ray-by-ray treatment of Schmid-Burgk 106(2)
Discrete space representation 108(4)
Exercises 109(1)
References 110(2)
Principle of invariance 112(34)
Glass plates theory 112(4)
The principle of invariance 116(1)
Diffuse reflection and transmission 117(2)
The invariance of the law of diffuse 119(1)
reflection
Evaluation of the scattering function 120(3)
An equation connecting I(0,μ) and 123(2)
S0(μ,μ)
The integral for S with p(cosΘ = 125(1)
σv;(1 + x cosΘ)
The principle of invariance in a finite 126(4)
medium
Integral equations for the scattering and 130(3)
transmission functions
The X- and the Y-functions 133(2)
Non-uniquesness of the solution in the 135(2)
conservative case
Particle counting method 137(2)
The exit function 139(7)
Exercises 143(1)
References 144(2)
Discrete space theory 146(47)
Introduction 146(1)
The rod model 147(1)
The interaction principle for the rod 148(2)
Multiple rods: star products 150(2)
The interaction principle for a slab 152(2)
The star product for the slab 154(3)
Emergent radiation 157(1)
The internal radiation field 158(5)
Reflecting surface 163(1)
Monochromatic equation of transfer 163(5)
Non-negativity and flux conservation in 168(3)
cell matrices
Solution of the spherically symmetric 171(8)
equation
Solution of line transfer in spherical 179(6)
symmetry
Integral operator method 185(8)
Exercises 190(1)
References 191(2)
Transfer equation in moving media: the 193(24)
observer frame
Introduction 193(1)
Observer's frame in plane parallel 194(5)
geometry
Wave motion in the observer's frame 199(2)
Observer's frame and spherical symmetry 201(16)
Ray-by-ray method 201(4)
Observer's frame and discrete space 205(4)
theory
Integral form due to Averett and Loeser 209(6)
Exercises 215(1)
References 215(2)
Radiative transfer equation in the comoving 217(47)
frame
Introduction 217(1)
Transfer equation in the comoving frame 218(2)
Impact parameter method 220(5)
Application of discrete space theory to 225(13)
the comoving frame
Lorentz transformation and aberration and 238(6)
advection
The equation of transfer in the comoving 244(3)
frame
Aberration and advection with 247(4)
monochromatic radiation
Line formation with aberration and 251(3)
advection
Method of adaptive mesh 254(10)
Exercises 261(1)
References 262(2)
Escape probability methods 264(66)
Surfaces of constant radial velocity 264(2)
Sobolev method of escape probability 266(9)
Generalized Sobolev method 275(7)
Core-saturation method of Rybicki (1972) 282(5)
Scharmer's method 287(10)
Probabilistic equations for line source 297(6)
function
Empirical basis for probabilistic 297(3)
formulations
Exact equation for S/B 300(1)
Approximate probabilistic equations 301(2)
Probabilistic radiative transfer 303(7)
Mean escape probability for resonance 310(2)
lines
Probability of quantum exit 312(18)
The resolvents and Milne equations 319(5)
Exercises 324(2)
References 326(4)
Operator perturbation methods 330(32)
Introduction 330(1)
Non-local perturbation technique of Cannon 331(7)
Multi-level calculations using the 338(7)
approximate lambda operator
Complete linearization method 345(3)
Approximate lambda operator (ALO) 348(5)
Characteristics rays and ALO-ALI 353(9)
techniques
Exercises 359(1)
References 359(3)
Polarization 362(54)
Elliptically polarized beam 363(2)
Rayleigh scattering 365(2)
Rotation of the axes and Stokes parameters 367(1)
Transfer equation for I(θs;, 368(5)
φs;)
Polarization under the assumption of 373(3)
axial symmetry
Polarization in spherically symmetric 376(11)
media
Rayleigh scattering and scattering using 387(10)
planetary atmospheres
Resonance line polarization 397(19)
Exercises 412(1)
References 413(3)
Polarization in magnetic media 416(25)
Polarized light in terms of I, Q, U, V 416(2)
Transfer equation for the Stokes vector 418(3)
Solution of the vector transfer equation 421(2)
with the Milne-Eddington approximation
Zeeman line transfer: the Feautrier method 423(3)
Lambda operator method for Zeeman line 426(2)
transfer
Solution of the transfer equation for 428(5)
polarized radiation
Polarization approximate lambda iteration 433(8)
(PALI) methods
Exercises 438(1)
References 439(2)
Multi-dimensional radiative transfer 441(28)
Introduction 441(1)
Reflection effect in binary stars 442(7)
Two-dimensional transfer and discrete 449(3)
space theory
Three-dimensional radiative transfer 452(3)
Time dependent radiative transfer 455(5)
Radiative transfer, entropy and local 460(6)
potentials
Radiative transfer in masers 466(3)
Exercises 466(1)
References 467(2)
Symbol index 469(8)
Index 477