Preface ...................................................... xiii
Part I Setting the Stage
1 Introduction ................................................. 3
1.1 General Scenario and Historical Background .............. 3
1.2 Diagnostic Insight into Circumstellar Dust Shells ....... 7
1.3 Circumstellar Dust in the Laboratory ................... 15
1.4 Circumstellar Shell Dynamics and Stellar Winds ......... 19
2 Evolutionary Status of Dust-Enshrouded Objects .............. 29
2.1 Evolution from the Main Sequence toward the AGB ........ 30
2.2 Abundance Changes by First and Second "Dredge-Up" ...... 33
2.3 The Thermally Pulsing AGB .............................. 36
2.4 Abundance Changes on the AGB by the Third Dredge-Up .... 42
2.5 Post-AGB Evolution ..................................... 50
2.6 Elemental Abundances ................................... 54
Part II Theoretical Description of Circumstellar Dust Shells
3 Theory of Circumstellar Dust Shells ......................... 63
3.1 Multicomponent Medium .................................. 63
3.2 General Conservation Laws and Balance Equations ........ 69
3.3 Multicomponent Mass Equations of Change ................ 71
3.4 Momentum Equations of Change ........................... 76
3.5 Multicomponent Approaches .............................. 81
3.6 Stellar Mass Loss and Winds ............................ 84
4 Energy Equation for Matter .................................. 95
4.1 Total Energy Density and the Bulk Energy Equation ...... 95
4.2 External Energy Sources: Gravity and Radiation ......... 96
4.3 Multicomponent Energy Equations ....................... 100
4.4 Equations of Change for the Inner Energy Reservoirs ... 104
4.5 Elementary Forms of Internal Energy ................... 105
4.6 Temperature Equations ................................. 106
4.7 Completion of the System of Transport Equations of
Matter ................................................ 109
5 Radiative Transfer ......................................... 110
5.1 Basic Definitions ..................................... 110
5.2 Angular Moments of the Radiation Field ................ 114
5.3 Equation of Radiative Transfer ........................ 116
5.4 Transport Coefficients ................................ 117
5.5 Stationary Radiative Transfer Equation ................ 119
5.6 Stationary Moment Equations of Radiative Transfer ..... 120
5.7 Radiation Force Density and Radiative Net Energy
Transfer Rate ......................................... 122
5.8 Symmetric Situations .................................. 125
6 Interaction between Gas and Dust Particles ................. 130
6.1 Some Basic Considerations ............................. 130
6.2 Collision Rate between Gas and Dust ................... 136
6.3 Momentum Transfer between Gas and Dust ................ 141
6.4 Specular Reflection ................................... 144
6.5 Particle Sticking ..................................... 148
6.6 Thermal Accommodation ................................. 150
6.7 Diffuse Reflection .................................... 152
6.8 Particle Drift ........................................ 153
6.9 Drag Force ............................................ 163
7 Extinction by Dust Grains .................................. 167
7.1 Optical Constants ..................................... 168
7.2 Models for the Dielectric Function .................... 174
7.3 Absorption and Scattering by Grains ................... 186
7.4 Optical Constants of Abundant Dust Materials .......... 198
7.5 Absorption by Dust .................................... 205
7.6 Radiation Pressure on Dust Grains ..................... 211
8 Approaches to the Temperature Equations .................... 216
8.1 Radiative Equilibrium ................................. 216
8.2 Local Thermal Equilibrium ............................. 218
8.3 Radiative Equilibrium Temperature with Local Thermal
Equilibrium ........................................... 224
8.4 Non-Local Thermal Equilibrium Aspects ................. 227
9 Chemistry in Thermodynamic Equilibrium ..................... 229
9.1 The Basic Thermodynamic Relations ..................... 230
9.2 Equilibrium Conditions for Gases and Solids ........... 232
9.3 Constraints Set by Element Abundances ................. 234
9.4 Some Results of Statistical Mechanics ................. 239
9.5 Thermodynamic Data .................................... 245
10 Gas-Phase Chemical Composition ............................. 247
10.1 Qualitative Considerations on Molecule Formation ...... 247
10.2 Restrictions from Element Abundances and Bond
Energies .............................................. 252
10.3 Calculation of Chemical Equilibrium Compositions ...... 257
10.4 Results for Cosmic Element Mixtures ................... 267
10.5 Nonequilibrium Chemistry .............................. 274
11 Gas-Solid Chemical Equilibria .............................. 292
11.1 Equilibria in Gas-Solid Mixtures ...................... 292
11.2 Condensation Equilibria of Pure Phases I: O-Rich
Mixture ............................................... 299
11.3 Condensation Equilibria of Pure Phases II: C-Rich
Mixture ............................................... 314
11.4 Solid Solutions ....................................... 324
12 Growth of Dust Grains ...................................... 332
12.1 Theoretical Description of Growth Processes ........... 332
12.2 Theoretical Description of Vaporization Processes ..... 344
12.3 Calculation of Vapor Composition ...................... 348
12.4 Equation for Grain Growth ............................. 352
12.5 Equations for Some Important Dust Materials ........... 365
12.6 Solid Solutions ....................................... 373
12.7 Experimental Data for Condensation Coefficients ....... 385
12.8 Core-Mantle Grains .................................... 388
12.9 Formation of Crystalline Dust ......................... 393
13 Formation of Seed Nuclei ................................... 397
13.1 Homogeneous and Heterogeneous Nucleation .............. 398
13.2 Bond Energies of Small Clusters ....................... 400
13.3 Kinetic Theory of Homogeneous Condensation ............ 402
13.4 Cluster Densities in Thermodynamic Equilibrium ........ 409
13.5 Nucleation Rate and Cluster Size Spectrum ............. 414
13.6 Candidates for the Nucleation Process ................. 417
13.7 Classical Nucleation Theory ........................... 423
14 Moment Equations ........................................... 439
14.1 Growth of an Ensemble of Dust Grains in Stellar
Outflows .............................................. 439
14.2 Moments of the Distribution Function .................. 441
14.3 Consumption of Condensible Material ................... 446
14.4 Types of Size Distributions ........................... 450
14.5 Particle Drift ........................................ 452
Part III Applications
15 Modeling of Circumstellar Dust Shells ...................... 459
15.1 Basic Ingredients for Reliable Shell Modeling ......... 459
15.2 Spherical Stationary Stellar Dust Winds ............... 462
15.3 Shell Chemistry and Transport Coefficients ............ 465
15.4 Stationary Dust-Driven Winds .......................... 468
15.5 Models of Stationary Dust-Driven Winds ................ 474
15.6 Two-Fluid Wind Models ................................. 488
15.7 Parameter Limitations for Stationary Dust-Driven
Winds ................................................. 500
15.8 General Properties of Stationary Dust-Driven Mass
Loss .................................................. 504
15.9 Reliability of Purely Dust-Driven Wind Models ......... 519
16 Miras and Long-Period Variables ............................ 521
16.1 Basic Model Ingredients ............................... 521
16.2 Steps toward a Reliable Modeling ...................... 522
16.3 Consistent Modeling of Pulsational Circumstellar
Dust Shells ........................................... 526
16.4 Modeling Procedure .................................... 535
16.5 Consistent Models of Pulsating C-Star Shells .......... 537
16.6 Space-Time Evolution of the Isothermal Reference
Model ................................................. 545
16.7 Multiperiodicity ...................................... 554
16.8 Radiative Transfer and Spectral Appearance ............ 563
16.9 Main Results of Carbon-Rich Shells .................... 568
16.10 Oxygen-Rich Miras and LPVs ........................... 569
17 Mass-Loss Formulas ......................................... 581
17.1 Formulas Based on Empirical Correlations .............. 582
17.2 Synthetic Relations Based on Consistent Models ........ 587
17.3 Effects of the Model Parameters ....................... 597
17.4 Superwind ............................................. 600
18 R Coronae Borealis Stars ................................... 607
18.1 Light Curves of RCrB Stars ............................ 607
18.2 Stellar Pulsations .................................... 609
18.3 Attempts at Modeling .................................. 610
Part IV Appendices Appendix 1 Solution of the Radiative-
Transfer Problem for Spherical Symmetry ....................... 623
A1.1 Method of Mihalas and Hummer ............................. 623
A1.2 Lucy Approximation ....................................... 628
A1.3 Unno-Kondo Approach ...................................... 632
Appendix 2 Numerics of Time-Dependent Problems ................ 637
A2.1 Full Discretization and Courant-Friedrichs-Lewy
Condition ................................................ 637
A2.2 Semidiscretization ....................................... 638
A2.3 Basic Characterization of Available Codes ................ 639
A2.4 Rezoning Scheme .......................................... 640
Appendix 3 Non-LTE Effects and Molecular Cooling Functions .... 641
A3.1 Radiative Energy Exchange ................................ 641
Appendix 4 Thermochemical Data for Some Solids ................ 650
A4.1 Vapor Pressure of Ice .................................... 650
Appendix 5 Symbols for Mineral Names .......................... 653
Bibliography .................................................. 655
Index ......................................................... 673
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