Atomic Astrophysics and Spectroscopy

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
Acknowledgements......Page 13
1.1 Atomic astrophysics and spectroscopy......Page 15
1.2 Chemical and physical properties of elements......Page 16
1.3 Electromagnetic spectrum and observatories......Page 18
1.4 Astrophysical and laboratory plasmas......Page 19
1.5 Particle distributions......Page 20
1.5.2.1 Black-body radiation and the Sun......Page 21
1.5.2.2 Maxwellian particle distribution......Page 23
1.6.2 Fermi–Dirac statistics......Page 24
1.7.1 Photometry and imaging......Page 25
1.8 Spectroscopic notation......Page 26
1.9 Units and dimensions......Page 27
2 Atomic structure......Page 29
2.1.1 Angular equation......Page 30
2.1.3 Rydberg states and hydrogenic energy levels......Page 31
2.1.4 Hydrogenic wavefunctions......Page 32
2.2 Quantum numbers and parity......Page 33
2.3 Spectral lines and the Rydberg formula......Page 34
2.4 Spectroscopic designation......Page 35
2.5.1 Non-equivalent electron states......Page 37
2.5.2 Equivalent electron states......Page 38
2.7 Intermediate coupling and jj coupling......Page 39
2.8 Hund\'s rules......Page 40
2.9 Rydberg formula with quantum defect......Page 41
2.10 Multi-electron atomic systems......Page 43
2.11 The Hartree–Fock method......Page 44
2.11.1 Configuration mixing......Page 47
2.12 Central-field approximation......Page 49
2.12.1 Thomas–Fermi–Dirac approximation......Page 50
2.13.1 Spin–orbit interaction......Page 51
2.13.2 The Dirac equation......Page 52
2.13.4 Dirac equation in a central field......Page 54
2.13.5 Multi-electron systems and the Breit equation......Page 56
2.13.6 Dirac–Fock approximation......Page 57
2.13.7 Z-scaling of fine structure......Page 58
3 Atomic processes......Page 60
3.1 Bound, continuum and resonance states......Page 61
3.2.1 Detailed balance......Page 63
3.2.3 Electron impact excitation......Page 64
3.2.6 Electron impact ionization......Page 65
3.2.7 Charge exchange recombination and ionization......Page 66
3.3 Theoretical approximations......Page 67
3.3.1 Channels in atomic processes......Page 68
3.3.2 Scattering phase shift......Page 69
3.4 The close coupling approximation......Page 70
3.4.1 Scattering matrices and cross section......Page 71
3.5.1 Single-channel problem......Page 73
3.5.2 Multi-channel problem......Page 74
3.5.3 Inner region......Page 75
3.5.4 Outer region......Page 76
3.5.6 Bound states: all channels closed......Page 77
3.5.7 The R-matrix codes......Page 78
3.6 Approximate methods......Page 79
3.6.1 Distorted wave method......Page 80
3.6.2 Coulomb–Born approximation......Page 82
3.6.5 Quantum defect theory......Page 83
4 Radiative transitions......Page 86
4.1 Einstein A and B coefficients......Page 87
4.2 Electron motion in an electromagnetic field......Page 89
4.2.1 Radiative transition probability......Page 90
4.3 Transition matrix elements......Page 91
4.5 Electric dipole approximation......Page 92
4.5.2 Oscillator strengths......Page 94
4.6 Central-field approximation......Page 95
4.7 Length, velocity and acceleration......Page 98
4.8 Oscillator strengths for hydrogen......Page 99
4.9 Configuration interaction......Page 100
4.10 Fine structure......Page 101
4.11 R-matrix transition probabilities......Page 102
4.12 Higher-order multipole transitions......Page 105
4.14 Dipole and non-dipole transitions in He-like ions......Page 107
4.15.1 Fine structure components of LS multiplets......Page 108
5 Electron–ion collisions......Page 111
5.1.1 Cross section......Page 112
5.1.2 Collision strength......Page 113
5.2 Theoretical approximations......Page 115
5.2.2 Multi-channel scattering matrix......Page 116
5.2.3 Multi-channel quantum defect theory......Page 117
5.3 Excitation rate coefficients......Page 118
5.4.1.1 Target eigenfunctions for Fe XVII......Page 119
5.4.2 Channel coupling......Page 122
5.4.4 Exchange......Page 123
5.4.6 Relativistic effects......Page 124
5.5 Scaling of collision strengths......Page 125
5.6 Comparison with experiments......Page 126
5.8 Electron impact ionization......Page 129
5.8.2 Semi-empirical formulae......Page 130
5.9 Auger effect......Page 131
5.9.1 Z-dependence of X-ray transitions......Page 133
6 Photoionization......Page 134
6.1 Hydrogen and helium......Page 135
6.3 Bound–free transition matrix element......Page 136
6.4 Central potential......Page 138
6.4.1 Energy dependence......Page 139
6.5 Generalized bound–free transition probability......Page 140
6.5.1 R-matrix photoionization calculations......Page 141
6.6 Channel coupling and resonances......Page 142
6.6.1 Partial cross sections......Page 143
6.6.2 Types of resonance......Page 144
6.6.2.2 Resonances below threshold in LS coupling......Page 145
6.6.2.3 Resonances below threshold due to fine structure......Page 146
6.6.2.4 Highly-excited core (HEC) resonances......Page 147
6.6.2.5 Photo-excitation of core (PEC) resonances......Page 148
6.6.2.6 Equivalent-electron quasi-bound resonances......Page 150
6.8 Resonance-averaged cross section......Page 151
6.9 Radiation damping of resonances......Page 153
6.9.1 Differential oscillator strength......Page 154
6.9.3 Resonance profiles......Page 155
6.9.4 Shape and Feshbach resonances......Page 157
6.10 Angular distribution and asymmetry......Page 158
7 Electron–ion recombination......Page 161
7.2 Total electron–ion recombination rate......Page 162
7.3.2 Dielectronic recombination......Page 163
7.3.2.1 Quantum probability......Page 166
7.4.1 Rate coefficients......Page 167
7.4.2 Level-specific rate coefficients......Page 168
7.4.3 DR cross sections......Page 169
7.4.4 Multiple resonant features......Page 172
7.4.5 Comparison between experiment and theory......Page 173
7.5 Photorecombination and dielectronic recombination......Page 177
7.6.1 Temperature diagnostics......Page 178
7.6.2 Dielectronic satellite line strengths......Page 181
7.6.2.1 Correspondence between isolated and unified approximations......Page 182
7.8 Ionization equilibrium......Page 183
7.8.1 Photoionization equilibrium......Page 185
7.8.2 Collisional equilibrium......Page 186
7.9 Effective recombination rate coefficient......Page 187
7.10 Plasma effects......Page 188
8 Multi-wavelength emission spectra......Page 189
8.1.1 Atomic rates and lifetimes......Page 190
8.1.2 Collisional and radiative rates......Page 191
8.2 Collisional-radiative model......Page 192
8.3.1 Optical lines: [OII], [SII], [OIII]......Page 193
8.3.1.1 Density dependence of [O II] and [S II] lines......Page 194
8.3.2 Hydrogen and helium recombination lines......Page 196
8.4.1 Density diagnostic ratio R = f / i......Page 197
8.4.3 Electron impact excitation of X-ray lines......Page 198
8.4.4 R and G ratios with fine structure......Page 200
8.4.5 Transient X-ray sources......Page 201
8.5 Far-infrared lines: the boron isoelectronic sequence......Page 205
9.1 Optical depth and column density......Page 208
9.2 Line broadening......Page 209
9.2.1 Natural radiation damping......Page 210
9.2.1.1 Damping constant and classical oscillator......Page 211
9.2.2 Doppler broadening......Page 212
9.2.3 Collisional broadening......Page 213
9.2.3.1 The classical impact approximation......Page 214
9.2.3.3 The nearest-neighbour approximation......Page 215
9.2.3.4 The Holtsmark distribution......Page 216
9.2.3.5 Debye screening potential......Page 217
9.2.3.6 Electron impact broadening......Page 218
9.3 Absorption lines......Page 219
9.3.1 Equivalent width......Page 220
9.3.2 Curve of growth......Page 222
9.4 Radiative transfer......Page 223
9.4.1 Intensity and flux......Page 224
9.4.2 Transfer equation and the source function......Page 225
9.4.4 The two-level atom......Page 226
9.4.5 Scattering......Page 227
9.4.6 Plane-parallel approximation......Page 228
9.4.8 The lambda-operator......Page 229
9.5.2 Boltzmann equation......Page 230
9.5.3 Saha equation......Page 231
9.5.4 Non-LTE rate equation and equation-of-state......Page 232
10.1 Luminosity......Page 234
10.2 Spectral classification – HR diagram......Page 235
10.3 Stellar population – mass and age......Page 238
10.5 Colour, extinction and reddening......Page 239
10.6 Stellar structure and evolution......Page 240
10.6.3 White dwarfs......Page 242
10.6.6 Pulsating stars......Page 243
Novae and Type Ia supernovae......Page 244
10.8 Atmospheres......Page 245
10.9.1 Photosphere......Page 246
10.9.4 Solar corona......Page 249
10.10 Cool and hot stars......Page 250
10.11 Luminous blue variables......Page 251
11.1 Radiative and convective envelope......Page 253
11.2 Equations of stellar structure......Page 254
11.3.1 Diffusion approximation......Page 255
11.4.1 Equation-of-state......Page 257
11.4.1.1 Partition function and occupation probability......Page 258
11.4.2 Radiative atomic processes......Page 260
11.4.2.3 Free–free transitions: inverse bremsstrahlung......Page 261
11.4.3 Monochromatic opacities......Page 262
11.4.4 Abundances, mixtures and atomic data......Page 263
11.5 Radiative forces and levitation......Page 266
11.5.1 Atomic processes and momemtum transfer......Page 267
11.5.2 Radiative acceleration......Page 268
11.6 Opacities and accelerations database......Page 269
12.2 Physical model and atomic species......Page 271
12.3 Ionization structure......Page 273
12.4 Spectral diagnostics......Page 275
12.4.1.1 Case A and Case B recombination......Page 276
12.4.1.2 Cascade coefficients and emissivities......Page 277
12.4.2 Departures from LTE......Page 278
12.4.3 Collisional excitation and photoionization rates......Page 279
12.4.4.1 [FeII] lines......Page 280
12.4.4.3 [Fe IV] lines......Page 283
12.5.2 Continuum fluorescence......Page 286
12.5.2.1 Fluorescence of Ni II......Page 287
12.6 Abundance analysis......Page 289
12.7 Atomic parameters for nebular emission lines......Page 291
13 Active galactic nuclei and quasars......Page 292
13.1 Morphology, energetics and spectra......Page 293
13.1.2 Supermassive black holes: the central engines......Page 295
13.1.4 The M.–sigma relation......Page 298
13.1.6 States of black hole activity......Page 299
13.1.7 Radio intensity......Page 301
13.2 Spectral characteristics......Page 302
13.3 Narrow-line region......Page 304
13.5 Fe II spectral formation......Page 305
13.5.1 Fe II Excitation Mechanisms......Page 306
13.5.2 Fe I–Fe III emission line strengths......Page 307
13.5.3 Spectral properties and the central source......Page 308
13.6 The central engine – X-ray spectroscopy......Page 309
13.6.1 Fe Kalpha X-ray lines and relativistic broadening......Page 310
13.6.2 Warm absorber (WA)......Page 313
13.6.4 L-shell lines......Page 314
13.6.5 K-shell lines......Page 316
14 Cosmology......Page 319
14.1 Hubble expansion......Page 320
14.2 Recombination epoch......Page 321
14.3 Reionization and Lyα forests......Page 322
14.3.1 Damped Lyman alpha systems......Page 323
14.4 CMB anisotropy......Page 324
14.5 Helium abundance......Page 326
14.6 Dark matter: warm–hot intergalactic medium......Page 327
14.7 Time variation of fundamental constants......Page 328
14.8.1 Parallax......Page 330
14.8.3 Cepheid distance scale......Page 331
14.8.4 Rotation velocity and luminosity......Page 332
14.8.5 Supernovae......Page 333
14.8.6 Acceleration of the Universe and dark energy......Page 336
Appendix A Periodic table......Page 338
Appendix B Physical constants......Page 339
C.1 3-j symbols......Page 342
C.3 Vector and tensor components......Page 343
C.4 Generalized radiative transitions......Page 344
Appendix D Coefficients of the fine structure components of an LS multiplet......Page 347
Appendix E Effective collision strengths and A-values......Page 351
References......Page 362
Index......Page 371