Astrophysics: Decoding the Cosmos

Astrophysics......Page 0
Contents......Page 9
Preface......Page 15
Acknowledgments......Page 17
Introduction......Page 19
Appendix: dimensions, units and equations......Page 24
PART I THE SIGNAL OBSERVED......Page 31
1.1 The power of light - luminosity and spectral power......Page 33
1.2 Light through a surface - flux and flux density......Page 37
1.3 The brightness of light - intensity and specific intensity......Page 39
1.4 Light from all angles - energy density and mean intensity......Page 43
1.5 How light pushes - radiation pressure......Page 46
1.6.1 Apparent magnitude......Page 49
1.6.2 Absolute magnitude......Page 52
1.6.3 The colour index, bolometric correction, and HR diagram......Page 53
1.6.4 Magnitudes beyond stars......Page 54
Problems......Page 55
2.1 Spectral filters and the panchromatic universe......Page 59
2.2 Catching the signal - the telescope......Page 62
2.2.1 Collecting and focussing the signal......Page 64
2.2.2 Detecting the signal......Page 66
2.2.3 Field of view and pixel resolution......Page 67
2.2.4 Diffraction and diffraction-limited resolution......Page 68
2.3 The Corrupted signal - the atmosphere......Page 71
2.3.1 Atmospheric refraction......Page 72
2.3.2 Seeing......Page 73
2.3.3 Adaptive optics......Page 75
2.3.5 Atmospheric reddening......Page 78
2.4.1 Correcting the signal......Page 79
2.5 Analysing the signal......Page 80
2.6 Visualizing the signal......Page 82
Problems......Page 85
Appendix: refraction in the Earth\'s atmosphere......Page 88
PART II MATTER AND RADIATION ESSENTIALS......Page 93
3.1 The Big Bang......Page 95
3.2 Dark and light matter......Page 96
3.3.2 Stellar evolution and ISM enrichment......Page 100
3.3.3 Supernovae and explosive nucleosynthesis......Page 105
3.3.4 Abundances in the Milky Way, its star formation history and the IMF......Page 107
3.4 The gaseous universe......Page 112
3.4.1 Kinetic temperature and the Maxwell-Boltzmann velocity distribution......Page 114
3.4.2 The ideal gas......Page 118
3.4.3 The mean free path and collision rate......Page 119
3.4.4 Statistical equilibrium, thermodynamic equilibrium, and LTE......Page 123
3.4.5 Excitation and the Boltzmann Equation......Page 126
3.4.6 Ionization and the Saha Equation......Page 130
3.4.7 Probing the gas......Page 131
3.5 The dusty Universe......Page 134
3.5.1 Observational effects of dust......Page 135
3.5.2 Structure and composition of dust......Page 139
3.5.3 The origin of dust......Page 141
3.6.1 Cosmic ray composition......Page 142
3.6.2 The cosmic ray energy spectrum......Page 143
3.6.3 The origin of cosmic rays......Page 147
Problems......Page 148
Appendix: the electron/proton ratio in cosmic rays......Page 151
4.1 Black body radiation......Page 153
4.1.1 The brightness temperature......Page 157
4.1.2 The Rayleigh-Jeans Law and Wien\'s Law......Page 159
4.1.3 Wien\'s Displacement Law and stellar colour......Page 160
4.1.4 The Stefan-Boltzmann Law, stellar luminosity and the HR diagram......Page 162
4.2 Grey bodies and planetary temperatures......Page 164
4.2.1 The equilibrium temperature of a grey body......Page 166
4.2.2 Direct detection of extrasolar planets......Page 170
Problems......Page 173
4.A.1 The statistical weight......Page 176
4.A.2 The mean energy per state......Page 177
4.A.3 The specific energy density and specific intensity......Page 178
PART III THE SIGNAL PERTURBED......Page 181
5 The interaction of light with matter......Page 183
5.1 The photon redirected - scattering......Page 184
5.1.1 Elastic scattering......Page 187
5.1.2 Inelastic scattering......Page 195
5.2.1 Particle kinetic energy - heating......Page 198
5.2.2 Change of state - ionization and the Stro¨mgren sphere......Page 199
5.3 The wavefront redirected - refraction......Page 202
5.4.2 Dynamics of opacity – pulsation and stellar winds......Page 205
5.5 The opacity of dust - extinction......Page 212
Problems......Page 213
6.1 Types of energy transfer......Page 217
6.2 The equation of transfer......Page 219
6.3.1 Case A: no cloud......Page 221
6.3.3 Case C: emitting, but not absorbing cloud......Page 222
6.3.5 Case E: emitting and absorbing cloud......Page 223
6.3.6 Case F: emitting and absorbing cloud in LTE......Page 224
6.4.1 Implications for temperature......Page 225
6.4.2 Observability of emission and absorption lines......Page 226
6.4.3 Determining temperature and optical depth of HI clouds......Page 230
Problems......Page 234
7.1 Space and time......Page 237
7.2.1 The Doppler shift - deciphering dynamics......Page 240
7.2.2 The expansion redshift......Page 247
7.2.3 The gravitational redshift......Page 249
7.3.1 Geometry and mass of a gravitational lens......Page 250
7.3.2 Microlensing - MACHOs and planets......Page 255
7.3.3 Cosmological distances with gravitational lenses......Page 256
7.4 Time variability and source size......Page 257
Problems......Page 258
PART IV THE SIGNAL EMITTED......Page 263
8 Continuum emission......Page 265
8.1 Characteristics of continuum emission – thermal and non-thermal......Page 266
8.2.1 The thermal Bremsstrahlung spectrum......Page 267
8.2.2 Radio emission from HII and other ionized regions......Page 272
8.2.3 X-ray emission from hot diffuse gas......Page 275
8.3 Free–bound (recombination) emission......Page 281
8.4 Two-photon emission......Page 283
8.5 Synchrotron (and cyclotron) radiation......Page 285
8.5.1 Cyclotron radiation – planets to pulsars......Page 288
8.5.2 The synchrotron spectrum......Page 292
8.5.3 Determining synchrotron source properties......Page 298
8.5.4 Synchrotron sources - spurs, bubbles, jets, lobes and relics......Page 300
8.6 Inverse Compton radiation......Page 303
Problems......Page 306
9 Line emission......Page 309
9.1.1 Electronic transitions - optical and UV lines......Page 310
9.1.2 Rotational and vibrational transitions - molecules, IR and mm-wave spectra......Page 311
9.1.3 Nuclear transitions -g-rays and high energy events......Page 316
9.2 The line strengths, thermalization, and the critical gas density......Page 318
9.3 Line broadening......Page 320
9.3.1 Doppler broadening and temperature diagnostics......Page 321
9.3.2 Pressure broadening......Page 325
9.4 Probing physical conditions via electronic transitions......Page 326
9.4.1 Radio recombination lines......Page 327
9.4.2 Optical recombination lines......Page 332
9.4.3 The 21 cm line of hydrogen......Page 337
9.5.1 The CO molecule......Page 341
Problems......Page 343
PART V THE SIGNAL DECODED......Page 347
10.1.1 Isolating the signal......Page 349
10.1.2 Modelling the signal......Page 351
10.2 Case studies - the active, the young, and the old......Page 355
10.2.1 Case study 1: the Galactic Centre......Page 356
10.2.2 Case study 2: the Cygnus star forming complex......Page 359
10.2.3 Case study 3: the globular cluster, NGC 6397......Page 361
10.3 The messenger and the message......Page 365
Problems......Page 366
A.2 Binomial expansion......Page 369
A.5 Properties of the ellipse......Page 370
B.1 One-dimensional and two-dimensional angles......Page 373
B.2 Solid angle and the spherical coordinate system......Page 374
C.1 The hydrogen spectrum and principal quantum number......Page 377
C.2 Quantum numbers, degeneracy, and statistical weight......Page 382
C.3 Fine structure and the Zeeman effect......Page 383
C.4 The l 21 cm line of neutral hydrogen......Page 384
Appendix D: Scattering processes......Page 387
D.1.1 Scattering from free electrons – Thomson scattering......Page 388
D.1.2 Scattering from bound electrons I: the oscillator model......Page 389
D.1.3 Scattering from bound electrons II: quantum mechanics......Page 392
D.1.4 Scattering from bound electrons III: resonance scattering and the natural line shape......Page 393
D.1.5 Scattering from bound electrons IV: Rayleigh scattering......Page 396
D.2 Inelastic scattering – Compton scattering from free electrons......Page 397
D.3 Scattering by dust......Page 399
Appendix E: Plasmas, the plasma frequency, and plasma waves......Page 403
F.1 Kinematics of the Universe......Page 407
F.2 Dynamics of the Universe......Page 413
F.3 Kinematics, dynamics and high redshifts......Page 416
Appendix G: Tables and figures......Page 419
References......Page 431
Index......Page 437
Colour insert......Page 448