The physics of interstellar dust

Contents......Page 8
Preface......Page 20
1.1.1 Electric field and magnetic induction......Page 26
1.1.2 Electric polarization of the medium......Page 27
1.1.3 The dependence of the dielectric permeability on direction and frequency......Page 28
1.1.4 The physical meaning of the electric susceptibility χ......Page 29
1.1.5 Magnetic polarization of the medium......Page 31
1.1.7 Dielectrics and metals......Page 32
1.1.8 Free charges and polarization charges......Page 33
1.1.9 The field equations......Page 34
1.2.1 The wave equation......Page 35
1.2.2 The wavenumber......Page 36
1.2.3 The optical constant or refractive index......Page 37
1.2.4 Energy dissipation of a grain in a variable field......Page 38
1.3.1 The Lorentz model......Page 40
1.3.2 Free oscillations......Page 41
1.3.3 The general solution to the oscillator equation......Page 42
1.3.4 Dissipation of energy in a forced oscillation......Page 43
1.3.5 Dissipation of energy in a free oscillation......Page 44
1.3.7 Dispersion relation of the dielectric permeability......Page 45
1.4 The harmonic oscillator and light......Page 47
1.4.1 Attenuation and refraction of light......Page 48
1.4.2 Retarded potentials of a moving charge......Page 49
1.4.3 Emission of an harmonic oscillator......Page 51
1.4.4 Radiation of higher order......Page 52
1.4.5 Radiation damping......Page 53
1.4.6 The cross section of an harmonic oscillator......Page 54
1.4.7 The oscillator strength......Page 55
1.4.8 The natural linewidth......Page 56
1.5 Waves in a conducting medium......Page 57
1.5.1 The dielectric permeability of a conductor......Page 58
1.5.2 Conductivity and the Drude profile......Page 59
1.5.3 Electromagnetic waves in a plasma with a magnetic field......Page 61
1.5.4 Group velocity of electromagnetic waves in a plasma......Page 62
1.6.1 Polarization in a constant field......Page 63
1.6.2 Polarization in a time-variable field......Page 64
1.6.3 Relaxation after switching off the field......Page 65
1.6.4 The dielectric permeability in Debye relaxation......Page 66
2.1.1 Cross section for scattering, absorption and extinction......Page 69
2.1.2 Cross section for radiation pressure......Page 71
2.2.1 The intensity of forward scattered light......Page 72
2.2.2 The refractive index of a dusty medium......Page 75
2.3 Mie theory for a sphere......Page 76
2.3.2 Separation of variables......Page 77
2.3.4 Expansion coefficients......Page 79
2.3.5 Scattered and absorbed power......Page 81
2.4.1 The amplitude scattering matrix......Page 82
2.4.2 Angle-dependence of scattering......Page 83
2.4.3 The polarization ellipse......Page 85
2.4.4 Stokes parameters......Page 86
2.4.5 Stokes parameters of scattered light for a sphere......Page 87
2.5.1 Mathematical formulation of the relations......Page 89
2.5.2 The electric susceptibility and causality......Page 91
2.5.4 Extension to metals......Page 92
2.5.5 Dispersion of the magnetic susceptibility......Page 93
2.5.6 Three corollaries of the KK relation......Page 94
2.6 Composite grains......Page 96
2.6.1 Effective medium theories......Page 97
2.6.2 Garnett’s mixing rule......Page 98
2.6.4 Composition of grains in protostellar cores......Page 99
2.6.5 How size, ice and porosity change the absorption coefficient......Page 101
3.1.1 When is a particle in the Rayleigh limit?......Page 105
3.1.2 Efficiencies of small spheres from Mie theory......Page 106
3.1.3 A dielectric sphere in a constant electric field......Page 107
3.1.4 Scattering and absorption in the electrostatic approximation......Page 109
3.1.5 Polarization and angle-dependent scattering......Page 110
3.1.6 Small-size effects beyond Mie theory......Page 111
3.2.1 Slowly varying field......Page 112
3.2.3 The penetration depth......Page 114
3.3 Tiny ellipsoids......Page 115
3.3.1 Elliptical coordinates......Page 116
3.3.2 An ellipsoid in a constant electric field......Page 117
3.3.3 Cross section and shape factor......Page 118
3.3.5 Pancakes and cigars......Page 120
3.3.6 Rotation about the axis of greatest moment of inertia......Page 122
3.4.1 Internal field and depolarization field......Page 124
3.4.2 Depolarization field and the distribution of surface charges......Page 125
3.4.4 The Clausius–Mossotti relation......Page 126
3.5.1 Babinet’s theorem......Page 128
3.5.2 Reflection and transmission at a plane surface......Page 129
3.5.3 Huygens’ principle......Page 131
3.5.4 Fresnel zones and a check on Huygens’ principle......Page 134
3.5.6 Diffraction by a circular hole or a sphere......Page 136
3.5.7 Diffraction behind a half-plane......Page 138
3.5.8 Particles of small refractive index......Page 141
3.5.9 X-ray scattering......Page 142
4.1.1 Pure scattering......Page 144
4.1.2 A weak absorber......Page 145
4.1.3 A strong absorber......Page 147
4.1.5 Efficiency versus cross section and volume coefficient......Page 148
4.1.6 The atmosphere of the Earth......Page 151
4.2.1 The scattering diagram......Page 152
4.2.2 The polarization of scattered light......Page 153
4.2.3 The intensity of scattered light in a reflection nebula......Page 156
4.3 Coated spheres......Page 157
4.4 Surface modes in small grains......Page 158
4.5.1 Dielectric sphere consisting of identical harmonic oscillators......Page 161
4.5.2 Dielectric sphere with Debye relaxation......Page 163
4.5.3 Magnetic and electric dipole absorption of small metal spheres......Page 164
4.5.4 Efficiencies for Drude profiles......Page 166
4.5.5 Elongated metallic particles......Page 167
5.1.1 The probability of an arbitrary energy distribution......Page 170
5.1.2 The distribution of maximum probability......Page 171
5.1.3 Partition function and population of energy cells......Page 172
5.1.5 The Maxwellian velocity distribution......Page 174
5.2.1 The unit cell h3 of the phase space......Page 176
5.2.2 Bosons and fermions......Page 177
5.2.3 Bose statistics......Page 179
5.2.4 Bose statistics for photons......Page 181
5.2.5 Fermi statistics......Page 182
5.2.6 Ionization equilibrium and the Saha equation......Page 183
5.3.1 The ergodic hypothesis......Page 185
5.3.2 Definition of entropy and temperature......Page 187
5.3.3 The canonical distribution......Page 188
5.3.4 Thermodynamic relations for a gas......Page 189
5.3.5 Equilibrium conditions of the state functions......Page 191
5.3.7 The work done by magnetization......Page 193
5.3.8 Susceptibility and specific heat of magnetic substances......Page 194
5.4.1 The Planck function......Page 195
5.4.2 Low- and high-frequency limit......Page 196
5.4.3 Wien’s displacement law and the Stefan–Boltzmann law......Page 197
5.4.4 The Planck function and harmonic oscillators......Page 198
6.1.1 The classical Hamiltonian......Page 200
6.1.2 The Hamiltonian of an electron in an electromagnetic field......Page 201
6.1.3 The Hamilton operator in quantum mechanics......Page 202
6.1.5 The quantized harmonic oscillator......Page 204
6.2.2 The transition probability......Page 206
6.2.3 Transition probability for a time-variable perturbation......Page 207
6.3.1 Induced and spontaneous transitions......Page 208
6.3.3 Quantization of the electromagnetic field......Page 211
6.3.4 Quantum-mechanical derivation of A and B......Page 213
6.4.2 Potential walls and Fermi energy......Page 217
6.4.3 Rectangular potential barriers......Page 219
6.4.4 The double potential well......Page 223
7.1.1 Translational symmetry......Page 226
7.1.2 Lattice types......Page 228
7.2 Binding in crystals......Page 232
7.2.1 Covalent bonding......Page 233
7.2.2 Ionic bonding......Page 234
7.2.3 Metals......Page 236
7.2.4 van der Waals forces and hydrogen bridges......Page 238
7.3.1 Stellar photometry......Page 239
7.3.2 The interstellar extinction curve......Page 241
7.3.3 Two-color diagrams......Page 244
7.3.4 Spectral indices......Page 245
7.3.5 The mass absorption coefficient......Page 247
7.4.1 Origin of the two major dust constituents......Page 249
7.4.2 The bonding in carbon......Page 250
7.4.3 Carbon compounds......Page 252
7.4.4 Silicates......Page 257
7.4.5 A standard set of optical constants......Page 258
7.5.1 The size distribution......Page 259
7.5.2 Collisional fragmentation......Page 261
8.1.1 The emissivity of dust......Page 264
8.1.2 Thermal emission of grains......Page 265
8.1.3 Absorption and emission in thermal equilibrium......Page 266
8.1.4 Equipartition of energy......Page 267
8.2.2 Approximate absorption efficiency at infrared wavelengths......Page 268
8.2.3 Temperature estimates......Page 270
8.2.4 Relation between grain size and grain temperature......Page 272
8.2.5 Temperature of dust grains near a star......Page 273
8.2.6 Dust temperatures from observations......Page 274
8.3.1 Constant temperature and low optical depth......Page 276
8.3.2 Constant temperature and arbitrary optical depth......Page 278
8.4.1 Normal coordinates......Page 279
8.4.2 Internal energy of a grain......Page 281
8.4.3 Standing waves in a crystal......Page 282
8.4.4 The density of vibrational modes in a crystal......Page 283
8.4.5 Specific heat......Page 284
8.4.6 Two-dimensional lattices......Page 286
8.5 Temperature fluctuations of very small grains......Page 287
8.5.2 The transition matrix......Page 288
8.5.3 Practical considerations......Page 290
8.5.4 The stochastic time evolution of grain temperature......Page 291
8.6.1 Small and moderate fluctuations......Page 293
8.6.2 Strong fluctuations......Page 295
8.6.3 Temperature fluctuations and flux ratios......Page 297
9.1.1 Gas accretion on grains......Page 300
9.1.2 Physical adsorption and chemisorption......Page 301
9.1.3 The sticking probability......Page 304
9.1.4 Thermal hopping, evaporation and reactions with activation barrier......Page 306
9.1.5 Tunneling between surface sites......Page 308
9.1.6 Scanning time......Page 309
9.2.1 Charge equilibrium in the absence of a UV radiation field......Page 310
9.2.2 The photoelectric effect......Page 311
9.3.2 The drag on a grain subjected to a constant outer force......Page 314
9.3.3 Brownian motion of a grain......Page 317
9.3.4 The disorder time......Page 318
9.3.5 Laminar and turbulent friction......Page 320
9.3.6 A falling rain drop......Page 321
9.3.7 The Poynting–Robertson effect......Page 322
9.4.1 Mass balance in the Milky Way......Page 323
9.4.2 Destruction processes......Page 324
9.5.1 Evaporation temperature of dust......Page 326
9.5.2 Vapor pressure of small grains......Page 329
9.5.3 Critical saturation......Page 330
9.5.4 Equations for time-dependent homogeneous nucleation......Page 332
9.5.5 Equilibrium distribution and steady-state nucleation......Page 333
9.5.6 Solutions to time-dependent homogeneous nucleation......Page 336
9.5.7 Similarity relations......Page 341
10.1.1 Normal incidence and picket fence alignment......Page 344
10.1.3 Rotating cylinders......Page 347
10.1.4 Absorption efficiency as a function of wavelength......Page 350
10.2.1 Effective optical depth and degree of polarization p(λ)......Page 352
10.2.2 The Serkowski curve......Page 354
10.2.3 Polarization p(λ) of infinite cylinders......Page 356
10.2.4 Polarization p(λ) of ellipsoids in the Rayleigh limit......Page 359
10.2.5 Polarization p(λ) of spheroids at optical wavelengths......Page 362
10.2.6 Polarization and reddening......Page 363
10.3 Polarized emission......Page 364
10.3.2 Infrared emission of spheroids......Page 365
10.3.3 Polarized emission versus polarized extinction......Page 366
10.4 Circular polarization......Page 367
10.4.1 The phase shift induced by grains......Page 368
10.4.2 The wavelength dependence of circular polarization......Page 369
11.1.1 Euler’s equations for a rotating body......Page 372
11.1.2 Symmetric tops......Page 374
11.1.4 Rotational Brownian motion......Page 376
11.1.5 Suprathermal rotation......Page 378
11.2.2 Paramagnetism......Page 380
11.2.3 Ferromagnetism......Page 382
11.2.4 The magnetization of iron above and below the Curie point......Page 383
11.2.5 Paramagnetic dissipation: spin–spin and spin–lattice relaxation......Page 384
11.2.6 The magnetic susceptibility for spin–lattice relaxation......Page 385
11.2.7 The magnetic susceptibility in spin–spin relaxation......Page 387
11.3 Magnetic alignment......Page 389
11.3.1 A rotating dipole in a magnetic field......Page 390
11.3.2 Timescales for alignment and disorder......Page 392
11.3.3 Super-paramagnetism......Page 393
11.3.4 Ferromagnetic relaxation......Page 394
11.3.5 Alignment of angular momentum with the axis of greatest inertia......Page 396
11.3.6 Mechanical and magnetic damping......Page 397
11.4.1 Gas streaming......Page 398
11.4.2 Anisotropic illumination......Page 400
12.1.1 What are PAHs?......Page 402
12.1.2 Microcanonic emission of PAHs......Page 403
12.1.3 The vibrational modes of anthracene......Page 404
12.1.4 Microcanonic versus thermal level population......Page 406
12.1.5 Does an ensemble of PAHs have a temperature?......Page 407
12.2.1 Photoexcitation of PAHs......Page 409
12.2.2 Cutoff wavelength for electronic excitation......Page 410
12.2.3 Photo-destruction and ionization......Page 411
12.2.4 Cross sections and line profiles of PAHs......Page 412
12.3 Big grains and ices......Page 413
12.3.2 Icy grain mantles......Page 414
12.4 An overall dust model......Page 415
12.4.1 The three dust components......Page 417
12.4.3 Extinction coefficient in protostellar cores......Page 420
13.1.1 Radiative intensity and flux......Page 421
13.1.2 The transfer equation and its formal solution......Page 423
13.1.3 The brightness temperature......Page 425
13.1.4 The main-beam-brightness temperature of a telescope......Page 426
13.2 Spherical clouds......Page 427
13.2.1 Moment equations for spheres......Page 428
13.2.2 Frequency averages......Page 429
13.2.3 Differential equations for the intensity......Page 430
13.2.5 Practical hints......Page 432
13.3.1 Radiative transfer in a plane parallel layer......Page 434
13.3.2 The grazing angle in an inflated disk......Page 439
13.4.1 Hot spots in a spherical stellar cluster......Page 440
13.4.2 Low and high luminosity stars......Page 441
13.5.1 Absorption coefficient and absorption profile......Page 443
13.5.2 The excitation temperature of a line......Page 444
13.5.3 Radiative transfer in lines......Page 445
14.1.1 Global parameters......Page 450
14.1.2 The relevance of dust......Page 451
14.2 Molecular clouds......Page 452
14.2.1 The CO molecule......Page 453
14.2.2 Population of levels in CO......Page 456
14.2.4 Formation of molecular hydrogen on dust surfaces......Page 460
14.3.1 General properties of the diffuse gas......Page 463
14.3.2 The 21 cm line of atomic hydrogen......Page 464
14.3.3 How the hyperfine levels of atomic hydrogen are excited......Page 465
14.3.4 Gas density and temperature from the 21 cm line......Page 468
14.3.5 The deuterium hyperfine line......Page 469
14.3.6 Electron density and magnetic field in the diffuse gas......Page 471
14.4.1 Ionization and recombination......Page 473
14.4.2 Dust–free HII regions......Page 475
14.4.3 Dusty HII regions......Page 478
14.4.4 Bremsstrahlung......Page 480
14.4.5 Recombination lines......Page 481
14.5.1 From optically thin CO lines......Page 482
14.5.2 From the CO luminosity......Page 483
14.5.3 From dust emission......Page 484
15.1.1 Nuclear burning and the creation of elements......Page 486
15.1.2 The binding energy of an atomic nucleus......Page 488
15.1.3 Hydrogen burning......Page 490
15.1.4 The 3α process......Page 492
15.1.5 Lifetime and luminosity of stars......Page 494
15.1.6 The initial mass function......Page 495
15.2.1 Virialized clouds......Page 496
15.2.2 Isothermal cloud in pressure equilibrium......Page 499
15.2.3 Structure and stability of Ebert–Bonnor spheres......Page 500
15.2.4 Free-fall of a gas ball......Page 504
15.2.5 The critical mass for gravitational instability......Page 505
15.2.6 Implications of the Jeans criterion......Page 507
15.2.7 Magnetic fields and ambipolar diffusion......Page 509
15.3.1 The presolar nebula......Page 511
15.3.2 Hydrodynamic collapse simulations......Page 512
15.3.3 Similarity solutions of collapse......Page 516
15.4.1 Viscous laminar flows......Page 519
15.4.2 Dynamical equations of the thin accretion disk......Page 522
15.4.3 The Kepler disk......Page 523
15.4.4 Why a star accretes from a disk......Page 524
15.4.6 The α-disk......Page 526
15.4.7 Disk heating by viscosity......Page 528
16.1.1 Globules......Page 530
16.1.2 Isothermal gravitationally-bound clumps......Page 531
16.2.1 The density structure of a protostar......Page 533
16.2.2 Dust emission from a solar-type protostar......Page 538
16.2.3 Kinematics of protostellar collapse......Page 540
16.3.1 A flat blackbody disk......Page 543
16.3.2 A flat non-blackbody disk......Page 546
16.3.3 Radiative transfer in an inflated disk......Page 547
16.4 Reflection nebulae......Page 549
16.5 Cold and warm dust in galaxies......Page 551
16.6.1 Repetitive bursts of star formation......Page 556
16.6.2 Dust emission from starburst nuclei......Page 560
Appendix A: Mathematical formulae......Page 564
Appendix B: List of symbols......Page 570
References......Page 574
C......Page 577
D......Page 578
E......Page 579
H......Page 580
M......Page 581
P......Page 582
S......Page 583
Z......Page 584