THE PHYSICS OF INTERSTELLAR DUST
CONTENTS THE DIELECTRIC PERMEABILITY MAXWELL’S EQUATIONS ELECTRIC ?ELD AND MAGNETIC INDUCTION ELECTRIC POLARIZATION OF THE MEDIUM THE DEPENDENCE OF THE DIELECTRIC PERMEABILITY ON DIRECTION AND FREQUENCY THE PHYSICAL MEANING OF THE ELECTRIC SUSCEPTIBILITY ? MAGNETIC POLARIZATION OF THE MEDIUM THE MAGNETIC SUSCEPTIBILITY DIELECTRICS AND METALS FREE CHARGES AND POLARIZATION CHARGES THE ?ELD EQUATIONS WAVES IN A DIELECTRIC MEDIUM THE WAVE EQUATION THE WAVENUMBER THE OPTICAL CONSTANT OR REFRACTIVE INDEX ENERGY DISSIPATION OF A GRAIN IN A VARIABLE ?ELD THE HARMONIC OSCILLATOR THE LORENTZ MODEL FREE OSCILLATIONS THE GENERAL SOLUTION TO THE OSCILLATOR EQUATION DISSIPATION OF ENERGY IN A FORCED OSCILLATION DISSIPATION OF ENERGY IN A FREE OSCILLATION THE PLASMA FREQUENCY DISPERSION RELATION OF THE DIELECTRIC PERMEABILITY THE HARMONIC OSCILLATOR AND LIGHT ATTENUATION AND REFRACTION OF LIGHT RETARDED POTENTIALS OF A MOVING CHARGE EMISSION OF AN HARMONIC OSCILLATOR RADIATION OF HIGHER ORDER RADIATION DAMPING THE CROSS SECTION OF AN HARMONIC OSCILLATOR THE OSCILLATOR STRENGTH THE NATURAL LINEWIDTH WAVES IN A CONDUCTING MEDIUM THE DIELECTRIC PERMEABILITY OF A CONDUCTOR CONDUCTIVITY AND THE DRUDE PRO?LE ELECTROMAGNETIC WAVES IN A PLASMA WITH A MAGNETIC ?ELD GROUP VELOCITY OF ELECTROMAGNETIC WAVES IN A PLASMA POLARIZATION THROUGH ORIENTATION POLARIZATION IN A CONSTANT ?ELD POLARIZATION IN A TIME-VARIABLE ?ELD RELAXATION AFTER SWITCHING OFF THE ?ELD THE DIELECTRIC PERMEABILITY IN DEBYE RELAXATION HOW TO EVALUATE GRAIN CROSS SECTIONS DE?NING CROSS SECTIONS CROSS SECTION FOR SCATTERING, ABSORPTION AND EXTINCTION CROSS SECTION FOR RADIATION PRESSURE EF?CIENCIES, MASS AND VOLUME COEF?CIENTS THE OPTICAL THEOREM THE INTENSITY OF FORWARD SCATTERED LIGHT THE REFRACTIVE INDEX OF A DUSTY MEDIUM MIE THEORY FOR A SPHERE THE GENERATING FUNCTION SEPARATION OF VARIABLES SERIES EXPANSION OF WAVES EXPANSION COEF?CIENTS SCATTERED AND ABSORBED POWER ABSORPTION AND SCATTERING EF?CIENCIES POLARIZATION AND SCATTERING THE AMPLITUDE SCATTERING MATRIX ANGLE-DEPENDENCE OF SCATTERING THE POLARIZATION ELLIPSE STOKES PARAMETERS STOKES PARAMETERS OF SCATTERED LIGHT FOR A SPHERE THE KRAMERS–KRONIG RELATIONS MATHEMATICAL FORMULATION OF THE RELATIONS THE ELECTRIC SUSCEPTIBILITY AND CAUSALITY THE KRAMERS–KRONIG RELATION FOR THE DIELECTRIC PERMEABILITY EXTENSION TO METALS DISPERSION OF THE MAGNETIC SUSCEPTIBILITY THREE COROLLARIES OF THE KK RELATION COMPOSITE GRAINS EFFECTIVE MEDIUM THEORIES GARNETT’S MIXING RULE THE MIXING RULE OF BRUGGEMAN COMPOSITION OF GRAINS IN PROTOSTELLAR CORES HOW SIZE, ICE AND POROSITY CHANGE THE ABSORPTION COEF?CIENT VERY SMALL AND VERY BIG PARTICLES TINY SPHERES WHEN IS A PARTICLE IN THE RAYLEIGH LIMIT? EF?CIENCIES OF SMALL SPHERES FROM MIE THEORY A DIELECTRIC SPHERE IN A CONSTANT ELECTRIC ?ELD SCATTERING AND ABSORPTION IN THE ELECTROSTATIC APPROXIMATION POLARIZATION AND ANGLE-DEPENDENT SCATTERING SMALL-SIZE EFFECTS BEYOND MIE THEORY A SMALL METALLIC SPHERE IN A MAGNETIC ?ELD SLOWLY VARYING ?ELD THE MAGNETIC POLARIZABILITY THE PENETRATION DEPTH LIMITING VALUES OF THE MAGNETIC POLARIZABILITY TINY ELLIPSOIDS ELLIPTICAL COORDINATES AN ELLIPSOID IN A CONSTANT ELECTRIC ?ELD CROSS SECTION AND SHAPE FACTOR RANDOMLY ORIENTED ELLIPSOIDS PANCAKES AND CIGARS ROTATION ABOUT THE AXIS OF GREATEST MOMENT OF INERTIA THE ?ELDS INSIDE A DIELECTRIC PARTICLE INTERNAL ?ELD AND DEPOLARIZATION ?ELD DEPOLARIZATION ?ELD AND THE DISTRIBUTION OF SURFACE CHARGES THE LOCAL ?ELD AT AN ATOM THE CLAUSIUS–MOSSOTTI RELATION VERY LARGE PARTICLES BABINET’S THEOREM RE?ECTION AND TRANSMISSION AT A PLANE SURFACE HUYGENS’ PRINCIPLE FRESNEL ZONES AND A CHECK ON HUYGENS’ PRINCIPLE THE RECIPROCITY THEOREM DIFFRACTION BY A CIRCULAR HOLE OR A SPHERE DIFFRACTION BEHIND A HALF-PLANE PARTICLES OF SMALL REFRACTIVE INDEX X-RAY SCATTERING CASE STUDIES OF MIE CALCULUS EF?CIENCIES OF BARE SPHERES PURE SCATTERING A WEAK ABSORBER A STRONG ABSORBER A METAL SPHERE EF?CIENCY VERSUS CROSS SECTION AND VOLUME COEF?CIENT THE ATMOSPHERE OF THE EARTH SCATTERING BY BARE SPHERES THE SCATTERING DIAGRAM THE POLARIZATION OF SCATTERED LIGHT THE INTENSITY OF SCATTERED LIGHT IN A RE?ECTION NEBULA COATED SPHERES SURFACE MODES IN SMALL GRAINS EF?CIENCIES OF IDEALIZED DIELECTRICS AND METALS DIELECTRIC SPHERE CONSISTING OF IDENTICAL HARMONIC OSCILLATORS DIELECTRIC SPHERE WITH DEBYE RELAXATION MAGNETIC AND ELECTRIC DIPOLE ABSORPTION OF SMALL METAL SPHERES EF?CIENCIES FOR DRUDE PRO?LES ELONGATED METALLIC PARTICLES PARTICLE STATISTICS BOLTZMANN STATISTICS THE PROBABILITY OF AN ARBITRARY ENERGY DISTRIBUTION THE DISTRIBUTION OF MAXIMUM PROBABILITY PARTITION FUNCTION AND POPULATION OF ENERGY CELLS THE MEAN ENERGY OF HARMONIC OSCILLATORS THE MAXWELLIAN VELOCITY DISTRIBUTION QUANTUM STATISTICS THE UNIT CELL H3 OF THE PHASE SPACE BOSONS AND FERMIONS BOSE STATISTICS BOSE STATISTICS FOR PHOTONS FERMI STATISTICS IONIZATION EQUILIBRIUM AND THE SAHA EQUATION THERMODYNAMICS THE ERGODIC HYPOTHESIS DE?NITION OF ENTROPY AND TEMPERATURE THE CANONICAL DISTRIBUTION THERMODYNAMIC RELATIONS FOR A GAS EQUILIBRIUM CONDITIONS OF THE STATE FUNCTIONS SPECI?C HEAT OF A GAS THE WORK DONE BY MAGNETIZATION SUSCEPTIBILITY AND SPECI?C HEAT OF MAGNETIC SUBSTANCES BLACKBODY RADIATION THE PLANCK FUNCTION LOW- AND HIGH-FREQUENCY LIMIT WIEN’S DISPLACEMENT LAW AND THE STEFAN–BOLTZMANN LAW THE PLANCK FUNCTION AND HARMONIC OSCILLATORS THE RADIATIVE TRANSITION PROBABILITY A CHARGED PARTICLE IN AN ELECTROMAGNETIC ?ELD THE CLASSICAL HAMILTONIAN THE HAMILTONIAN OF AN ELECTRON IN AN ELECTROMAGNETIC ?ELD THE HAMILTON OPERATOR IN QUANTUM MECHANICS THE DIPOLE MOMENT IN QUANTUM MECHANICS THE QUANTIZED HARMONIC OSCILLATOR SMALL PERTURBATIONS THE PERTURBATION ENERGY THE TRANSITION PROBABILITY TRANSITION PROBABILITY FOR A TIME-VARIABLE PERTURBATION THE EINSTEIN COEF?CIENTS A AND B INDUCED AND SPONTANEOUS TRANSITIONS SELECTION RULES AND POLARIZATION RULES QUANTIZATION OF THE ELECTROMAGNETIC ?ELD QUANTUM-MECHANICAL DERIVATION OF A AND B POTENTIAL WELLS AND TUNNELING WAVEFUNCTION OF A PARTICLE IN A CONSTANT POTENTIAL POTENTIAL WALLS AND FERMI ENERGY RECTANGULAR POTENTIAL BARRIERS THE DOUBLE POTENTIAL WELL STRUCTURE AND COMPOSITION OF DUST CRYSTAL STRUCTURE TRANSLATIONAL SYMMETRY LATTICE TYPES THE RECIPROCAL LATTICE BINDING IN CRYSTALS COVALENT BONDING IONIC BONDING METALS VAN DER WAALS FORCES AND HYDROGEN BRIDGES REDDENING BY INTERSTELLAR GRAINS STELLAR PHOTOMETRY THE INTERSTELLAR EXTINCTION CURVE TWO-COLOR DIAGRAMS SPECTRAL INDICES THE MASS ABSORPTION COEF?CIENT CARBONACEOUS GRAINS AND SILICATE GRAINS ORIGIN OF THE TWO MAJOR DUST CONSTITUENTS THE BONDING IN CARBON CARBON COMPOUNDS SILICATES A STANDARD SET OF OPTICAL CONSTANTS GRAIN SIZES AND OPTICAL CONSTANTS THE SIZE DISTRIBUTION COLLISIONAL FRAGMENTATION DUST RADIATION KIRCHHOFF’S LAW THE EMISSIVITY OF DUST THERMAL EMISSION OF GRAINS ABSORPTION AND EMISSION IN THERMAL EQUILIBRIUM EQUIPARTITION OF ENERGY THE TEMPERATURE OF BIG GRAINS THE ENERGY EQUATION APPROXIMATE ABSORPTION EF?CIENCY AT INFRARED WAVELENGTHS TEMPERATURE ESTIMATES RELATION BETWEEN GRAIN SIZE AND GRAIN TEMPERATURE TEMPERATURE OF DUST GRAINS NEAR A STAR DUST TEMPERATURES FROM OBSERVATIONS THE EMISSION SPECTRUM OF BIG GRAINS CONSTANT TEMPERATURE AND LOW OPTICAL DEPTH CONSTANT TEMPERATURE AND ARBITRARY OPTICAL DEPTH CALORI?C PROPERTIES OF SOLIDS NORMAL COORDINATES INTERNAL ENERGY OF A GRAIN STANDING WAVES IN A CRYSTAL THE DENSITY OF VIBRATIONAL MODES IN A CRYSTAL SPECI?C HEAT TWO-DIMENSIONAL LATTICES TEMPERATURE ?UCTUATIONS OF VERY SMALL GRAINS THE PROBABILITY DENSITY P(T ) THE TRANSITION MATRIX PRACTICAL CONSIDERATIONS THE STOCHASTIC TIME EVOLUTION OF GRAIN TEMPERATURE THE EMISSION SPECTRUM OF VERY SMALL GRAINS SMALL AND MODERATE ?UCTUATIONS STRONG ?UCTUATIONS TEMPERATURE ?UCTUATIONS AND ?UX RATIOS DUST AND ITS ENVIRONMENT GRAIN SURFACES GAS ACCRETION ON GRAINS PHYSICAL ADSORPTION AND CHEMISORPTION THE STICKING PROBABILITY THERMAL HOPPING, EVAPORATION AND REACTIONS WITH ACTIVATION BARRIER TUNNELING BETWEEN SURFACE SITES SCANNING TIME GRAIN CHARGE CHARGE EQUILIBRIUM IN THE ABSENCE OF A UV RADIATION ?ELD THE PHOTOELECTRIC EFFECT GRAIN MOTION RANDOM WALK THE DRAG ON A GRAIN SUBJECTED TO A CONSTANT OUTER FORCE BROWNIAN MOTION OF A GRAIN THE DISORDER TIME LAMINAR AND TURBULENT FRICTION A FALLING RAIN DROP THE POYNTING–ROBERTSON EFFECT GRAIN DESTRUCTION MASS BALANCE IN THE MILKY WAY DESTRUCTION PROCESSES GRAIN FORMATION EVAPORATION TEMPERATURE OF DUST VAPOR PRESSURE OF SMALL GRAINS CRITICAL SATURATION EQUATIONS FOR TIME-DEPENDENT HOMOGENEOUS NUCLEATION EQUILIBRIUM DISTRIBUTION AND STEADY-STATE NUCLEATION SOLUTIONS TO TIME-DEPENDENT HOMOGENEOUS NUCLEATION SIMILARITY RELATIONS 10 POLARIZATION 10 1 EF?CIENCY OF IN?NITE CYLINDERS 10 1 1 NORMAL INCIDENCE AND PICKET FENCE ALIGNMENT 10 1 2 OBLIQUE INCIDENCE 10 1 3 ROTATING CYLINDERS 10 1 4 ABSORPTION EF?CIENCY AS A FUNCTION OF WAVELENGTH 10 2 LINEAR POLARIZATION THROUGH EXTINCTION 10 2 1 EFFECTIVE OPTICAL DEPTH AND DEGREE OF POLARIZATION P(?) 10 2 2 THE SERKOWSKI CURVE 10 2 3 POLARIZATION P(?) OF IN?NITE CYLINDERS 10 2 4 POLARIZATION P(?) OF ELLIPSOIDS IN THE RAYLEIGH LIMIT 10 2 5 POLARIZATION P(?) OF SPHEROIDS AT OPTICAL WAVELENGTHS 10 2 6 POLARIZATION AND REDDENING 10 3 POLARIZED EMISSION 10 3 1 THE WAVELENGTH DEPENDENCE OF POLARIZED EMISSION FOR CYLINDERS 10 3 2 INFRARED EMISSION OF SPHEROIDS 10 3 3 POLARIZED EMISSION VERSUS POLARIZED EXTINCTION 10 4 CIRCULAR POLARIZATION 10 4 1 THE PHASE SHIFT INDUCED BY GRAINS 10 4 2 THE WAVELENGTH DEPENDENCE OF CIRCULAR POLARIZATION 11 GRAIN ALIGNMENT 11 1 GRAIN ROTATION 11 1 1 EULER’S EQUATIONS FOR A ROTATING BODY 11 1 2 SYMMETRIC TOPS 11 1 3 ATOMIC MAGNET IN A MAGNETIC ?ELD 11 1 4 ROTATIONAL BROWNIAN MOTION 11 1 5 SUPRATHERMAL ROTATION 11 2 MAGNETIC DISSIPATION 11 2 1 DIAMAGNETISM 11 2 2 PARAMAGNETISM 11 2 3 FERROMAGNETISM 11 2 4 THE MAGNETIZATION OF IRON ABOVE AND BELOW THE CURIE POINT 11 2 5 PARAMAGNETIC DISSIPATION: SPIN–SPIN AND SPIN–LATTICE RELAXATION 11 2 6 THE MAGNETIC SUSCEPTIBILITY FOR SPIN–LATTICE RELAXATION 11 2 7 THE MAGNETIC SUSCEPTIBILITY IN SPIN–SPIN RELAXATION 11 3 MAGNETIC ALIGNMENT 11 3 1 A ROTATING DIPOLE IN A MAGNETIC ?ELD 11 3 2 TIMESCALES FOR ALIGNMENT AND DISORDER 11 3 3 SUPER-PARAMAGNETISM 11 3 4 FERROMAGNETIC RELAXATION 11 3 5 ALIGNMENT OF ANGULAR MOMENTUM WITH THE AXIS OF GREATEST INERTIA 11 3 6 MECHANICAL AND MAGNETIC DAMPING 11 4 NON-MAGNETIC ALIGNMENT 11 4 1 GAS STREAMING 11 4 2 ANISOTROPIC ILLUMINATION 12 PAHS AND SPECTRAL FEATURES OF DUST 12 1 THERMODYNAMICS OF PAHS 12 1 1 WHAT ARE PAHS? 12 1 2 MICROCANONIC EMISSION OF PAHS 12 1 3 THE VIBRATIONAL MODES OF ANTHRACENE 12 1 4 MICROCANONIC VERSUS THERMAL LEVEL POPULATION 12 1 5 DOES AN ENSEMBLE OF PAHS HAVE A TEMPERATURE? 12 2 PAH EMISSION 12 2 1 PHOTOEXCITATION OF PAHS 12 2 2 CUTOFF WAVELENGTH FOR ELECTRONIC EXCITATION 12 2 3 PHOTO-DESTRUCTION AND IONIZATION 12 2 4 CROSS SECTIONS AND LINE PRO?LES OF PAHS 12 3 BIG GRAINS AND ICES 12 3 1 THE SILICATE FEATURES AND THE BAND AT 3 4 µM 12 3 2 ICY GRAIN MANTLES 12 4 AN OVERALL DUST MODEL 12 4 1 THE THREE DUST COMPONENTS 12 4 2 EXTINCTION COEF?CIENT IN THE DIFFUSE MEDIUM 12 4 3 EXTINCTION COEF?CIENT IN PROTOSTELLAR CORES 13 RADIATIVE TRANSPORT 13 1 BASIC TRANSFER RELATIONS 13 1 1 RADIATIVE INTENSITY AND ?UX 13 1 2 THE TRANSFER EQUATION AND ITS FORMAL SOLUTION 13 1 3 THE BRIGHTNESS TEMPERATURE 13 1 4 THE MAIN-BEAM-BRIGHTNESS TEMPERATURE OF A TELESCOPE 13 2 SPHERICAL CLOUDS 13 2 1 MOMENT EQUATIONS FOR SPHERES 13 2 2 FREQUENCY AVERAGES 13 2 3 DIFFERENTIAL EQUATIONS FOR THE INTENSITY 13 2 4 INTEGRAL EQUATIONS FOR THE INTENSITY 13 2 5 PRACTICAL HINTS 13 3 PASSIVE DISKS 13 3 1 RADIATIVE TRANSFER IN A PLANE PARALLEL LAYER 13 3 2 THE GRAZING ANGLE IN AN IN?ATED DISK 13 4 GALACTIC NUCLEI 13 4 1 HOT SPOTS IN A SPHERICAL STELLAR CLUSTER 13 4 2 LOW AND HIGH LUMINOSITY STARS 13 5 LINE RADIATION 13 5 1 ABSORPTION COEF?CIENT AND ABSORPTION PRO?LE 13 5 2 THE EXCITATION TEMPERATURE OF A LINE 13 5 3 RADIATIVE TRANSFER IN LINES 14 DIFFUSE MATTER IN THE MILKY WAY 14 1 OVERVIEW OF THE MILKY WAY 14 1 1 GLOBAL PARAMETERS 14 1 2 THE RELEVANCE OF DUST 14 2 MOLECULAR CLOUDS 14 2 1 THE CO MOLECULE 14 2 2 POPULATION OF LEVELS IN CO 14 2 3 MOLECULAR HYDROGEN 14 2 4 FORMATION OF MOLECULAR HYDROGEN ON DUST SURFACES 14 3 CLOUDS OF ATOMIC HYDROGEN 14 3 1 GENERAL PROPERTIES OF THE DIFFUSE GAS 14 3 2 THE 21 CM LINE OF ATOMIC HYDROGEN 14 3 3 HOW THE HYPER?NE LEVELS OF ATOMIC HYDROGEN ARE EXCITED 14 3 4 GAS DENSITY AND TEMPERATURE FROM THE 21 CM LINE 14 3 5 THE DEUTERIUM HYPER?NE LINE 14 3 6 ELECTRON DENSITY AND MAGNETIC ?ELD IN THE DIFFUSE GAS 14 4 HII REGIONS 14 4 1 IONIZATION AND RECOMBINATION 14 4 2 DUST–FREE HII REGIONS 14 4 3 DUSTY HII REGIONS 14 4 4 BREMSSTRAHLUNG 14 4 5 RECOMBINATION LINES 14 5 MASS ESTIMATES OF INTERSTELLAR CLOUDS 14 5 1 FROM OPTICALLY THIN CO LINES 14 5 2 FROM THE CO LUMINOSITY 14 5 3 FROM DUST EMISSION 15 STARS AND THEIR FORMATION 15 1 STARS ON AND BEYOND THE MAIN SEQUENCE 15 1 1 NUCLEAR BURNING AND THE CREATION OF ELEMENTS 15 1 2 THE BINDING ENERGY OF AN ATOMIC NUCLEUS 15 1 3 HYDROGEN BURNING 15 1 4 THE 3? PROCESS 15 1 5 LIFETIME AND LUMINOSITY OF STARS 15 1 6 THE INITIAL MASS FUNCTION 15 2 CLOUDS NEAR GRAVITATIONAL EQUILIBRIUM 15 2 1 VIRIALIZED CLOUDS 15 2 2 ISOTHERMAL CLOUD IN PRESSURE EQUILIBRIUM 15 2 3 STRUCTURE AND STABILITY OF EBERT–BONNOR SPHERES 15 2 4 FREE-FALL OF A GAS BALL 15 2 5 THE CRITICAL MASS FOR GRAVITATIONAL INSTABILITY 15 2 6 IMPLICATIONS OF THE JEANS CRITERION 15 2 7 MAGNETIC ?ELDS AND AMBIPOLAR DIFFUSION 15 3 GRAVITATIONAL COLLAPSE 15 3 1 THE PRESOLAR NEBULA 15 3 2 HYDRODYNAMIC COLLAPSE SIMULATIONS 15 3 3 SIMILARITY SOLUTIONS OF COLLAPSE 15 4 DISKS 15 4 1 VISCOUS LAMINAR ?OWS 15 4 2 DYNAMICAL EQUATIONS OF THE THIN ACCRETION DISK 15 4 3 THE KEPLER DISK 15 4 4 WHY A STAR ACCRETES FROM A DISK 15 4 5 THE STATIONARY ACCRETION DISK 15 4 6 THE ?-DISK 15 4 7 DISK HEATING BY VISCOSITY 16 EMISSION FROM YOUNG STARS 16 1 THE EARLIEST STAGES OF STAR FORMATION 16 1 1 GLOBULES 16 1 2 ISOTHERMAL GRAVITATIONALLY-BOUND CLUMPS 16 2 THE COLLAPSE PHASE 16 2 1 THE DENSITY STRUCTURE OF A PROTOSTAR 16 2 2 DUST EMISSION FROM A SOLAR-TYPE PROTOSTAR 16 2 3 KINEMATICS OF PROTOSTELLAR COLLAPSE 16 3 ACCRETION DISKS 16 3 1 A ?AT BLACKBODY DISK 16 3 2 A ?AT NON-BLACKBODY DISK 16 3 3 RADIATIVE TRANSFER IN AN IN?ATED DISK 16 4 RE?ECTION NEBULAE 16 5 COLD AND WARM DUST IN GALAXIES 16 6 STARBURST NUCLEI 16 6 1 REPETITIVE BURSTS OF STAR FORMATION 16 6 2 DUST EMISSION FROM STARBURST NUCLEI REFERENCES