Charles Keeton. Principles of Astrophysics. Using Gravity and Stellar Physics. to Explore the Cosmos. ^ Springer

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1 Charles Keeton Principles of Astrophysics Using Gravity and Stellar Physics to Explore the Cosmos ^ Springer

2 Contents 1 Introduction: Tools of the Trade What Is Gravity? Dimensions and Units Fundamental Dimensions Constants of Nature Astrophysical Units Dimensional Analysis Using the Tools Phases of an Electron Gas Stars, Familiar and Exotic 14 Problems 16 References 17 Part I Using Gravity and Motion to Measure Mass 2 Celestial Mechanics Motions in the Sky Laws of Motion Law of Gravity 28 Problems 33 References 34 3 Gravitational One-Body Problem Deriving Kepler's Laws Using Kepler III: Motion -> Mass The Black Hole at the Center of the Milky Way Supermassive Black Holes in Other Galaxies Active Galactic Nuclei Related Concepts Sphere of Influence Stellar Dynamical Evaporation 49 xi

3 xjj Contents Problems 50 References 51 4 Gravitational Two-Body Problem Equivalent One-Body Problem Setup Motion Energy and Angular Momentum Velocity Curve Application to the Solar System Kepler III Revisited Binary Stars Background: Inclination Visual Binary Spectroscopic Binary Eclipsing Binary Extrasolar Planets Doppler Planets Transiting Planets Status of Exoplanet Research 73 Problems 75 References 77 5 Tidal Forces Derivation of the Tidal Force Effects of Tidal Forces Earth/Moon Jupiter's Moon Io Extrasolar Planets Tidal Disruption 85 Problems 86 References 88 6 Gravitational Three-Body Problem Two "Stars" and One "Planet" Theory: Lagrange Points Applications One "Planet" and Two "Moons" Theory: Resonances Applications 95 Problems 96 References 98 7 Extended Mass Distributions: Spiral Galaxies Galaxy Properties Luminosity Profiles Concepts of Motion 102

4 Contents xl" 7.2 Equations of Motion Spherical Symmetry Axial Symmetry Rotational Dynamics Predictions Observations and Interpretation Cold Dark Matter Is Dark Matter Real? Beyond Rotation Tangential Motion Vertical Motion Radial Motion Application to Spiral Arms 119 Problems 124 References N-Body Problem: Elliptical Galaxies Gravitational N-Body Problem Equations of Motion Conservation of Energy Virial Theorem A Simple Application: N = Elliptical Galaxies Potential Energy Kinetic Energy Mass Estimate Galaxy Interactions Fly-By Collision Other N-Body Problems 140 Problems 140 References Bending of Light by Gravity Principles of Gravitational Lensing Gravitational Deflection Lens Equation Lensing by a Point Mass Distortion and Magnification Time Delay Microlensing ' Theory Observations Binary Lenses Planets 159

5 xiv Contents 9.3 Strong Lensing Extended Mass Distribution Circular Mass Distribution Singular Isothermal Sphere Singular Isothermal Ellipsoid Spherical Galaxy with External Shear Science with Galaxy Strong Lensing Weak Lensing 168 Problems 171 References Relativity Space and Time: Classical View Special Theory of Relativity Lorentz Transformation Loss of Simultaneity Time Dilation Doppler Effect Length Contraction General Theory of Relativity Concepts of General Relativity Principle of Equivalence Curvature of Spacetime Gravitational Redshift and Time Dilation Applications of General Relativity Mercury's Perihelion Shift (1916) Bending of Light (1919) Gravitational Redshift on Earth (1960) Gravitational Redshift from a White Dwarf (1971) Flying Clocks (1971) Global Positioning System (1989) Mathematics of Relativity Spacetime Interval Vectors Relativistic Momentum and Energy Black Holes Schwarzschild Metric Spacetime Geometry Particle in a Circular Orbit General Motion Around a Black Hole Gravitational Deflection Other Effects 216 Problems 217 References 219

6 Contents xv 11 Cosmology: Expanding Universe Hubble's Law and the Expanding Universe Relativistic Cosmology Robertson-Walker Metric The Friedmann Equation Einstein's Greatest Blunder FRW Cosmology Observational Cosmology Cosmological Redshift Cosmological Distances Results 233 Problems 237 References 239 Part II Using Stellar Physics to Explore the Cosmos 12 Planetary Atmospheres Kinetic Theory of Gases Temperature and the Boltzmann Distribution Maxwell-Boltzmann Distribution of Particle Speeds Pressure and the Ideal Gas Law Assumptions in the Ideal Gas Law Hydrostatic Equilibrium Planetary Atmospheres Density Profile Exosphere Evaporation 255 Problems 259 Reference Planetary Temperatures Blackbody Radiation Luminosity Spectrum Color Pressure Predicting Planet Temperatures Atmospheric Heating One Layer Many Layers Optical Depth Interaction of Light with Matter Photoionization Electron Excitation Molecular Vibration 276

7 xvj Contents Molecular Rotation Recap Greenhouse Effect and Climate Change Earth Venus 281 Problems 282 References Stellar Atmospheres Atomic Excitation and Ionization Energy Level Occupation Ionization Stages Application to Hydrogen Stellar Spectral Classification 293 Problems 295 References Nuclear Fusion What Powers the Sun? Physics of Fusion Mass and Energy Scales Requirements for Fusion Cross Section Reaction Rate Nuclear Reactions in Stars Cast of Characters Masses and Binding Energies Burning Hydrogen Into Helium Solar Neutrinos Neutrino Production in the Sun Neutrino Detection (I) Neutrino Oscillations Neutrino Detection (II) 318 Problems 321 References Stellar Structure and Evolution Energy Transport Conduction Convection Stellar Models Equations of Stellar Structure The Sun Other Stars 335

8 Contents xvii 16.3 Evolution of Low-Mass Stars (M < 8 M0) Hydrogen, Helium, and Beyond Observations Evolution of High-Mass Stars {M > 8 MQ) Beyond Carbon and Oxygen Explosion: Supernova Beyond Iron 346 Problems 347 References Stellar Remnants Cold, Degenerate Gas White Dwarfs Equation of State Polytropic Stars Testing the Theory Neutron Stars and Pulsars 361 Problems 362 References Charting the Universe with Stars Stellar Pulsations Observations Theory Standard Candles 370 Problems 374 References Star and Planet Formation Gravitational Collapse Equilibrium: Virial Temperature Conditions for Collapse Fragmentation Collapse Time Scale Gas Cooling Halting the Collapse Cessation of Cooling Radiation Pressure Other Effects Protoplanetary Disks Temperature Structure Picture of Planet Formation 389 Problems 391 References 393

9 xviii Contents 20 Cosmology: Early Universe Cosmic Microwave Background Radiation Hot Big Bang Theory : Recombination Temperature Observations Implications Big Bang Nucleosynthesis Theory: "The First Three Minutes" Observations: Primordial Abundances How Did We Get Here? 408 Problems 408 References 409 Part III Appendices A Technical Background 413 A.l Cartesian and Polar Coordinates 413 A.2 Cylindrical and Spherical Coordinates 415 A.3 Rotating Reference Frame 416 A.4 Angular Momentum 418 A.5 Taylor Series Approximation 419 A.6 Numerical Solution of Differential Equations 420 A.7 Useful Integrals 421 References 422 B Solutions 423 Index 429

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