Principles of astrophysics: using gravity and stellar physics to explore the cosmos

✍ Scribed by Keeton, Charles

• Publisher: Springer
• Year: 2014
• Tongue: English
• Leaves: 444
• Series: Undergraduate lecture notes in physics
• Category: Library

✦ Synopsis

Provides a physics-centered analysis of a broad range of astronomical systems that appeals to a large audience of advanced undergraduate students in physics and engineering



This book gives a survey of astrophysics at the advanced undergraduate level. It originates from a two-semester course sequence at Rutgers University that is meant to appeal not only to astrophysics students but also more broadly to physics and engineering students. The organization is driven more by physics than by astronomy; in other words, topics are first developed in physics and then applied to astronomical systems that can be investigated, rather than the other way around.

The first half of the book focuses on gravity. Gravity is the dominant force in many astronomical systems, so a tremendous amount can be learned by studying gravity, motion and mass. The theme in this part of the book, as well as throughout astrophysics, is using motion to investigate mass. The goal of Chapters 2-11 is to develop a progressively richer understanding of gravity as it applies to objects ranging from planets and moons to galaxies and the universe as a whole. The second half uses other aspects of physics to address one of the big questions. While "Why are we here?" lies beyond the realm of physics, a closely related question is within our reach: "How did we get here?" The goal of Chapters 12-20 is to understand the physics behind the remarkable story of how the Universe, Earth and life were formed. This book assumes familiarity with vector calculus and introductory physics (mechanics, electromagnetism, gas physics and atomic physics); however, all of the physics topics are reviewed as they come up (and vital aspects of vector calculus are reviewed in the Appendix).

✦ Table of Contents

Preface......Page 8
Acknowledgements......Page 10
Contents......Page 12
Unit Conversions......Page 20
Mathematical Symbols......Page 21
1.1 What Is Gravity?......Page 23
1.2 Dimensions and Units......Page 26
1.2.1 Fundamental Dimensions......Page 27
1.2.2 Constants of Nature......Page 28
1.2.3 Astrophysical Units......Page 29
Planetary Motion......Page 30
Black Hole......Page 31
1.3 Using the Tools......Page 32
Classical Degenerate Gas......Page 33
Phase Diagram......Page 35
1.3.2 Stars, Familiar and Exotic......Page 36
Classical Degenerate Gas......Page 37
Problems......Page 38
References......Page 39
Part I Using Gravity and Motion to Measure Mass......Page 40
2.1 Motions in the Sky......Page 41
2.2 Laws of Motion......Page 45
2.3 Law of Gravity......Page 48
Application: Escape......Page 51
Problems......Page 53
References......Page 54
3.1 Deriving Kepler's Laws......Page 55
3.2.1 The Black Hole at the Center of the Milky Way......Page 60
NGC 4258......Page 62
A Supermassive Black Hole in Every Galaxy?......Page 64
3.2.3 Active Galactic Nuclei......Page 66
3.3.1 Sphere of Influence......Page 67
3.3.2 Stellar Dynamical Evaporation......Page 69
Problems......Page 70
References......Page 71
4.1.1 Setup......Page 72
4.1.2 Motion......Page 73
4.1.3 Energy and Angular Momentum......Page 75
4.1.4 Velocity Curve......Page 76
4.1.5 Application to the Solar System......Page 78
4.1.6 Kepler III Revisited......Page 80
4.2.1 Background: Inclination......Page 81
4.2.2 Visual Binary......Page 83
Double-Line System......Page 84
Single-Line System......Page 85
4.3 Extrasolar Planets......Page 86
4.3.1 Doppler Planets......Page 87
4.3.2 Transiting Planets......Page 89
Application to HD 209458......Page 91
4.3.3 Status of Exoplanet Research......Page 92
Problems......Page 94
References......Page 96
5.1 Derivation of the Tidal Force......Page 98
5.2.1 Earth/Moon......Page 101
5.2.2 Jupiter's Moon Io......Page 103
5.3 Tidal Disruption......Page 104
Problems......Page 105
References......Page 107
6.1.1 Theory: Lagrange Points......Page 108
6.1.2 Applications......Page 111
6.2 One Planet'' and TwoMoons''......Page 112
6.2.1 Theory: Resonances......Page 113
6.2.2 Applications......Page 114
Problems......Page 115
References......Page 117
7.1 Galaxy Properties......Page 118
7.1.1 Luminosity Profiles......Page 120
7.1.2 Concepts of Motion......Page 121
7.2.1 Spherical Symmetry......Page 123
7.3 Rotational Dynamics......Page 124
7.3.1 Predictions......Page 125
7.3.2 Observations and Interpretation......Page 126
7.3.3 Cold Dark Matter......Page 129
7.3.4 Is Dark Matter Real?......Page 132
7.4.1 Tangential Motion......Page 133
7.4.2 Vertical Motion......Page 134
Application: Disk Thickness......Page 135
7.4.3 Radial Motion......Page 136
Example: Point Mass......Page 137
7.4.4 Application to Spiral Arms......Page 138
Problems......Page 143
References......Page 145
8.1.1 Equations of Motion......Page 146
8.1.2 Conservation of Energy......Page 147
8.1.3 Virial Theorem......Page 149
8.1.4 A Simple Application: N = 2......Page 150
8.2.1 Potential Energy......Page 152
Example: Finite Isothermal Sphere with Radius R......Page 153
8.2.2 Kinetic Energy......Page 154
8.2.3 Mass Estimate......Page 155
8.3.1 Fly-By......Page 156
8.3.2 Collision......Page 158
Problems......Page 159
References......Page 161
9.1.1 Gravitational Deflection......Page 162
Example: Deflection of Light by the Sun......Page 164
9.1.2 Lens Equation......Page 165
9.1.3 Lensing by a Point Mass......Page 167
9.1.4 Distortion and Magnification......Page 168
Point Mass......Page 172
9.2 Microlensing......Page 173
9.2.1 Theory......Page 174
9.2.2 Observations......Page 175
9.2.3 Binary Lenses......Page 176
9.2.4 Planets......Page 178
9.3.1 Extended Mass Distribution......Page 180
9.3.2 Circular Mass Distribution......Page 181
9.3.3 Singular Isothermal Sphere......Page 182
9.3.4 Singular Isothermal Ellipsoid......Page 183
9.3.5 Spherical Galaxy with External Shear......Page 184
9.3.6 Science with Galaxy Strong Lensing......Page 185
9.4 Weak Lensing......Page 187
Problems......Page 190
References......Page 194
10.1 Space and Time: Classical View......Page 195
10.2 Special Theory of Relativity......Page 196
10.2.1 Lorentz Transformation......Page 197
10.2.2 Loss of Simultaneity......Page 199
10.2.3 Time Dilation......Page 200
10.2.4 Doppler Effect......Page 201
10.3 General Theory of Relativity......Page 202
10.3.2 Principle of Equivalence......Page 203
10.3.3 Curvature of Spacetime......Page 204
Example: Earth......Page 206
10.3.4 Gravitational Redshift and Time Dilation......Page 207
Example: Surface of Earth......Page 208
10.4.1 Mercury's Perihelion Shift (1916)......Page 209
10.4.3 Gravitational Redshift on Earth (1960)......Page 211
10.4.4 Gravitational Redshift from a White Dwarf (1971)......Page 212
10.4.5 Flying Clocks (1971)......Page 213
10.4.6 Global Positioning System (1989)......Page 216
10.5.1 Spacetime Interval......Page 217
Example: Straight Line......Page 218
10.5.2 4-Vectors......Page 219
10.5.3 Relativistic Momentum and Energy......Page 221
10.6.1 Schwarzschild Metric......Page 222
10.6.2 Spacetime Geometry......Page 224
10.6.3 Particle in a Circular Orbit......Page 225
Example: Circular Orbit Around Sgr A*......Page 226
10.6.4 General Motion Around a Black Hole......Page 227
10.6.5 Gravitational Deflection......Page 231
10.7 Other Effects......Page 234
Problems......Page 235
References......Page 237
11.1 Hubble's Law and the Expanding Universe......Page 238
11.2 Relativistic Cosmology......Page 239
11.2.1 Robertson-Walker Metric......Page 240
11.2.2 The Friedmann Equation......Page 241
11.2.3 Einstein's Greatest Blunder......Page 244
11.2.4 FRW Cosmology......Page 245
11.3 Observational Cosmology......Page 246
11.3.1 Cosmological Redshift......Page 247
11.3.2 Cosmological Distances......Page 248
11.3.3 Results......Page 250
Problems......Page 254
References......Page 256
Part II Using Stellar Physics to Explore the Cosmos......Page 257
12.1.1 Temperature and the Boltzmann Distribution......Page 258
12.1.2 Maxwell-Boltzmann Distribution of Particle Speeds......Page 259
12.1.3 Pressure and the Ideal Gas Law......Page 262
12.1.4 Assumptions in the Ideal Gas Law......Page 264
12.2 Hydrostatic Equilibrium......Page 266
12.3.1 Density Profile......Page 267
Example: How Thick Is Earth's Atmosphere?......Page 268
12.3.2 Exosphere......Page 269
12.3.3 Evaporation......Page 270
Example: Earth and Moon......Page 271
Example: Earth......Page 273
Problems......Page 274
Reference......Page 276
13.1.1 Luminosity......Page 277
13.1.2 Spectrum......Page 278
Example: What Is the Peak Wavelength of Sunlight?......Page 281
13.1.4 Pressure......Page 282
13.2 Predicting Planet Temperatures......Page 283
13.3 Atmospheric Heating......Page 284
13.3.1 One Layer......Page 285
13.3.2 Many Layers......Page 286
13.4 Interaction of Light with Matter......Page 288
13.4.1 Photoionization......Page 289
13.4.3 Molecular Vibration......Page 290
13.4.4 Molecular Rotation......Page 292
13.5.1 Earth......Page 293
13.5.2 Venus......Page 295
Problems......Page 296
References......Page 297
14.1 Atomic Excitation and Ionization......Page 298
14.1.2 Ionization Stages......Page 300
14.1.3 Application to Hydrogen......Page 302
14.2 Stellar Spectral Classification......Page 306
Problems......Page 308
References......Page 310
15.1 What Powers the Sun?......Page 311
15.2.1 Mass and Energy Scales......Page 313
Classical Analysis......Page 314
Quantum Analysis......Page 315
15.2.3 Cross Section......Page 317
Tunneling Probability......Page 318
15.2.4 Reaction Rate......Page 319
Application to Hydrogen in the Sun......Page 321
15.3.1 Cast of Characters......Page 322
15.3.2 Masses and Binding Energies......Page 323
15.3.3 Burning Hydrogen Into Helium......Page 324
Proton-Proton (PP) Chain......Page 325
CNO Cycle......Page 326
15.4.1 Neutrino Production in the Sun......Page 327
15.4.2 Neutrino Detection (I)......Page 328
15.4.3 Neutrino Oscillations......Page 329
Super-Kamiokande......Page 330
Sudbury Neutrino Observatory......Page 331
Problems......Page 333
References......Page 335
16.1.1 Conduction......Page 337
Random Walk......Page 339
Example: What Is the Thermal Diffusivity of Earth's Atmosphere?......Page 340
16.1.2 Convection......Page 341
16.2 Stellar Models......Page 343
16.2.1 Equations of Stellar Structure......Page 344
16.2.2 The Sun......Page 346
16.2.3 Other Stars......Page 347
16.3.1 Hydrogen, Helium, and Beyond......Page 350
16.3.2 Observations......Page 352
16.4 Evolution of High-Mass Stars (M 8M)......Page 353
16.4.1 Beyond Carbon and Oxygen......Page 354
16.4.2 Explosion: Supernova......Page 355
16.4.3 Beyond Iron......Page 358
Problems......Page 359
References......Page 361
17.1 Cold, Degenerate Gas......Page 363
17.2 White Dwarfs......Page 365
17.2.2 Polytropic Stars......Page 366
17.2.3 Testing the Theory......Page 370
17.3 Neutron Stars and Pulsars......Page 373
Problems......Page 374
References......Page 376
18.1.1 Observations......Page 377
18.1.2 Theory......Page 379
18.2 Standard Candles......Page 382
Problems......Page 386
References......Page 387
19.1.1 Equilibrium: Virial Temperature......Page 389
19.1.2 Conditions for Collapse......Page 391
19.1.3 Fragmentation......Page 392
19.2 Gas Cooling......Page 394
19.3 Halting the Collapse......Page 396
19.3.2 Radiation Pressure......Page 397
Aside: Quasars......Page 398
Recap......Page 399
19.4.1 Temperature Structure......Page 400
19.4.2 Picture of Planet Formation......Page 401
Problems......Page 403
References......Page 405
20.1 Cosmic Microwave Background Radiation......Page 407
20.1.1 Hot Big Bang......Page 408
20.1.2 Theory: Recombination Temperature......Page 409
20.1.3 Observations......Page 410
20.1.4 Implications......Page 412
20.2.1 Theory: ``The First Three Minutes''......Page 413
20.2.2 Observations: Primordial Abundances......Page 417
Problems......Page 420
References......Page 421
Part III Appendices......Page 423
A.1 Cartesian and Polar Coordinates......Page 424
A.2 Cylindrical and Spherical Coordinates......Page 426
A.3 Rotating Reference Frame......Page 427
A.4 Angular Momentum......Page 429
A.5 Taylor Series Approximation......Page 430
A.6 Numerical Solution of Differential Equations......Page 431
A.7 Useful Integrals......Page 432
References......Page 433
Chapter 2......Page 434
Chapter 7......Page 435
Chapter 11......Page 436
Chapter 16......Page 437
Chapter 20......Page 438
Index......Page 439

✦ Subjects

Science;Physics;Astronomy