Astrofísica para Todos

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 12-21 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).

This volume is aimed at undergraduate students majoring in astrophysics, physics or engineering.

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Summary

1 Introduction: Tools of the Trade 
1.1 What Is Gravity?
1.2 Dimensions and Units
1.2.1 Fundamental Dimensions
1.2.2 Constants of Nature
1.2.3 Astrophysical Units
1.2.4 Dimensional Analysis
1.3 Using the Tools
1.3.1 Phases of an Electron Gas
1.3.2 Stars, Familiar and Exotic

Part I Using Gravity and Motion to Measure Mass
2 Celestial Mechanics
2.1 Motions in the Sky
2.2 Laws of Motion
2.3 Law of Gravity

3 Gravitational One-Body Problem
3.1 Deriving Kepler’s Laws
3.2 Using Kepler III: Motion ! Mass
3.2.1 The Black Hole at the Center of the Milky Way
3.2.2 Supermassive Black Holes in Other Galaxies
3.2.3 Active Galactic Nuclei
3.3 Related Concepts
3.3.1 Sphere of Influence
3.3.2 Stellar Dynamical Evaporation
4 Gravitational Two-Body Problem 
4.1 Equivalent One-Body Problem
4.1.1 Setup
4.1.2 Motion
4.1.3 Energy and Angular Momentum
4.1.4 Velocity Curve
4.1.5 Application to the Solar System
4.1.6 Kepler III Revisited
4.2 Binary Stars
4.2.1 Background: Inclination
4.2.2 Visual Binary
4.2.3 Spectroscopic Binary
4.2.4 Eclipsing Binary
4.3 Extrasolar Planets
4.3.1 Doppler Planets
4.3.2 Transiting Planets
4.3.3 Status of Exoplanet Research

5 Tidal Forces
5.1 Derivation of the Tidal Force
5.2 Effects of Tidal Forces
5.2.1 Earth/Moon
5.2.2 Jupiter’s Moon Io
5.2.3 Extrasolar Planets
5.3 Tidal Disruption

6 Gravitational Three-Body Problem 
6.1 Two “Stars” and One “Planet”
6.1.1 Theory: Lagrange Points
6.1.2 Applications
6.2 One “Planet” and Two “Moons”
6.2.1 Theory: Resonances
6.2.2 Applications

7 Extended Mass Distributions: Spiral Galaxies
7.1 Galaxy Properties
7.1.1 Luminosity Profiles
7.1.2 Concepts of Motion
7.2 Equations of Motion
7.2.1 Spherical Symmetry
7.2.2 Axial Symmetry
7.3 Rotational Dynamics
7.3.1 Predictions
7.3.2 Observations and Interpretation
7.3.3 Cold Dark Matter
7.3.4 Is Dark Matter Real?
7.4 Beyond Rotation
7.4.1 Tangential Motion
7.4.2 Vertical Motion
7.4.3 Radial Motion
7.4.4 Application to Spiral Arms

8 N-Body Problem: Elliptical Galaxies
8.1 Gravitational N-Body Problem
8.1.1 Equations of Motion
8.1.2 Conservation of Energy
8.1.3 Virial Theorem
8.1.4 A Simple Application: N = 2
8.2 Elliptical Galaxies
8.2.1 Potential Energy
8.2.2 Kinetic Energy
8.2.3 Mass Estimate
8.3 Galaxy Interactions
8.3.1 Fly-By
8.3.2 Collision
8.4 Other N-Body Problems
9 Bending of Light by Gravity
9.1 Principles of Gravitational Lensing
9.1.1 Gravitational Deflection
9.1.2 Lens Equation
9.1.3 Lensing by a Point Mass
9.1.4 Distortion and Magnification
9.1.5 Time Delay
9.2 Microlensing
9.2.1 Theory
9.2.2 Observations
9.2.3 Binary Lenses
9.2.4 Planets
9.3 Strong Lensing
9.3.1 Extended Mass Distribution
9.3.2 Circular Mass Distribution
9.3.3 Singular Isothermal Sphere
9.3.4 Singular Isothermal Ellipsoid
9.3.5 Spherical Galaxy with External Shear
9.3.6 Science with Galaxy Strong Lensing
9.4 Weak Lensing

10 Relativity 
10.1 Space and Time: Classical View
10.2 Special Theory of Relativity
10.2.1 Lorentz Transformation
10.2.2 Loss of Simultaneity
10.2.3 Time Dilation
10.2.4 Doppler Effect
10.2.5 Length Contraction
10.3 General Theory of Relativity
10.3.1 Concepts of General Relativity
10.3.2 Principle of Equivalence
10.3.3 Curvature of Spacetime
10.3.4 Gravitational Redshift and Time Dilation
10.4 Applications of General Relativity
10.4.1 Mercury’s Perihelion Shift (1916)
10.4.2 Bending of Light (1919)
10.4.3 Gravitational Redshift on Earth (1960)
10.4.4 Gravitational Redshift from a White Dwarf (1971)
10.4.5 Flying Clocks (1971)
10.4.6 Global Positioning System (1989)
10.5 Mathematics of Relativity
10.5.1 Spacetime Interval
10.5.2 4-Vectors
10.5.3 Relativistic Momentum and Energy
10.6 Black Holes
10.6.1 Schwarzschild Metric
10.6.2 Spacetime Geometry
10.6.3 Particle in a Circular Orbit
10.6.4 General Motion Around a Black Hole
10.6.5 Gravitational Deflection
10.7 Other Effects

11 Cosmology: Expanding Universe 
11.1 Hubble’s Law and the Expanding Universe
11.2 Relativistic Cosmology
11.2.1 Robertson-Walker Metric
11.2.2 The Friedmann Equation
11.2.3 Einstein’s Greatest Blunder
11.2.4 FRW Cosmology
11.3 Observational Cosmology
11.3.1 Cosmological Redshift
11.3.2 Cosmological Distances
11.3.3 Results

Part II Using Stellar Physics to Explore the Cosmos
12 Planetary Atmospheres
12.1 Kinetic Theory of Gases
12.1.1 Temperature and the Boltzmann Distribution
12.1.2 Maxwell-Boltzmann Distribution of Particle Speeds
12.1.3 Pressure and the Ideal Gas Law
12.1.4 Assumptions in the Ideal Gas Law
12.2 Hydrostatic Equilibrium
12.3 Planetary Atmospheres
12.3.1 Density Profile
12.3.2 Exosphere
12.3.3 Evaporation

13 Planetary Temperatures
13.1 Blackbody Radiation
13.1.1 Luminosity
13.1.2 Spectrum
13.1.3 Color
13.1.4 Pressure
13.2 Predicting Planet Temperatures
13.3 Atmospheric Heating
13.3.1 One Layer
13.3.2 Many Layers
13.3.3 Optical Depth
13.4 Interaction of Light with Matter
13.4.1 Photoionization
13.4.2 Electron Excitation
13.4.3 Molecular Vibration

13.4.4 Molecular Rotation
13.4.5 Recap
13.5 Greenhouse Effect and Climate Change
13.5.1 Earth
13.5.2 Venus

14 Stellar Atmospheres 
14.1 Atomic Excitation and Ionization
14.1.1 Energy Level Occupation
14.1.2 Ionization Stages
14.1.3 Application to Hydrogen
14.2 Stellar Spectral Classification

15 Nuclear Fusion 
15.1 What Powers the Sun?
15.2 Physics of Fusion
15.2.1 Mass and Energy Scales
15.2.2 Requirements for Fusion
15.2.3 Cross Section
15.2.4 Reaction Rate
15.3 Nuclear Reactions in Stars
15.3.1 Cast of Characters
15.3.2 Masses and Binding Energies
15.3.3 Burning Hydrogen Into Helium
15.4 Solar Neutrinos
15.4.1 Neutrino Production in the Sun
15.4.2 Neutrino Detection (I)
15.4.3 Neutrino Oscillations
15.4.4 Neutrino Detection (II)

16 Stellar Structure and Evolution
16.1 Energy Transport
16.1.1 Conduction
16.1.2 Convection
16.2 Stellar Models
16.2.1 Equations of Stellar Structure
16.2.2 The Sun
16.2.3 Other Stars
16.3 Evolution of Low-Mass Stars (M . 8 Mˇ)
16.3.1 Hydrogen, Helium, and Beyond
16.3.2 Observations
16.4 Evolution of High-Mass Stars (M & 8 Mˇ)
16.4.1 Beyond Carbon and Oxygen
16.4.2 Explosion: Supernova
16.4.3 Beyond Iron

17 Stellar Remnants 
17.1 Cold, Degenerate Gas
17.2 White Dwarfs
17.2.1 Equation of State
17.2.2 Polytropic Stars
17.2.3 Testing the Theory
17.3 Neutron Stars and Pulsars

18 Charting the Universe with Stars
18.1 Stellar Pulsations
18.1.1 Observations
18.1.2 Theory
18.2 Standard Candles

19 Star and Planet Formation
19.1 Gravitational Collapse
19.1.1 Equilibrium: Virial Temperature
19.1.2 Conditions for Collapse
19.1.3 Fragmentation
19.1.4 Collapse Time Scale
19.2 Gas Cooling
19.3 Halting the Collapse
19.3.1 Cessation of Cooling
19.3.2 Radiation Pressure
19.3.3 Other Effects
19.4 Protoplanetary Disks
19.4.1 Temperature Structure
19.4.2 Picture of Planet Formation

20 Cosmology: Early Universe
20.1 Cosmic Microwave Background Radiation
20.1.1 Hot Big Bang
20.1.2 Theory: Recombination Temperature
20.1.3 Observations
20.1.4 Implications
20.2 Big Bang Nucleosynthesis
20.2.1 Theory: “The First Three Minutes”
20.2.2 Observations: Primordial Abundances
20.3 How Did We Get Here?
Author: Charles Keeton