Introduction to Astrophysics

Preface and Acknowledgments

1 Introduction

• 1.1 Astronomy and Astrophysics 1
  • 1.1.1 What distinguishes them? What are they? 1
  • 1.1.2 Characteristics of astrophysics 1
• 1.2 Quick history of some pre-astrophysics discoveries 3
  • 1.2.1 Copernicus gets Solar System geometry, but no scale 3
  • 1.2.2 Parallax of Mars, transits of Venus determine scale 4
  • 1.2.3 Newton's Law of Gravitation gives mass of Sun 6
  • 1.2.4 Compare Sun to candle to get its "candlepower" 7
  • 1.2.5 Stellar distances from Parallax across Earth's orbit 8
  • 1.2.6 Luminosities in modern units (watts) 9

2 The Astronomical Context

• 2.1 Angular and positional measurements 11
  • 2.1.1 Angles between objects measured "on the sky" - i.e., in projection 11
  • 2.1.2 Coordinate systems in the sky 12
  • 2.1.3 Angular separations from coordinates in Sky 14
  • 2.1.4 Solid angles 14
• 2.2 Brightness measurements 15
  • 2.2.1 Flux and UBV system 15
  • 2.2.2 Apparent magnitude 17
  • 2.2.3 Absolute Magnitude 18
  • 2.2.4 Spectra 19
• 2.3 Velocity measurements 20
• 2.4 Distance measurements 22

3 Radiation

• 3.1 Photon description of light 26
  • 3.1.1 Photons 26
  • 3.1.2 Phase space density 26
  • 3.1.3 Brightness 30
• 3.2 Wave description of light 31
  • 3.2.1 Waves 31
  • 3.2.2 Connection between particle and wave descriptions 32
• 3.3 Radiation units 33
  • 3.3.1 Specific intensity I 33
  • 3.3.2 Specific intensity I 34
  • 3.3.3 Net flux 34
  • 3.3.4 Energy density and radiation pressure 35
  • 3.3.5 ExampleSphere of uniform brightness 38
• 3.4 Telescopes 39
  • 3.4.1 Astronomical Telescopes 39
  • 3.4.2 Telescopes you look through (e.g. binoculars) 41
• 3.5 Thermal ("Black Body") Radiation 43
  • 3.5.1 Black Body radiation is universal 43
  • 3.5.2 Derivation of the Planck spectrum 44
  • 3.5.3 Asymptotics of the Planck spectrum 46
  • 3.5.4 Integral of the Planck spectrumStephan-Boltzman law 50
  • 3.5.5 Color temperature and brightness temperature 52
  • 3.5.6 Radiative temperature balance of the Earth 53
  • 3.5.7 The spectral sequence of stars 55
• 3.6 Radiation emission mechanisms briefly described 58
  • 3.6.1 Synchrotron radiation 58
  • 3.6.2 Thermal bremsstrahlung 59
  • 3.6.3 Line emission from atoms 59

4 Classical Dynamics

• 4.1 Newtonian gravity 61
  • 4.1.1 Basic law of attraction 61
  • 4.1.2 The little known codicil to Newton's 3rd law 62
  • 4.1.3 Gravitational Potential 63
• 4.2 The 2-body problem 64
  • 4.2.1 Conservation laws for 2-body orbits 64
  • 4.2.2 Two-body orbits 68
  • 4.2.3 Shapes of the orbits 73
  • 4.2.4 Orbital elements 79
  • 4.2.5 The mass of the Sun and the masses of binary stars 82
  • 4.2.6 Supernovae in binary systems 88
• 4.3 Tides and Roche effects 91
  • 4.3.1 Weak tides 93
  • 4.3.2 Tidal drag and the lengthening of the day 97
  • 4.3.3 Roche stability limit for satellites 100
  • 4.3.4 Roche Lobe overflow 101
  • 4.3.5 Effect of mass transfer on binary orbits 103
  • 4.3.6 Accretion disks 104
  • 4.3.7 The Lagrange points 105
• 4.4 The virial theorem 111

5 Stars and Stellar Structure

• 5.1 Phenomenology of stars 114
  • 5.1.1 Elemental abundances, populations I and II 114
  • 5.1.2 Nuclear reactions 118
• 5.2 Stellar structure 120
  • 5.2.1 Order-of-magnitude stellar structure 120
  • 5.2.2 Quantities describing the stellar interior 124
  • 5.2.3 Equations of stellar structure 126
  • 5.2.4 PolytropesThe Lane-Emden equation 128
  • 5.2.5 Boundary conditions and Lane-Emden functions 130
  • 5.2.6 Physical properties of polytropes 131
• 5.3 Specific cases of polytropic models 134
  • 5.3.1 Adiabatic indices for a perfect gas 134
  • 5.3.2 Fully convective stars 136
  • 5.3.3 Equation of state for degenerate matter 137
  • 5.3.4 White dwarf stars 142
  • 5.3.5 Stellar structure virial theorem 146
• 5.4 Beyond the Chandrasekhar mass 148
  • 5.4.1 Inverse fi decay 149
  • 5.4.2 Neutron stars and pulsars 149
  • 5.4.3 Black holes 152

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