8.901 Lecture Notes Astrophysics I, Spring 2019 I.J.M. Crossfield (with S. Hughes and E. Mills)* MIT 6th February, 2019 – 15th May, 2019 Contents 1 Introduction to Astronomy and Astrophysics 6 2 The Two-Body Problem and Kepler’s Laws 10 3 The Two-Body Problem, Continued 14 4 Binary Systems 21 4.1 Empirical Facts about binaries................... 21 4.2 Parameterization of Binary Orbits................. 21 4.3 Binary Observations......................... 22 5 Gravitational Waves 25 5.1 Gravitational Radiation........................ 27 5.2 Practical Effects............................ 28 6 Radiation 30 6.1 Radiation from Space......................... 30 6.2 Conservation of Specific Intensity................. 33 6.3 Blackbody Radiation......................... 36 6.4 Radiation, Luminosity, and Temperature............. 37 7 Radiative Transfer 38 7.1 The Equation of Radiative Transfer................. 38 7.2 Solutions to the Radiative Transfer Equation........... 40 7.3 Kirchhoff’s Laws........................... 41 8 Stellar Classification, Spectra, and Some Thermodynamics 44 8.1 Classification.............................. 44 8.2 Thermodynamic Equilibrium.................... 46 8.3 Local Thermodynamic Equilibrium................ 47 8.4 Stellar Lines and Atomic Populations............... 48 *[email protected] 1 Contents 8.5 The Saha Equation.......................... 48 9 Stellar Atmospheres 54 9.1 The Plane-parallel Approximation................. 54 9.2 Gray Atmosphere........................... 56 9.3 The Eddington Approximation................... 59 9.4 Frequency-Dependent Quantities.................. 61 9.5 Opacities................................ 62 10 Timescales in Stellar Interiors 67 10.1 Photon collisions with matter.................... 67 10.2 Gravity and the free-fall timescale................. 68 10.3 The sound-crossing time....................... 71 10.4 Radiation transport.......................... 72 10.5 Thermal (Kelvin-Helmholtz) timescale............... 72 10.6 Nuclear timescale........................... 73 10.7 A Hierarchy of Timescales...................... 73 10.8 The Virial Theorem.......................... 74 11 Stellar Structure 79 11.1 Formalism............................... 79 11.2 Equations of Stellar Structure.................... 80 11.3 Pressure................................ 86 11.4 The Equation of State......................... 88 11.5 Summary................................ 90 12 Stability, Instability, and Convection 92 12.1 Thermal stability........................... 92 12.2 Mechanical and Dynamical Stability................ 92 12.3 Convection............................... 94 12.4 Another look at convection vs. radiative transport........ 97 12.5 XXXX – extra material on convection in handwritten notes... 101 13 Polytropes 102 13.1 XXXX – extra material in handwritten notes........... 105 14 An Introduction to Nuclear Fusion 106 14.1 Useful References........................... 106 14.2 Introduction.............................. 106 14.3 Nuclear Binding Energies...................... 106 14.4 Let’s Get Fusing............................ 107 14.5 Reaction pathways.......................... 110 15 Nuclear Reaction Pathways 115 15.1 Useful references........................... 115 15.2 First fusion: the p-p chain...................... 115 15.3 The triple-a process.......................... 116 15.4 On Beyond 12C............................ 117 2 16 End Stages of Nuclear Burning 119 16.1 Useful references........................... 119 16.2 Introduction.............................. 119 16.3 Degeneracy Pressure......................... 119 16.4 Implications of Degeneracy Pressure................ 123 16.5 Comparing Equations of State.................... 124 17 Stellar Evolution: The Core 126 17.1 Useful References........................... 126 17.2 Introduction.............................. 126 17.3 The Core................................ 126 17.4 Equations of State........................... 127 17.5 Nuclear Reactions........................... 129 17.6 Stability................................. 130 17.7 A schematic overview of stellar evolution............. 130 17.8 Timescales: Part Deux........................ 132 18 Stellar Evolution: The Rest of the Picture 133 18.1 Stages of Protostellar Evolution: The Narrative.......... 133 18.2 Some Physical Rules of Thumb................... 137 18.3 The Jeans mass and length...................... 138 18.4 Time Scales Redux.......................... 139 18.5 Protostellar Evolution: Some Physics................ 140 18.6 Stellar Evolution: End of the Line.................. 142 18.7 Red Giants and Cores........................ 143 19 On the Deaths of Massive Stars 145 19.1 Useful References........................... 145 19.2 Introduction.............................. 145 19.3 Eddington Luminosity........................ 145 19.4 Core Collapse and Neutron Degeneracy Pressure........ 146 19.5 Supernova Nucleosynthesis..................... 150 19.6 Supernovae Observations and Classification........... 152 20 Compact Objects 154 20.1 Useful references........................... 154 20.2 Introduction.............................. 154 20.3 White Dwarfs Redux......................... 155 20.4 White Dwarf Cooling Models.................... 160 21 Neutron Stars 164 21.1 Neutronic Chemistry......................... 164 21.2 Tolman-Oppenheimer-Volkoff.................... 165 21.3 Neutron star interior models.................... 166 21.4 A bit more neutron star structure.................. 166 21.5 Neutron Star Observations...................... 168 21.6 Pulsars................................. 169 3 Contents 22 Black Holes 175 22.1 Useful references........................... 175 22.2 Introduction.............................. 175 22.3 Observations of Black Holes..................... 175 22.4 Non-Newtonian Orbits........................ 176 22.5 Gravitational Waves and Black Holes............... 179 23 Accretion 181 23.1 Useful references........................... 181 23.2 Lagrange Points and Equilibrium.................. 181 23.3 Roche Lobes and Equipotentials.................. 183 23.4 Roche Lobe Overflow......................... 184 23.5 Accretion Disks............................ 185 23.6 Alpha-Disk model.......................... 186 23.7 Observations of Accretion...................... 196 24 Fluid Mechanics 200 24.1 Useful References........................... 200 24.2 Vlasov Equation and its Moments................. 200 24.3 Shocks: Rankine-Hugoniot Equations............... 202 24.4 Supernova Blast Waves........................ 205 24.5 Rayleigh-Taylor Instability...................... 208 25 The Interstellar Medium 213 25.1 Useful References........................... 213 25.2 Introduction.............................. 213 25.3 H2: Collapse and Fragmentation.................. 213 25.4 H ii Regions.............................. 214 25.5 Plasma Waves............................. 215 25.6 ISM as Observatory: Dispersion and Rotation Measures.... 220 26 Exoplanet Atmospheres 222 26.1 Temperatures............................. 222 26.2 Surface-Atmosphere Energy Balance................ 223 26.3 Transmission Spectroscopy..................... 225 26.4 Basic scaling relations for atmospheric characterization..... 227 26.5 Thermal Transport: Atmospheric Circulation........... 228 27 The Big Bang, Our Starting Point 233 27.1 A Human History of the Universe................. 233 27.2 A Timeline of the Universe..................... 234 27.3 Big Bang Nucleosynthesis...................... 235 27.4 The Cosmic Microwave Background................ 235 27.5 The first stars and galaxies...................... 236 4 28 Thermal and Thermodynamic Equilibrium 237 28.1 Molecular Excitation......................... 237 28.2 Typical Temperatures and Densities................ 240 28.3 Astrochemistry............................ 241 29 Energy Transport 245 29.1 Opacity................................. 245 29.2 The Temperature Gradient...................... 247 30 References 251 31 Acknowledgements 252 5 1.Introduction to Astronomy and Astrophysics 1 Introduction to Astronomy and Astrophysics 6 8.901 Course Notes 2 Lecture 1 • Course overview. Hand out syllabus, discuss schedule & assignments. • Astrophysics: effort to understand the nature of astronomical objects. Union of quite a few branches of physics --- gravity, E&M, stat mech, quantum, fluid dynamics, relativity, nuclear, plasma --- all matter, and have impact over a wide range of length & time scales • Astronomy: providing the observational data upon which astrophysics is built. Thousands of years of history, with plenty of intriguing baggage. E.g.: ◦ Sexagesimal notation: Base-60 number system, originated in Sumer in ~3000 BC. Origin uncertain (how could it not be?), but we still use this today for time and angles: 60’’ in 1’, 60’ in 1o, 360o in one circle. ◦ Magnitudes: standard way of measuring brightnesses of stars and galaxies. ▪ Originally based on the human eye by Hipparchus of Greece (~135 BC), who divided visible stars into six primary brightness bins. This arbitrary system continued for ~2000 years, and it makes it fun to read old astronomy papers (“I observed a star of the first magnitude,” etc.). ▪ Revised by Pogson (1856), who semi-arbitrarily decreed that a one-magnitude jump meant a star was ~2.512x brighter. This is only an approximation to how the eye works! So given two stars with brightness l1 and l2: ▪ Apparent/relative magnitude: m1 – m2 = 2.5 log10 (l1/l2) (2 stars) • So 2.5 mag difference = 10x brighter. •