1101_19_Sun_Fusion_Lifetime

Astronomy 1101 Lecture 13 Hydrostatic equilibrium and the Sun’s lifetime Astronomy 1101 High Altitude Observatory/ National Center for Atmospheric Research 94 Key Ideas Stars are in hydrostatic equilibrium: balance between pressure and gravity. Stars shine because they are hot. Need an internal energy source to stay hot. What is it? Chemical reactions? Gravity? Nope. Both too inefficient. Sun would have run out of gas long ago. Nuclear Fusion Energy • Energy from fusion of 4 Hydrogen into 1 Helium • Proton-Proton nuclear reaction chain Evidence for fusion. 95 Main Sequence High mass High L. Low mass. Low L. The main sequence is a mass sequence. 20M sun 10M sun 5M sun 1M sun 0.5M sun 0.1M sun 96 Why is it a sphere? 99

Astronomy 1101 Lecture 13 P P P P G G G G Gravity and Pressure are in exact balance. The star neither expands nor contracts . The life of a star is a constant tension between Gravity & Pressure. Hydrostatic Equilibrium is the balance between gravity and internal pressure inside a star. Pressure supports the star against the inward crush of Gravity. Gravity makes the star contract. Pressure makes the star expand. Most stars obey “ideal gas law”: P = n k B T (n is number density) Hydrostatic Equilibrium: Gravity confines the gas against the outward push of Pressure. 102 Structure: Hot, dense, compact Core Hydrostatic Equilibrium naturally results in a Core/Envelope structure. Outer layers press down on the inner layers. The deeper you go into a star, the greater the pressure. The greater the Pressure, the bigger the temperature and density. Cooler, lower density extended Envelope 103 Example: The Internal Structure of the Sun Core : Radius = 0.25 R sun T = 15.7 Million K Density = 150 g/cm 3 ~50% of the Mass Envelope : At Surface: Convection = boiling pot! Radius = R sun = 700,000 km T = 5770 K (surface) Density = 10 - 3 g/cm 3 104 How long can the Sun shine? To stay hot, stars must make up for the lost energy, otherwise they would cool and eventually fade out. Need two numbers : How much internal energy there is in the Sun. How fast this energy is lost ( Luminosity ). Example: 100,000 calories / 2000 calories per day: Lifetime = 50 days. 114

Astronomy 1101 Lecture 13 P G Luminosity radiates away heat, and the internal Pressure drops... P 119 Balance tips in favor of gravity, so the Sun contracts, becoming more tightly bound... 120 Contraction makes core heat up, increasing the internal Pressure. 121 Balance restored, but with higher gravity, pressure & temperature than before... Starts the cycle all over again... 122

Astronomy 1101 Lecture 13 Gravity is also inefficient. Total gravitational energy is E = GM 2 /R = 4 x 10 48 ergs. But, the Sun radiates 4 x 10 33 ergs/s. Lifetime ~ E/L ~ 10 15 s ~ 30 million yrs But, in 1880s geologists say Earth is at least 2 Billion years old. Kelvin & Helmholz say: The geologists are wrong . Nature: Kelvin & Helmholtz are wrong! New physics. 123 Nuclear Energy 1896: Röntgen & Becquerel discover radioactivity. Pioneering work by Marie & Pierre Curie. 1905 : Einstein demonstrates equivalence of Mass & Energy: E = mc 2 1920s : Eddington noted that 4 protons have 0.7% more mass than 1 Helium nucleus (2p+2n). If 4 protons fuse into 1 Helium nucleus, the remaining 0.7% of mass is converted to energy 128 Hydrogen Fusion Question : How do you fuse 4 1 H (p) into 4 He (2p+2n)? Issues : • 4 protons colliding at once is unlikely. • Must turn 2 of the protons into neutrons. • Must be hot & dense: >10 Million K to get protons close enough to fuse together (Two positive charges repel!). 129 Proton-Proton Chain: 3-step Fusion Chain 130

Astronomy 1101 Lecture 13 Neutrinos Postulated in 1930 by Wofgang Pauli to account for anomalies in neutron decay experiments. Named by Enrico Fermi. What are they? - Neutral subatomic particles. - Very nearly massless. - Travel very near the speed of light. - Interact with matter via the “weak force.” They do rarely interact with our detectors on Earth and we can infer the neutrino luminosity from the Sun! About 61 billion pass through every square cm of your body every second. 135 Super-Kamiokande Neutrino Observatory A neutrino enters the tank, is absorbed by a proton in the water, produces an energetic anti-electron, which produces a flash of blue light. (Cerenkov Radiation) NEUTRINOS DETECTED!! 136 (Un)Controlled Nuclear Fusion? Nuclear fusion is Temperature sensitive : • Higher Core Temperature = More Fusion BUT, • More fusion makes the core hotter , • Hotter core leads to even more fusion, which leads to a hotter core, which … Why don’t stars explode like H-Bombs? 139 Hydrostatic Thermostat If fusion reactions run too fast: • Core heats up, leading to higher pressure • Higher pressure makes the core expand, because it overwhelms gravity. • Expansion cools core, slowing fusion. If fusion reactions run too slow: • Core cools, leading to lower pressure • Lower pressure makes the core contract, because of gravity overwhelms lower pressure. • Contraction heats core, increasing fusion Thus, balance. Fusion coupled to Hydrostatic Equlibrium, but heat needs to be transported out of the core. ࠵? = ࠵? ࠵? ! ࠵? 140

Astronomy 1101 Lecture 13 Transport Heat always flows from hotter regions into cooler regions. In a star, heat flows f rom the hot dense fusing core, out through the envelope, to the surface where it is radiated as light. How? Radiation (photons diffuse) & Convection (a pot boiling). 141 Diffusion Energy is carried by photons • Photon leaves the core • Hits an electron or atom in ~ 1cm and scatters • Slowly staggers to the surface in a “ random walk ” • Called diffusion. Takes of order 1 Million years to reach the surface 142 Energy Transport in Stars Normal Stars : • Mix of Radiation & Convection transports energy from the core to the surface. • Sun has a radiative core and convective envelope. 143 Energy generation rate = Star’s Luminosity Thermal Equilibrum is when energy generation in the core is balanced by the transport of that energy to the surface Balance: • Make more energy than L, star expands • Make less energy than L, star contracts Combined with hydrostatic equilibrium, this is how stars “know” how much to shine. 144

Astronomy 1101 Lecture 13 Stars = Cars? Part I A low-mass star is like an economy car: • Small fuel tank • Low-power engine (low energy output) • Excellent “ gas mileage ” Consumes fuel very slowly, so “ runs ” for a long time. Result: Low-Mass stars stay on the Main Sequence for a very long time. 152 Stars = Cars? Part II A high-mass star is like a Hummer: • Large fuel tank • High-Power engine (high energy output) • Low “ gas mileage ” Consumes fuel very quickly Result: High-Mass stars run out of fuel and leave the Main Sequence after a very short time. 153 Main Sequence Lifetime t life = f ε Mc 2 /L M-L Relation: L = L Sun (M/M Sun ) 4 Combine them: t life = 10 Gyr (M Sun /M) 3 Consequences: • High-Mass M-S stars have short M-S lifetimes • Low-Mass M-S stars have long M-S lifetimes 154 Examples: Sun: • M = 1 M sun , t life ~ 10 Gyr ~ Age of Universe Massive Star (10 M sun ) • t life ~ 10 Gyr / (10 M sun ) 3 = 10 Gyr/1000 • t life ~ 10 Million Years! Low-mass Star (0.1 M sun ) • t life ~ 10 Gyr / (0.1 M sun ) 3 = 10 Gyr/0.001 • t life ~ 10 Trillion Years! >> Age of Universe 155

Astronomy 1101 Lecture 13 Some Consequences (think infants!!): • If you see an O or B star, it must be young because they evolve after only 10 Million years. • You can’t tell how old a 0.1M sun main sequence star is because they live a very long time & age very slowly. • The Sun is ~ 5 Billion years old. t life ~10 Gyr, so it will live on the main sequence for another ~ 5 Billion years. • Then, it runs out of Hydrogen in its core … 156 How long a star lives on the Main Sequence depends on its mass . High-mass M-S Stars: 10M sun has t life ~10 Million years Live fast, die young… Low-mass M-S Stars: 0.1M sun has t life ~10 Trillion years! Live very long lives. The Sun: t life ~10 Billion years! t life,MS ~10Gyr (M sun /M) 3 157