1101_20_fusion_MSlifetime

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Astronomy

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Oct 30, 2023

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Astronomy 1101 Lecture 13 Fusion and the lifetime of stars Astronomy 1101 High Altitude Observatory/ National Center for Atmospheric Research 140 Some questions Light: How are wavelength and frequency related? How is a gamma-ray different than a radio wave? What is the speed of light? What is the Doppler effect? Blackbodies: What is a blackbody spectrum? If one blackbody is hotter than another, but they have the same size, which is more luminous? Which is bluer? If one blackbody is bigger than another, but have the same temperature, which is more luminous? More light: What is the difference between luminosity and brightness? If two objects have the same brightness, but one is further away, which is more luminous? Parallax: What is parallax, and what do we use it for? Stars: What is the HR diagram? What is the main sequence? How is the luminosity of a star related to its temperature and radius? Which stars have higher mass on the main sequence, blue O stars or red M stars? What is hydrostatic equilibrium? If gravity were suddenly made stronger, would stars collapse? If not, why not? What is pressure related to? What powers the Sun? How do we know? 141 PP Chain: Fuse 4 protons ( 1 H) into one 4 He nucleus plus the following reaction by-products: • 2 photons = Energy • 2 positrons = Energy (positive electrons, anti-electrons) • 2 neutrinos that leave the Sun carrying some energy Sun fuses ~600 Million Tons of H into He per second, ~4 Million tons of matter into energy per second ( E = mc 2 ), Sun contains ~10 21 Million tons of H (only ~10% is hot enough for fusion). Lifetime: for 10 billion years. 142 (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? 143

Astronomy 1101 Lecture 13 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. ࠵? = ࠵? ࠵? ! ࠵? 144 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). 145 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 146 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. 147

Astronomy 1101 Lecture 13 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. 148 Main Sequence Membership To be a Main Sequence Star: • It must be in Hydrostatic Equilibrium Pressure = Gravity • It must be in Thermal Equilibrium Energy Generation Rate = Luminosity • It must generate energy by fusing H into He in its core. Relax any of these conditions and the star leaves the Main Sequence. How long does a star live on the MS? 149 High mass! High L! Blue, hot Low mass! Low L! Red, cool 20M sun 10M sun 5M sun 1M sun 0.5M sun 0.1M sun Blue Red On the main sequence: 153 High mass! High L! Blue, hot Low mass! Low L! Red, cool 20M sun 10M sun 5M sun 1M sun 0.5M sun 0.1M sun Blue Red Which stars run out of fuel first on the Main Sequence? Which stars live the longest? 154

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