Stellar Interiors Nuclear Energy ASTR 2110 Sarazin Fusion the Key to the Stars
Energy Source for Stars For Sun, need total energy E = L t Sun = L x (10 10 years) ~ 10 51 erg N atoms = / m p ~ 10 57 atoms M E/atom ~ 10-6 erg ~ 10 6 ev = 1 MeV per atom E/mass ~ 1 Mton TNT equiv. / ton of Sun Chemistry, Electricity, Semiconductors, etc. è 1 ev/atom Nuclear Energy E/atom ~ 10 MeV ~ 10 7 ev Stars are powered by nuclear energy!!
Nuclear Physics Nuclei small Z = # of protons N = # of neutrons A = Z + N = # of nucleons element = fixed Z isotope = same element, different N Symbol: A Z 12 C è Z = 6, N = 6, A = 12 10-8 cm 10-13 cm atom
Nuclear Physics Nuclei small Z = # of protons N = # of neutrons A = Z + N = # of nucleons element = fixed Z isotope = same element, different N Symbol: A Z 12 C è Z = 6, N = 6, A = 12 10-8 cm 10-13 cm atom
Nuclear Physics Low energy nuclear physics rules: 1. Only p, n, lighter particles Strong force: p s stay p s, n s stay n s Weak force: (much slower) n p n p + + e +ν e Beta decay 2. Total number of nucleons is constant: A tot = const. A 1 Z 1 + A 2 Z 2 A 3 Z 3 + A 4 Z 4 A 1 + A 2 = A 3 + A 4
Nuclear Physics 3. Charge is conserved Define Z(e ) = 1, Z(e+) = +1 Z tot = const. E>0 free E A 1 Z 1 + A 2 Z 2 A 3 Z 3 + A 4 Z 4 Z 1 + Z 2 = Z 3 + Z 4 E<0 bound E gs 4. Only single or binary reactions 5. All nuclei decay to ground state rapidly Define E bind = - E gs binding energy
Nuclear Energy To produce nuclear energy, E gs ê è E bind é binding energy increases Since A tot = # of nucleons = constant Key quantity: E bind / A = binding energy / nucleon
Curve of Binding Energy 4 He E bind / A (MeV) 56 Fe 235 U 1 H A (# of nucleons)
Curve of Binding Energy E bind / A (MeV) Fusion Fission A (# of nucleons)
Fusion: A 1 + A 2 è A 3 A 3 56 Fission: A 1 è A 2 + A 3 A 1 200 Nuclear Energy High A elements very rare, H very common Fusion powers the stars!
Couloub Barrier Why no fusion on Earth? Coulomb barrier Strong nuclear force short range r 10-13 cm Longer range è electrostatic repulsion PE = Z 1Z 2 e 2 R 10 13 cm R PE Z 1 Z 2 MeV PE 0 10-13 cm r
Couloub Barrier In stars? In Sun, T(center) 10 7 K (3/2) k T ~ 10 3 ev << 10 6 ev No reactions? Maxwell-Boltzmann tail E reaction 20 kev tail
Couloub Barrier In stars? PE In Sun, T(center) 10 7 K (3/2) k T ~ 10 3 ev << 10 6 ev No reactions? 0 10-13 cm r Maxwell-Boltzmann tail E reaction 20 kev Barrier penetration Uncertainty principle
Couloub Barrier Fusion reactions in stars generally slow Long stellar lifetimes Reactions very temperature sensitive Increase very rapidly with temperature PE = Z 1 Z 2 e2 R Z 1 Z 2 MeV Lightest elements burn first H è He è C è O è Fe
Hydrogen Burning Want 4H = 4p è 4 He = (2p,2n) p è n, only by weak interaction Much slower than pure fusion protons Deuterium (pn) lifetime pep alternative Only low Z elements, works at low T ε ~ T 4
Hydrogen Burning C only catalyst net result 4 H è He Time scales for late A star
Helium Burning Triple Alpha
Helium Burning Triple Alpha First step endothermic è reversed unless another He hits first Requires high T ~ 10 8 K, high density
Carbon Burning, Etc. Explains why elements beyond Fe are very rare, can t be made by exothermic fusion reactions Explains why most common elements beyond H have Z = N = even = multiples of He
Fe
Carbon Burning, Etc. Explains why elements beyond Fe are very rare, can t be made by exothermic fusion reactions Explains why most common elements beyond H have Z = N = even = multiples of He
Fusion Reactions log ε (erg/s/gm) 6 4 2 0 Sun CNO pp 3α C burning -2 7 7.5 log T (K) 8
Thermal Stability of Stars Fusion: Makes lots of energy Very temperature sensitive } explosives hotter BANG more energy
Thermal Stability of Stars Why don t stars explode? Stars have negative heat capacity!
Energies is Stars PE = 2 TE E = TE TE TE 0 E E PE PE Stars have negative heat capacity If you add energy (heat), they get cooler!!
Thermal Stability of Stars Why don t stars explode? Stars have negative heat capacity! Add energy, get cooler Add energy, pressure increases, gas expands, gas gets cooler Cooler è less fusion è less energy Fusion in stars è perfect thermostat! Stars are incredibly stable!
Exceptions: Thermal Stability of Stars 1. Virial theorem applies to whole of star Parts of star exchange energy è pulsations 2. Thermal gas pressure only KE = E KE = (3/2) PV = (3/2) NkT V only if P = P gas Degeneracy pressure, KE = (3/2) P deg V, but P deg = func. of density only, not temperature Fusion in degenerate regions è explosion
Fusion The Key to the Stars
Fusion The Key to the Stars Make stellar energy, provide source of light Make all heavy elements (C, N, O, Fe, ) Make stars stable (or unstable) Change composition of stars they evolve Set lifetime of stars, t = E nucl / L
Tests of Stellar Structure Theory ASTR 2120 Sarazin Davis Solar Neutrino Experiment
Tests of Stellar Structure Theory At some level, all of astronomy (rest of this course) Critical tests? Sun is good since it is close
Solar Oscillations Helio-seismology P ~ (G ρ ) -1/2 But, many normal modes of oscillation Can also be done for other stars
Solar Oscillations One normal made of Sun (red and blue shifts)
Solar Oscillations Some modes probe surface, some deep interior
Solar Oscillations Spectrum of frequencies of oscillation
Solar Neutrino Experiments Test idea: Fusion powers stars Cannot see into Solar core with light, but neutrinos should escape Unfortunately, main neutrinos made by pp reaction are very low energy, hard to detect Detect side reactions
Solar Neutrino Experiments 14 Mev!
Solar Neutrino Experiments
Solar Neutrino Experiments
Davis Experiment Mainly detect 8 B ν s ν + 37 Cl 37 Ar + e - Normal chlorine - use 100,000 gal of C 2 Cl 4 (dry-cleaning fluid) Argon inert, bubble out of tank 37 Ar decays (beta decay), detect every single atom! Homestead Gold Mine, South Dakota
Davis Experiment
Davis Experiment
Davis Experiment
Davis Experiment Predict ~ 5.6 SNU (solar neutrino units) Observe only 1.8 ± 0.3 SNUs ~ 1/3 expected What is wrong? 1. Experiment wrong - No 2. Nuclear reaction rates wrong - No 3. Astronomy wrong (solar model incorrect) - No 4. Physics wrong - Yes! Neutrinos are NOT mass-less and stable
Neutrino Oscillations Three flavors of neutrinos ν e ν µ ν τ
Neutrino Oscillations
Sudbury Experiment
Super-Kamiokande Experiment
Neutrino Oscillations Three flavors of neutrinos ν e Yes! ν µ ν τ
Nobel Prize 2002