Black-body radiation: Planck distribution (Rayleigh-Jeans, Wien distributions) Wien’s Law

1. Black-body radiation: Planck distribution (Rayleigh-Jeans, Wien distributions) Wien’s Law Stefan(-Boltzmann) Law

5. supergiants (I) giants (III) mainsequence (V) whitedwarfs

6. Observational HRD may use colour in place of temperature, and magnitude (brightness) in place of luminosity

7. The main proton-proton chain

8. So, what’s SNU?

9. Mid -1968: Davis, Bahcall, Homestake mine experiment - only 1/3 of expected high-energy (PP-II, III) neutrinos found 1989, Kamiokande - only 1/2 of expected high-energy neutrinos Early 1990s, GALLEX, SAGE confirmed absence of low-energy neutrinos (important because dominant) Late 1990s, SuperKamiokande precisely confirmed high-energy deficit of mainly electron neutrinos but with some senitivity to other flavours (muon, tau) 2001 June 18 - Sudbury Neutrino Observatory, bigger deficit the SuperKamiokande, for the same energy electron neutrinos (only) 2002, Davis gets Nobel Prize

10. The solar neutrino problem: neutrino oscillations [the Mikheyev-Smirnov-Wolfenstein (MSW) effect]

11. In 1967, two years before his epochal paper with Gribov on solar neutrino oscillations was published, Bruno Pontecorvo wrote: "Unfortunately, the weight of the various thermonuclear reactions in the sun, and the central temperature of the sun are insufficiently well known in order to allow a useful comparison of expected and observed solar neutrinos..." In other words, the uncertainties in the solar model are so largethat they prevent a useful interpretation of solar neutrino measurements.

12. Bruno Pontecorvo's view was echoed more than two decades later when in 1990 Howard Georgi and Michael Luke wrote as the opening sentences in a paper on possible particle physics effects in solar neutrino experiments: "Most likely, the solar neutrino problem has nothing to do with particle physics. It is a great triumph that astrophysicists are able to predict the number of 8B neutrinos to within a factor of 2 or 3..." C. N. Yang stated on October 11, 2002, a few days after the awarding of the Nobel Prize in Physics to Ray Davis and Masatoshi Koshiba for the first cosmic detection of neutrinos, that: "I did not believe in neutrino oscillations even after Davis' painstaking work and Bahcall's careful analysis. The oscillations were, I believed, uncalled for."

16. Web page: http :// www.star.ucl.ac.uk/~idh/1B23 Neutrinos: different flavours have different masses Sum of masses: <1eV (?) Differences: O(0.1eV) (?)

17. The Hertzsprung-Russell Diagram is a plot of • Temperature (colour, spectral type) vs • Luminosity (brightness) • Most (90%) of stars lie on the Main Sequence, where stars • burning hydrogen to helium (proton-proton or CNO cycles) • are in hydrostatic equilbrium • Sun shines through proton-proton reactions, which emit • electron neutrinos • ‘Solar Neutrino Problem’ • discovery of ‘neutrino oscillations, neutrino mass How do stars get on to the main sequence, and what happens afterwards? – stellar evolution

20. Giant Molecular Clouds: Radii 50 pc Masses 100,000+ solar masses Temp few 10s of K Densities of order 10 molecules per cubic cm (10**20 smaller than the core of a star…) Collapse to from stars, ca. 0.1-100x solar mass

22. Main-sequence lifetime can be estimated

28. For 1 solar mass: Main Sequence lifetime: 1010 years (ZAMSTAMS) As 4H  1 He, number of particles falls, pressure drops core contracts core temperature rises  pressure rises  increased luminosity, increased radius (‘Mirror law: shrinking core  expanding envelope!) ZAMS NOW Temperature rise = 300K 6% increase in radius

30. End of core hydrogen burning  core cools, pressure decreases Cores shrinks  energy deposited in hydrogen burning shell (Kelvin-Helmholtz contraction; core temperature actually increases when fusion stops!) – CNO burning (thin) Luminosity increases, star expands, becomes a Red Giant: burning hydrogen to helium in a shell around a helium core (for about 10% of MS lifetime for a solar-mass star)

31. supergiants (I) giants (III) mainsequence (V) whitedwarfs

34. Hydrogen “ash” falls onto core, which contracts, • temperature rises; at 108 K core helium burning • (triple alpha) starts. Degenerate core: • temperature increases but pressure does not! • Helium flash (raises degeneracy) New configuration, core helium burning (+shell hydrogen burning) on the ‘horizontal branch’ (core expands, star contracts), for about 1% of the MS lifetime for a solar-mass star (helium burning goes fast)!

36. After core helium exhaustion, shell helium burning starts; the star becomes a second type of ‘red giant’: Main Sequence Red Giant Branch Horizontal Branch *Asymptotic Giant Branch (AGB) Helium in shell becomes exhausted Overlying hydrogen shell falls back & reignites  feeds helium shell, compressed, heated  helium shell flash (for degenerate cores) ‘thermal pulse’ Complicated! But result is an unstable star (a pulsating variable) which loses its outer layers

40. ‘Dredge-up’ – convection brings processed material from core • to surface on red-giant branches • First: during shell hydrogen burning • Second: during shell hydrogen burning • (Further dredge-ups possible) • Of some personal significance… • As the outer layers disperse the carbon-oxygen core (left • from core helium burning) is exposed • Planetary Nebula (lifetime ca. 10,000 years, from expansion) + remnant carbon-oxygen white dwarf (electron degenerate)

47. White dwarf mass-radius relation and the Chandrasekhar Limit

49. EVOLUTION OF MASSIVE STARS Initial stages (contraction onto MS, core hydrogen burning on MS) broadly similar (Radiation pressure prevents formation of very high masses, >100 solar masses) Higher masses  hotter cores; core H burning is through the CNO cycle AND later stages of `burning’ (beyond triple-alpha burning of helium) are possible at later stages of evolution

50. For stars > 4 solar masses, carbon-oxygen core is more massive than ‘Chandrasekhar limit’ Electron degeneracy can’t support core, so further heating & burning occurs: Carbon burning  O, Ne, Na, Mg >8 solar masses, neon burning (109K), then oxygen burning, silicon burning, oxygen burning, silicon burningvarious products (sulfur—iron) Faster and faster!! (C: few hundred years; Si, a day)