Mass Statistics

1. Mass Statistics • Add mass for main sequence to our plot • Masses vary little • Model: Stars are the same: mass determines rest • Heavy stars hot, luminous

2. Mass-Luminosity Relation • Find approximately • Borne out by models: Mass compresses star increasing rate of fusion • If amount of Hydrogen available for fusion is near constant fraction, big stars run out sooner • OB stars are young!

3. Main Sequence Stars • Stellar modeling matched to data tells us about how stars work • Main-Sequence stars fuse Hydrogen to Helium in core • Hydrostatic Equilibrium determines rate of fusion and density profile from mass

4. CNO Chain • In large stars core hot and CNO chain dominates fusion • Rate rises rapidly with temperature

5. Size Matters • Mechanisms of heat transfer depend on mass • In small stars, entire volume convective so all available to fuse in core • In large stars, radiation and convection zones inverted

6. Expansion by Contraction • As a main sequence star ages core enriched in Helium • Rate of fusion decreases – temperature and radiation pressure decrease • Number of particles decreases – thermodynamic pressure decreases • Core contracts and heats • Fusing region grows • Luminosity increases • Envelope expands • Sun now 25% brighter than when it formed • Core now 60% Helium • Continues to brighten – heating Earth • In 1-3Gy could be uninhabitable? • Orbit stable out to 1Gy?

7. Questions • For 90% of stars we have a good understanding of how they work • This comes from careful observation and detailed modeling • Where do the rest come from? • What happens when core is all Helium??

8. Modelling Collapse • Model a cloud of mass • Within a few Kyform opaque radiating photosphere of dust and later H- • Photosphere contracts from to at constant fueled by Kelvin-Helmholtz and deuterium fusion over 600Ky

9. Pre-Main Sequence • Initial photosphere contracts at constant T decreasing L • Rising ionization in center reduces opacity creating radiativezone increasing L • When fusion begins L decreases initially as core expands • In 40My settle down to MS equilibrium: KH time! • Larger stars go faster 105 106 107

10. Too Small • Below effective fusion does not occur is a brown dwarf type L, T, Y • How Many? 1:1? 1:5?

11. Too Big? Models suggest that collapse with fails as radiation pressure fragments cloud Recent record

12. On the Main Sequence • Hydrogen fusion in core supports envelope by thermal and radiation pressure • Luminosity, surface temperature determined by mass, composition, rotation, close binary partner, atmospheric and interstellar effects • Main Sequence thickened by variations in these • Over time core contracts and heats • Fusion rate increases • Envelope expands slowly with little change in temperature • Evolutionary track turns away from Main Sequence

13. Running Out of Gas • Inner 3% inert Helium core is isothermal • Hydrogen fusion in shell exceeds previous core luminosity • Envelope expands and cools • Inert core grows

14. Sub-Giant Branch • In isothermal core pressure gradient maintained by density gradient • If core too large cannot support outer layers. • Core collapses rapidly (KH scale) • Gravitational energy expands envelope • Temperature decreases • Sub-Giant Branch

15. Red Giant • Core collapses • Compression heats shell increasing luminosity • Envelope expands and cools, H-opacity creates deep convection • First dredge-up brings fusion products to atmosphere • Mass loss up to 28%

16. Then What? • Core does not collapse due to electron degeneracy pressure • Quantum effect of Pauli exclusion principle • Squeezing electrons into small space requires occupying higher energy states • Produces temperature-independent contribution to pressure • This is smaller than thermal pressure in Hydrogen core today • In compressed inert Helium core degeneracy pressure stops collapse

17. Helium Core Flash • When core temperature reaches 108K Helium fusion via triple-α process occurs explosively in degenerate core • For a few seconds produce galactic luminosity absorbed in atmosphere, possibly leading to mass loss • Expands shell decreasing output • Envelope contracts and heats

18. Horizontal Branch • Deep convection rises • Convective core fusing Helium to Carbon, Oxygen • Shell fusing Hydrogen to Helium • Core contracts • Envelope contracting and heating

19. Early Asymptotic Giant Branch • Inert CO core collapses to degeneracy • Helium fusion in shell • Hydrogen shell nearly inactive • Envelope expands and cools • Convective envelope deepens: second dredge-up • Mass loss in outer layer

20. Thermal Pulse AGB • Hydrogen shell reignites • Helium shell flashes intermittently • Flash expands Hydrogen shell, luminosity drops and envelope contracts heats • Hydrogen reignition increases luminosity envelope expands cools • Convection between shells and deep convective envelope: third dredge-up and Carbon stars • Rapid mass loss to superwind • s-process neutron capture nucleosynthesisproduces heavier elements

21. The End • Pulses eject envelope exposing inert degenerate CO core • Initially hot core cools • Expanding envelope ionized by UV radiation of white dwarf glows as ephemeral planetary nebula

22. M57

23. Ghost of Jupiter (NGC 3242)

24. Cat’s Eye

25. Hubble 5

26. NGC-2392 (Eskimo)

27. Clusters and the Model • Model predicts how clusters will evolve • Massive stars evolve faster • Later stages of evolution rapid • Can find cluster age from Main-Sequence turnoff • Main Sequence Matching leads to distance: Spectroscopic Parallax and other cluster distance measures

28. Does it Work? • IC 1795 – OB Association • NGC 2264 8My

29. Older • Orion Nebula Cluster 12My • M45 130My

30. And Older • NGC6494 300My • M44 800My

31. Oldest • M67 3.5Gy • M13 12Gy

32. Blue Stragglers • Some MS stars found past turnoff point • Mechanism: • Mass Transfer in close binary • Collision and Merger • Likely both

33. Populations • Astronomers distinguished Population II from Population I stars based on peculiar motion • Differ in metallicity: Population II metal-poor formed early • Globular Clusters are Population II • Population III: Conjectured first stars – essentially metal free

34. Variable Stars • Some Giants and Hypergiants exhibit regular periodic change in luminosity • Mira (Fabricius 1595) changes by factor of 100with period of 332d • LPV like Mira not well modelled

35. Instability Strip • A nearly vertical region traversed by most massive stars on HB • RR Lyrae: PII HB stars with periods of hours. Luminosity varies little (!) • Cepheids(PI) , W Virginis(PII) periods of days.

36. Why They Pulse • Cepheidsoscillate in size (radial oscillation) • Temperature and luminosity peak during rapid expansion • Eddington: Compression increases opacity in layer trapping energy and propelling layer up where it expands, releases energy • Problem: compression reduces opacity due to heating • Solution: compression ionizes Helium so less heating. Expansion reduces ionization – κ-mechanism • Instability strip has partially ionized Helium at suitable depth

37. Why We Care • Leavitt 1908: Period-Luminosity Relation for SMC cepheids • Luminous cepheids have longer periods • With calibration in globular clusters cepheids become standard candles • Later: W Virginis PLR less luminous for same period

38. Discovery • Bessel 1844: Sirius wobbles: a binary • Pup hard to find. Clark 1846 • Orbits: • Spectrum (Adams 1915): • Surface Gravity • Spectrum: Very broad Hydrogen absorption lines • Estimate: • No Hydrogen else fusion

39. Degenerate Matter • White dwarves are the degenerate cores of stars with • Composition is Carbon Oxygen • Masses • Significant mass loss • Chandrasekhar: • Relativity:

40. Mass-Radius