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
CNO Simulator

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 Ky form 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 radiative zone 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?
BD: MJ
229 T

11. Too Big? Models suggest that collapse with
fails as radiation pressure fragments cloud
Recent record
Eddington Limit
2010 discovery in Tarantula Nebula (LMC)- VV IR

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
Procyon A: M=1.42, R = 2 L = 7

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%
Ad-debran M=1.7 R = 44 L = 520

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
Core: 8e-4
He shell 9 e-4
Inert He: 2.9e-3
H shell: 5.6e-3
R = 44

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 nucleosynthesis produces heavier elements
Flash expands H shell stopping fusion. Reignites on contraction, collects He to flash, repeat every 100Ky
Carbon stars M> 2Modot. Mdot sim 10^{-4}Modot/yr!
Mira M = 1.18, R = , L = Variable later

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
sclock

28. Does it Work?
IC 1795 – OB Association
NGC My
Cone nebula

29. Older
Orion Nebula Cluster 12My
M45 130My

30. And Older
NGC My
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
NGC-6397

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 100 with 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 Cepheids oscillate 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
Shapley thought so Schwarzschild found it

37. Why We Care Later: W Virginis PLR less luminous for same period
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 Surface Gravity
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