1. radius density 0.01R  400 R  10 -6 g/cm 3 10 6 g/cm 3 mass 100 M  0.07M 

3. uses ~20,000 stars

4. Mass - Luminosity Relation

5. Stellar Evolution Models Observations Radius Mass L T Pressure Density Composition H-R Diagram [B-V, M v ] Evolution always faster for larger mass Stars pile up where times are long

6. Basic Stellar Structure Equations: 1) Eqtn of State: P  T P  1/V~  P  T so P=(k/  H)  T where 1/  = 2X + (3/4)Y + (1/2)Z with radiative P: P = (k/  H)  T + (a/3)T 4 2) Hydrostatic Equilibrium:  P(r)/  r = -GM(r)  (r)/r 2 3) Mass continuity:  M(r)/  r = 4  r 2  (r) 4) Luminosity gradient (in thermal equilibrium):  L(r)/  r = 4  r 2  (r)  ( ,T, comp) where  T 5) T gradient:  T(r)/  r = -3  (r)L(r)/16  acr 2 T(r) 3 where   T -3.5 ( opacity is bound-free, free-free, e - scattering ) R T=6000K  =3x10 -8 g/cm 3 0.5R T=3x10 6  =1 0.1R T=15x10 6  =100g/cm 3

7. Stellar Life Cycle 1. Birth [Molecular Clouds, T Tauri stars] 2. Middle Age [Main sequence, H>He fusion] 3. Giant-Supergiant [Shell burning, high z fusion] 4. Death [low mass-planetary nebula>white dwarf] [high mass- Supernova>pulsar, black hole]

8. Theory Observation Giant Molecular Clouds 10-100pc, 100,000M  T<100K Radio Collapse trigger: SN cloud-cloud collisions density wave O and B stars form winds smaller mass stars IR Herbig-Haro, T Tauri

9. Star Cluster NGC 2264

10. Minimum mass for collapse (Jean’s Mass) M J ~ (5kT/G  m H ) 3/2 (3/4  o ) 1/2 or M J ~ 3kTR/G  m H Minimum radius: R J ~ (15kT/4  G  m H  o ) 1/2 or R J ~ G  m H M/3kT Cloud fragments & collapses if M>M J, R>R J Free-fall time = (3  /32G  o ) 1/2 for T~150K, n~10 8 /cm 3,  ~2x10 -16 g/cm 3 t ff ~ 4700 yr Dense, cold regions can support only small masses (so collapse), while warm, diffuse regions can support larger masses (stable)

11. Unfortunately, no good quantitative theory to predict star formation rate or stellar mass distribution ! IMF = Initial Mass Function Big question: Is it universal?  (log m) = dN/d log m  m -  N is number of stars in logarithmic mass range log m + d log m  = 1.35 Salpeter slope (logarithmic) in linear units  (m)= dN/dm  m -  where  =  + 1 (= 2.35 Salpeter)

15. Birth Sequence trigger [SN, cloud-cloud, density wave] cloud fragments and collapses [Jeans mass and radius] early collapse isothermal - E radiated away interior becomes adiabatic [no heat transfer] - E trapped so T rises protostellar core forms [~ 5 AU] with free-falling gas above dust vaporizes as T increases convective period radiative period nuclear fusion begins [starts zero-age main sequence]

16. Pre–Main-Sequence Evolutionary Tracks

17. Hiyashi tracks convective radiative 10 5 yrs 10 7 yrs 10 6 yrs

18. Main sequence [stage of hydrostatic equilibrium] Mass >1.5 M sun [CNO cycle, convective core, radiative envelope] Mass = 0. 4 - 1.5M sun [p-p cycle, radiative core, convective envelope] Mass = 0. 08 - 0. 4M sun [p-p cycle, all convective interior] Mass = 10 - 80 M Jup [0. 01 - 0. 08M sun ][brown dwarf] Mass < 10M Jup [< 0.01M sun ][planets] Lifetime on Main Sequence = 10 10 M/L Gravity balance pressure Middle Age - stable stars

19. Energy in sun (stars) L = 4 x 10 33 ergs/s solar constant Age = 4.6 billion yrs (1.4 x 10 17 secs Total E = 6 x 10 50 ergs fusion is only source capable of this energy mass with T > 10 million E=1. 3 x 10 51 ergs lifetime = E available = 1. 3 x 10 51 ergs ~ 3 x 10 17 s ~ 10 billion yrs E loss rate 4 x 10 33 ergs/s test with neutrinos 37 Cl + 37 Ar + e - for E > 0.81 MeV 71 Ga + 71 Ge + e - for E > 0.23 MeV

20. 1) p + p  np + e + + 2) np + p  npp +  3) npp + npp  npnp + p + p 4H  1 He + energy 4.0132  4.0026 (  m=0.05 x 10 -24 g E = mc 2 = 0.05 x 10 -24 g (9 x 10 20 cm 2 /s 2 ) = 4 x 10 -5 ergs

21. 1 H + 1 H  2 H + e + + 2 H + 1 H  3 He +  3 He + 3 He  4 He + 2 1 H 3 He + 3 He  7 Be +  7 Be + e -  7 Li + 7 Be + 1 H  8 B +  7 Li + 1 H  4 He + 4 He 8 B  8 Be + e + + 8 Be  4 He + 4 He 99.8%0.25% 91% 9%ppI ppII ppIII 0.43 MeV 1.44 MeV 0.1%

22. High vs Low mass stars have different fusion reactions and different physical structure M > 1.5 M  CNO cycle; convective core and radiative envelope M < 1.5 M  p-p cycle; radiative core and convective envelope M < 0.4 M  p-p cycle; entire star is convective M < 0.7 M  H fusion never begins

23. Giant-Supergiant Stage H fusion stops - core contracts and heats up H shell burning starts - outer layers expand core T reaches 100 million K - He flash, He fusion starts high mass - multiple shell and fusion stages C to O, O to Ne, Ne to Si, Si to Fe Fusion stops at Fe

24. Post–Main-Sequence Evolution

25. He-C fusion : Triple Alpha 4 He + 4 He  8 Be +  8 Be + 4 He  12 C +  3He  1C energy = 1.17 x 10 -5 ergs

27. H-R Diagram of a Globular Cluster

28. Clusters of Different Ages

29. Main-sequence fitting for cluster distances 1. Use CCD to get b, v images of cluster stars 2. Plot color-mag diagram of v vs b-v 3. Find main sequence turnoff & lower MS stars 4. For the SAME B-V on lower MS, read m v from cluster and M v from H-R diagram 5. Use distance modulus m-M to calculate d

30. Stellar Death Low mass He or C,O core Planetary nebula Remnant < 1.4 M sun White Dwarf High mass Fe core Supernova Remant 3M sun Neutron star Black Hole Size ~ Earth ~15 km 0 Density (g/cm 3 ) 10 6 10 14 infinity MagField (G) 10 4 -10 8 10 12 ? Rotation minutes <sec <<sec Pressure e - degeneracy neutron degeneracy none

31. Low Mass Death - a White Dwarf degeneracy Pauli exclusion principle: no 2 electrons can be in the same state (position & momentum) as T increases, more states available P  T at high density, collisions restricted P   if all states full, gas is degenerate as star contracts,  increases so becomes degenerate as T increases, degeneracy is lifted when He - C fusion starts, core is degenerate He flash removes degeneracy WDs are totally degenerate up to 1. 4 M  degeneracy pressure stops the collapse

32. White Dwarf M-R Relation P   5/3 hydro-equil P  M 2 /R 4   M/R 3 M 2 /R 4  M 5/3 / R 5 M 1/3  1/R R  1/M 1/3

33. 1175 WDs from SDSS

35. WDs from SDSS

36. massive single stars a (WD binary, b,c massive single stars) Type I - no H, found in all galaxies Type II - H, only in spiral arms (massive stars)

38. Famous Supernovae Naked eye in Milky Way: 1054 Crab 1572 Tycho 1604 Kepler In LMC SN 1987a Feb 1987 neutrino burst seen We are overdue ~ 1/20 yrs/galaxy

40. Neutron stars=pulsars density=10 14 g/cm 3 mass < 3M  R ~ 10 km B ~ 10 12 G pulse 1-1000/sec found in radio 1967 LGM pulsting neutron star rotating neutron star

41. Black Body = thermal (Planck Function) Synchrotron = non-thermal (relativistic) c = eB/2  m e Wavelength Flux

42. Black Holes (R=0,  =  ) escape velocity = (2GM/R) 1/2 for light, v = c c= (2GM/R) 1/2 c 2 = 2GM/R for object in orbit around mass M at distance R: R s = 2GM/c 2 Schwarzschild radius R s is event horizon 1M   R s = 3km, 10M   R s = 30km, 150kg  R s = 10 -23 cm

43. Earth has Newtonian Physics; BHs have Relativistic Physics if you ride into a BH  you go in if you watch someone ride in  they stay at R s Proof of Black Hole: 1) Single-lined spectroscopic binary 2) strong X-ray emission Kepler’s Law M 1 +M 2 =P(K 1 +K 2 ) 3 /4  Gsin 3 i ~ 20M  spectral type M 1 shows M 1 ~ 10M  M 2 ~ 10M  but invisible 10 36-38 ergs/s