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  1. 100 M mass 400 R 10-6 g/cm3 density radius 0.01R 0.07M 106 g/cm3

  2. Location depend on: Mass Age Composition

  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, Mv] Stars pile up where times are long Evolution always faster for larger mass

  6. 0.5R T=3x106 =1 R T=6000K =3x10-8 g/cm3 0.1R T=15x106 =100g/cm3 Basic Stellar Structure Equations: 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)T4

  7. Basic Stellar Structure Equations: 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)T4 Hydrostatic Equilibrium: P(r)/r = -GM(r)(r)/r2 0.5R T=3x106 =1 R T=6000K =3x10-8 g/cm3 0.1R T=15x106 =100g/cm3

  8. Basic Stellar Structure Equations: 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)T4 Hydrostatic Equilibrium: P(r)/r = -GM(r)(r)/r2 Mass continuity: M(r)/r = 4r2(r) 0.5R T=3x106 =1 R T=6000K =3x10-8 g/cm3 0.1R T=15x106 =100g/cm3

  9. Basic Stellar Structure Equations: 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)T4 Hydrostatic Equilibrium: P(r)/r = -GM(r)(r)/r2 Mass continuity: M(r)/r = 4r2(r) Luminosity gradient (in thermal equilibrium): L(r)/r = 4r2(r)(,T, comp) where T 0.5R T=3x106 =1 R T=6000K =3x10-8 g/cm3 0.1R T=15x106 =100g/cm3

  10. Basic Stellar Structure Equations: 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)T4 Hydrostatic Equilibrium: P(r)/r = -GM(r)(r)/r2 Mass continuity: M(r)/r = 4r2(r) Luminosity gradient (in thermal equilibrium): L(r)/r = 4r2(r)(,T, comp) where T T gradient: T(r)/r = -3(r)L(r)/16acr2T(r)3 where  T-3.5 (opacity is bound-free, free-free, e- scattering) 0.5R T=3x106 =1 R T=6000K =3x10-8 g/cm3 0.1R T=15x106 =100g/cm3

  11. Observation Theory 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

  12. Birth Sequence • trigger [SN, cloud-cloud, density wave] • star formation “eats” its way into the cloud

  13. Cone nebula HST Clusters dissolve into the field in ~ 10 Myr

  14. Star Cluster NGC 2264

  15. Birth Sequence • trigger [SN, cloud-cloud, density wave] • cloud fragments and collapses [Jeans mass and radius] • free-fall [~4000 yr] Jean’s instability: Ugas = -1/2 Ω (internal energy vs g potential E

  16. Minimum mass for collapse (Jean’s Mass) MJ ~ (5kT/GmH)3/2 (3/4o)1/2 or MJ ~ 3kTR/GmH Minimum radius: RJ ~ (15kT/4GmH o)1/2 or RJ ~ GmHM/3kT Cloud fragments & collapses if M>MJ, R>RJ Free-fall time = (3/32Go)1/2 for T~150K, n~108/cm3, ~2x10-16 g/cm3 tff ~ 4700 yr Dense, cold regions can support only small masses (so collapse), while warm, diffuse regions can support larger masses (stable)

  17. Star Formation The dark region has just developed a Jeans instability. The central gases are heating as they fall into the newly forming protostar.

  18. Matthew Bate simulation of collapse and fragmentation of 500 solar mass cloud to produce a cluster of 183 stars and bds including 40 multiple systems

  19. Unfortunately, no good quantitative theory to predict star formation rate or stellar mass distribution ! IMF = Initial Mass Function •  (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) Big question: Is it universal?

  20. 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]

  21. Pre–Main-Sequence Evolutionary Tracks

  22. Hiyashi tracks 105 yrs 106 yrs radiative 107 yrs convective

  23. outflow gives P Cyg profiles

  24. XZ Tau binary HH-30 edge-on

  25. no magnetic field Disk accretes at ~10-7M /yr, disk ejects 1-10% in high velocity wind

  26. strong magnetic field

  27. Middle Age - stable stars Gravity balances pressure Main sequence [stage of hydrostatic equilibrium] • Mass >1.5 Msun [CNO cycle, convective core, radiative envelope] • Mass = 0. 4 - 1.5Msun[p-p cycle, radiative core, convective envelope] • Mass = 0. 08 - 0. 4Msun[p-p cycle, all convective interior] • Mass = 10 - 80 MJup [0. 01 - 0. 08Msun][brown dwarf] • Mass < 10MJup[< 0.01Msun][planets] Lifetime on Main Sequence = 1010 M/L

  28. Mass - Luminosity Relation M<0.7M;L/L=0.35(M/M)2.62 M> 0.7M;L/L=1.02 (M/M)3.92

  29. Energy in sun (stars) L = 4 x 1033 ergs/s solar constant Age = 4.6 billion yrs (1.4 x 1017 secs) Total E = 6 x 1050 ergs fusion is only source capable of this energy mass with T > 10 million E=1. 3 x 1051 ergs lifetime = E available = 1. 3 x 1051 ergs ~ 3 x 1017s ~ 10 billion yrs E loss rate 4 x 1033 ergs/s test with neutrinos 37Cl +  37Ar + e- for E > 0.81 MeV 71Ga +  71Ge + e- for E > 0.23 MeV

  30. p + p  np + e+ +  np + p  npp +  npp + npp  npnp + p + p 4H  1 He + energy 4.0132  4.0026 (m=0.05 x 10-24g) E = mc2 = 0.05 x 10-24g (9 x 1020cm2/s2) = 4 x 10-5 ergs

  31. 0.43 MeV 1.44 MeV 1H + 1H  2H + e+ +  1H + 1H  2H + e+ +  99.8% 0.25% 2H + 1H  3He +  91% ppI 3He + 3He 4He + 2 1H 9% 3He + 3He 7Be +  0.1% 7Be + e- 7Li +  7Be + 1H  8B +  7Li + 1H  4He + 4He 8B  8Be + e+ +  ppII 8Be  4He + 4He ppIII

  32. 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 < 0.07 MH fusion never begins

  33. CNO cycle

  34. Mass - Luminosity Relation

  35. 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

  36. Post–Main-Sequence Evolution

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

  38. He flash