Contraction of Giant Molecular Cloud Cores

1. HW #13read 9.4-endQuestions 9.9, 9.13,9.14Problems 9.7,9.8,9.9,9.11extra time due next Thursday!We are proceding to CHap 10 stellar old agechap 11 The death of high mass stars

2. Contraction of Giant Molecular Cloud Cores Horse Head Nebula • Thermal Energy (pressure) • Magnetic Fields • Rotation (angular momentum) • Turbulence External trigger required to initiate the collapse of clouds to form stars.

3. Sources of Shock Waves Triggering Star Formation d) Spiral arms in galaxies like our Milky Way: Spirals’ arms are probably rotating shock wave patterns.

4. Protostars Protostars = pre-birth state of stars: Hydrogen to Helium fusion not yet ignited Still enshrouded in opaque “cocoons” of dust => barely visible in the optical, but bright in the infrared.

5. Heating By Contraction As a protostar contracts, it heats up: Free-fall contraction → Heating ZAMS LINE

6. From Protostars to Stars Star emerges from the enshrouding dust cocoon Ignition of H He fusion processes

7. Globules Bok Globules: ~ 10 to 1000 solar masses; Contracting to form protostars

8. Globules (2) Evaporating Gaseous Globules (“EGGs”): Newly forming stars exposed by the ionizing radiation from nearby massive stars

9. The Source of Stellar EnergyQUICKY REVIEW Recall from our discussion of the sun: Stars produce energy by nuclear fusion of hydrogen into helium. In the sun, this happens primarily through the proton-proton (PP) chain

10. The CNO Cycle In stars slightly more massive than the sun, a more powerful energy generation mechanism than the PP chain takes over: The CNO Cycle.

11. Stellar Structure Energy transport via convection Sun Energy transport via radiation Flow of energy Energy generation via nuclear fusion Basically the same structure for all stars with approx. 1 solar mass or less. Temperature, density and pressure decreasing

12. Hydrostatic Equilibrium Gravity, i.e. the weight from all layers above Imagine a star’s interior composed of individual shells. Within each shell, two forces have to be in equilibrium with each other: Outward pressure from the interior • In building computer simulations of Stars we make • Assumptions as our first approach. • The Stars are spheres • Temperature, density and composition are spherically symmetric. IE. They depend only on the distance, r, from the center. Consider the shell at radius r with density r(r) then the amount of mass in this shell is dM = r (r) dV but dV = 4pr2 dr why???dM = 4pr2 r (r) dr { eq. 9.32b} dM/dr= 4pr2r (r) {9.33}=MASS CONTINUITY r Furthermore M(r) = 4p0r(r’) r’2 dr’ The total mass within a radius r!

13. Hydrostatic Equilibrium (2) Outward pressure force must exactly balance the weight of all layers above everywhere in the star. This condition uniquely determines the interior structure of the star. Consider in dr a cylinder, blown up here! FB r dr FG FB the buoyant force is balanced by FG gravitational Pull of mass within (M(r) ) FB is due to the pressure difference on the cylinder! Hydrostatic equilibrium FG +FB =0

14. Hydrostatic Equilibrium 3 P (r+dr)dA First, we consider cylinder with mass dm =r (r )dV=r ( r) drdA From Physics we know F = PA dP =P(r+dr) –P(r) in the usual calculus manner Hence FB =P( r) dA – P(r+dr) dA  FB = -dPdA…..why -? EQ 40 P (r)dA FG =-GM(r) dm /r2=-[GM( r)/r2 ] r ( r) drdA eq 37 Using HE  FG +FB =0 and equations 37 and 40 we get the equation of Hydrostatic Equilibrium(43) dP/dr = -[GM (r ) /r2] r ( r) Example 9.4..assume Sun has constant density r integrate 43 from 0 to R (solar radius) And Pressure from Pc(at center) to 0 at the surface we get an estimate for the central pressure in The Sun at 1 x 1016 which is 20 times too small with more sophisticated models Check out this problem ..be able to do it..

15. Energy Transport Structure Inner convective, outer radiative zone Inner radiative, outer convective zone CNO cycle dominant PP chain dominant

16. Building Computer Models We make various assumptions (hope intelligent) about the nature of the material, how energy is Created and Transported and use the equilibrium equation to build computer Models of stable stars. For example if we assume the star is an ideal gas you may have learned that PV=nRT conects P, V and T…we use a variation of this Equation of State for an ideal Gas namely P = (r/m) kT Using the Pc from before we can use this equation to estimate Tc for the Sun See Example 9.5 Energy Transport equations are justified in section 9.4.2 Showing how the temperature varies in a star (dT/dr) for radiation transport is derived..relating the luminosity L see messy equation 9.53 Also energy generation is discussed Namely, how does the luminosity change with radius depends on the energy generated at a given radius e ( r ) Equation 9.55 dL/dr = 4 p r2r (r ) e (r )

17. Main Sequence Stars- putting itall together on a computer The structure and evolution of a star is determined by the laws of • Hydrostatic equilibrium • Conservation of mass • Energy transport • Conservation of energy Radiation Equation 9.53 As dT/dr Computer model predicts that a star’s mass (and chemical composition) completely determines its properties.

18. H-R Diagram Main Sequence and beyond DOC How long do I have On the Main Sequence?

19. Evolution on the Main Sequence (2) A star’s life time T ~ energy reservoir / luminosity Energy reservoir ~ M Luminosity L ~ M3.5 T ~ M/L ~ 1/M2.5 Massive stars have short lives!

20. Evolution off the Main Sequence: Expansion into a Red Giant Hydrogen in the core completely converted into He: “Hydrogen burning” (i.e. fusion of H into He)ceases in the core. H burning continues in a shell around the core. He Core + H-burning shell produce more energy than needed for pressure support Expansion and cooling of the outer layers of the star Red Giant

21. Expansion onto the Giant Branch Expansion and surface cooling during the phase of an inactive He core and a H- burning shell Sun will expand beyond Earth’s orbit!

22. Degenerate Matter Matter in the He core has no energy source left. Not enough thermal pressure to resist and balance gravity Matter assumes a new state, called degenerate matter: Pressure in degenerate core is due to the fact that electrons can not be packed arbitrarily close together and have small energies.

23. Red Giant Evolution H-burning shell keeps dumping He onto the core. He-core gets denser and hotter until the next stage of nuclear burning can begin in the core: 4 H → He He He fusion through the “Triple-Alpha Process” 4He + 4He 8Be + g 8Be + 4He 12C + g

24. Helium Fusion He nuclei can fuse to build heavier elements: When pressure and temperature in the He core become high enough,

25. Red Giant Evolution (5 solar-mass star) C, O Inactive He

26. Fusion Into Heavier Elements Fusion into heavier elements than C, O: requires very high temperatures; occurs only in very massive stars (more than 8 solar masses).

27. Summary of Post Main-Sequence Evolution of Stars Supernova Fusion proceeds; formation of Fe core. Evolution of 4 - 8 Msun stars is still uncertain. Mass loss in stellar winds may reduce them all to < 4 Msun stars. M > 8 Msun Fusion stops at formation of C,O core. M < 4 Msun Red dwarfs: He burning never ignites M < 0.4 Msun

28. Evidence for Stellar Evolution: Star Clusters Stars in a star cluster all have approximately the same age! More massive stars evolve more quickly than less massive ones. If you put all the stars of a star cluster on a HR diagram, the most massive stars (upper left) will be missing!

29. HR Diagram of a Star Cluster

30. Example: HR diagram of the star cluster M 55 High-mass stars evolved onto the giant branch Turn-off point Low-mass stars still on the main sequence

31. Estimating the Age of a Cluster The lower on the MS the turn-off point, the older the cluster.

32. HW #13read 9.4-endQuestions 9.9, 9.13,9.14Problems 9.7,9.8,9.9,9.11extra time due next Thursday!We are proceding to CHap 10 stellar old agechap 11 The death of high mass stars

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