Lecture 10: Evolution in the HR Diagram

1. Lecture 10: Evolution in the HR Diagram July 16, 2010 PS119a. Evolution, single stars, 07.16.2010

2. PS119a. Evolution, single stars, 07.16.2010 9/9/09 ISM IGM, cosmo, our Gal. 2

3. PS119a. Evolution, single stars, 07.16.2010

4. Creation of the “rest” of the perodic table Heavier elements are made by reactions that are complex, but the net effect can be thought of as follows. The coulomb forces inhibiting the reactions are larger, so higher temperatures are needed. C+12 + He+4O+16 O+16 + He+4Ne+20 Ne+20 + He+4Mg+24 PS119a. Evolution, single stars, 07.16.2010 4

5. The heaviest elements • Above atomic no. 30, temps. are never high enough. • Fe can be made, but it requires an endothermic process to rearrange the nuclei. • The energy comes from the gas, which effectively cools the gas. • The star collapses, in what amounts to a catastrophe. PS119a. Evolution, single stars, 07.16.2010

6. The heaviest elements Elements can also be made by the production of free neutrons, which, when added to other nuclei, lead to radioactive isotopes, which decay into other, stable elements of a variety of atomic numbers, in particular, the odd atomic numbers (the reactions noted previously produce nuclei with even atomic numbers.) Such neutrons can be produced by reactions such as the following: Ne+20+H+1 Na+21 +  Na+21e +  + Ne+21 Ne+21 +  Mg+24 + n (n means neutron) PS119a. Evolution, single stars, 07.16.2010 6

7. Relative Number of Atoms Hydrogen Helium 5 10 Oxygen Carbon Iron 0 10 Nickel 10 10 0 20 40 60 80 Atomic Number (Average, in Universe) 11.06.09 PS119a. Evolution, single stars, 07.16.2010 PS119a.Lect 15.Star death.11.06.09 7 9/9/09 ISM IGM, cosmo, our Gal. 7

8. Conclusion In this way, all the elements in the periodic table are believed to be produced in stars, save hydrogen, deuterium, much of the helium and a trace of lithium which come from the Big Bang, as will be discussed in Phy Sci 120, in the next quarter. PS119a. Evolution, single stars, 07.16.2010 8

9. Summary of stellar features • Stars need a negative pressure gradient to form stable configurations. • Nuclear energy permits stars to be very old and explain the periodic table • Mean densities of atmospheres are 1 g/cm3. But the mean density [M=(4/3)r3]. Outer parts, 10-12 g/cm3. • Therefore, central densities must be very high, 100 g/cm3. Pc=1015 dyne/cm2 • Mean lifetimes 1010 years for solar type stars. • E=Lt=fMc2, e=0.007, f~0.1 for H, main sequence • (=0.0007 for He burning to C, so much less time is involved). PS119a. Evolution, single stars, 07.16.2010

10. Relation between L, M, t • L/Lo=(M/Mo)3.5 (empirical, from binaries) • Write, for the Sun and another MS star, the relation between • total nuclear energy, L and t on the main sequence: • (L/t)/(Loto)=Mc2ef/Moc2ef • L/Lo=(M/Mo)(to/t) • Or, t/to=(Mo/M)2.5 • In the HR diagram of globular clusters, the top part of the MS is missing. More massive stars evolve faster, so the stars once there evolved and moved to the right. • There are many stars on the MS, so equil. time is very long. PS119a. Evolution, single stars, 07.16.2010

11. Messier 5, Yerkes, 1900, ~5 hours, first plate PS119a. Evolution, single stars, 07.16.2010

12. Messier 15, Yerkes, 200 min, 1900 PS119a. Evolution, single stars, 07.16.2010

13. Messier 15 Hubble Space Telescope 1990s, ~2 hours PS119a. Evolution, single stars, 07.16.2010

14. Open clusters of different ages • Open clusters, turn off points, clusters of differing age • Why do stars move to the giant branch? • Run out of fuel, gravity drives collapse, core heats up. Edge of core gets hotter and burns H not previously hot enough to burn. But, it is closer to the surface, so surface expands. • Expansion means cooling (gets redder) but expansion means more surface area (L=4r2T4), so the star expands. PS119a. Evolution, single stars, 07.16.2010

15. Evolution of a new core • Eventually, the collapsing core gets hot enough to burn He (made on the MS) to carbon. The onset of He burning is called the He flash (108 K). • With an energy source restored, the equation of hydrostatic equilibrium is applicable again, and the star moves to the main sequence (defining the “horizontal branch”) • (The actual source of energy does not matter to the equilibrium structure, but is does affect the time scales.) • He burning stars eventually burn up their fuel, collapse, expand (He burning) and have a new onset of burning (carbon burning, 600 million K), return to the main sequence, etc. • More massive stars can make additional loops at the top of the HR diagram. PS119a. Evolution, single stars, 07.16.2010

16. HR diagram PS119a. Evolution, single stars, 07.16.2010

17. Appearance of Clusters of Stars of Different Ages • Youngest clusters show only the top of the HR diagram on the main sequence. Lower mass stars are still collapsing • (collapse times at low mass comparable to burning times at high mass). • B. Intermediate age clusters show the most massive, brightest stars are disappearing (lowest mass stars still forming) • C. Clusters older than the Sun who no upper main sequence and are forming a giant branch and a few horizontal branch stars. PS119a. Evolution, single stars, 07.16.2010

18. D. Older clusters have lower turnoff points and are starting to form more and more white dwarfs as solar mass stars burn out. E. Eventually, the clusters will contain white dwarfs (evolved) and red dwarfs (still on the main sequence) and will be tidally striped and fill the sky in bands. PS119a. Evolution, single stars, 07.16.2010

19. Extra radius defintions • L/Lo=4R2T4/4Ro2To • R/Ro=(To2/T2)(M/Mo)1.7 • These relations show that the radius changes more slowly than mass. PS119a. Evolution, single stars, 07.16.2010