1. The Red Giant Branch

2. L shell drives expansion L shell driven by M core - as |  |, |  T| increase outside contracting core shell narrows, also L core from contraction increases T shell L shell large,  r shell small so convection necessary 1 st dredge-up - envelope convection zone reaches material processed by H burning

3. The Red Giant Branch L shell drives expansion L shell driven by M core - as |  |, |  T| increase outside contracting core shell narrows, also L core from contraction increases T shell L shell large,  r shell small so convection necessary 1 st dredge-up - envelope convection zone reaches material processed by H burning

4. The Red Giant Branch L shell drives expansion L shell driven by M core - as |  |, |  T| increase outside contracting core shell narrows, also L core from contraction increases T shell L shell large,  r shell small so convection necessary 1 st dredge-up - envelope convection zone reaches material processed by H burning

5. The Red Giant Branch-Low Mass Stars e - degeneracy consider e - in a boltzmann distribution in phase space

6. The Red Giant Branch-Low Mass Stars max occupancy of phase space from Pauli exclusion volume of phase space cell dxdydzdp x dp y dp z =h 3 so in [p,p+dp] 4  dpdV/h 3 cells each with max occupancy of 2e - (spin ,  ) at low T or high n e distributions diverge from boltzmann due to occupancy of available states if all e - have lowest possible energy

7. The Red Giant Branch-Low Mass Stars all available states populated up to p f so for high n e v f  c Pressure = p flux through unit surface s flux through d  w/ [p,p+dp] dd  dd

8. The Red Giant Branch-Low Mass Stars

9. Relativistic vs. non-relativistic for x<<1 - non-relativistic for x>>1 - relativistic

10. The Red Giant Branch-Low Mass Stars Meanwhile, back in the star… Stars < ~2.25 M  have lower T core and lower entropy (higher  for a given T) Low T combined with high n e mean core becomes degenerate before reaching He burning T degenerate cores reach T ignition (~2e8 K) at 0.46 M  L  M core so L is ~ the same for all stars which undergo degenerate He ignition - max L of RGB for old clusters Tip of the RGB method for getting distance

11. The Red Giant Branch-Low Mass Stars When degenerate stars reach T~2x10 8 K Core is roughly isothermal, so a large volume is close to ignition P is not proportional to T since pressure is from degeneracy   T from burning does not result in   explosive burning

12. The Red Giant Branch-Low Mass Stars He flash Explosive burning of He to 12 C - not energetic enough to disrupt star, but may result in a puff of mass loss Energy release heats core until degeneracy is lifted - normal HSE resumes Hydrostatic He burning: triple  process –  (2 ,  ) 12 C –  ( ,  ) 8 Be stable by only 92keV lifetime of excited state  <<mean collision time unless there is a resonance Hoyle predicts resonant energy level in 8 Be( ,  ) 12 C, confirmed by nuclear physics experiments note  2 - 3 body reaction so very density sensitive -reason #1 for big bang nucleosynthesis cutoff

13. The Red Giant Branch-Low Mass Stars Hydrostatic He burning part II 12 C( ,  ) 16 O rate uncertain - too high and all He  O; too low and C/O too high at low Y 12C mostly  (2 ,  ) 12 C as Y he drops 12 C( ,  ) 16 O dominates due to Y 3 He dependence So Y 12C sensitive to ingestion of He at late times also sensitive to entropy - 3  rate   2 so lower at high S  more massive stars have higher 16 O/ 12 C 16 O( ,  ) 20 Ne slow at these temperatures 14 N( ,  ) 18 O depletes N very rapidly – 18 O( ,  ) 22 Ne 22 Ne( ,  ) 26 Mg 22 Ne( ,n) 25 Mg - neutron source

14. Post-RGB Evolution - Low Mass Once hydrostatic He burning has begun in the core Core expands, envelope contracts -  L surf  R Blue loops 1. RGB 2. He flash 3. Max extent of blue loop - X he ~ 0.1

15. Post-RGB Evolution - Low Mass Extent of blue loop depends on 1.metallicity - low z 

16. Post-RGB Evolution - Low Mass Extent of blue loop depends on 1.metallicity - low z  large blueward excursion 2.core size (  initial M) - higher mass  large blueward excursion 3.mixing and EOS influence max T eff Blue horizontal branch

17. Post-RGB Evolution - Low Mass Distance between subgiant branch and horizontal branch used as proxy for cluster age - depends only on composition & age - insensitive to reddening Width of subgiant branch also used - for clusters w/ poorly populated HB

18. Cepheids Stars of ~4 M  move far enough to the blue on the horizontal branch to enter a region of instability This strip extends to much lower luminosities and crosses the main sequence producing  Scuti stars

19. Cepheids The  mechanism Opacity will be large at temperatures close to the ionization temperature of H and He. Ionized material has high opacity, opacity drops precipitously upon recombination

20. Cepheids The  mechanism Opacity will be large at temperatures close to the ionization temperature of H and He. Ionized material has high opacity, opacity drops precipitously upon recombination Radiation pressure on a high  region causes it to expand and cool Sufficient expansion cools material enough for recombination  sharp  Pressure supports goes away and region contracts and heats, reionizing material - Carnot engine Pulsations occur only if not damped by too much mass above proper T, also must have enough mass to provide restoring force - hence instability strip