The Red Giant Branch

1. The Red Giant Branch

2. The Red Giant Branch • Lshell drives expansion • Lshell driven by Mcore - as ||, |T| increase outside contracting core shell narrows, also Lcore from contraction increases Tshell • Lshell large, rshell small so convection necessary • 1st dredge-up - envelope convection zone reaches material processed by H burning

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

4. The Red Giant Branch • Lshell drives expansion • Lshell driven by Mcore - as ||, |T| increase outside contracting core shell narrows, also Lcore from contraction increases Tshell • Lshell large, rshell small so convection necessary • 1st 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 dxdydzdpxdpydpz=h3 so in [p,p+dp] 4dpdV/h3 cells each with max occupancy of 2e- (spin ,) at low T or high ne 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 pf so for high nevfc d  Pressure = p flux through unit surface s flux through d w/ [p,p+dp] d

8. The Red Giant Branch-Low Mass Stars

9. The Red Giant Branch-Low Mass Stars 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 Tcore and lower entropy (higher  for a given T) • Low T combined with high nemean core becomes degenerate before reaching He burning T • degenerate cores reach Tignition (~2e8 K) at 0.46 M • L Mcore 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~2x108K • 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 12C - 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,)12C • (,)8Be stable by only 92keV lifetime of excited state <<mean collision time unless there is a resonance Hoyle predicts resonant energy level in 8Be(,)12C, 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 • 12C(,)16O • rate uncertain - too high and all He  O; too low and C/O too high • at low Y12Cmostly (2,)12C • as Yhe drops 12C(,)16O dominates due to Y3He dependence • So Y12C 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 16O/12C • 16O(,)20Ne slow at these temperatures • 14N(,)18O depletes N very rapidly • 18O(,)22Ne 22Ne(,)26Mg 22Ne(,n)25Mg - neutron source

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

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

16. Post-RGB Evolution - Low Mass Extent of blue loop depends on • metallicity - low z large blueward excursion • core size (initial M) - higher mass  large blueward excursion • mixing and EOS influence max Teff 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