1. Stellar Structure Section 6: Introduction to Stellar Evolution Lecture 16 – Evolution of core after S-C instability Formation of red giant Evolution up giant branch He ignition (low-mass stars: He flash) Asymptotic giant branch Double-shell source stars Thermal pulsing and mixing Evolution beyond He-burning

2. Evolution after S-C instability Initial core collapse catastrophic – but heating destroys isothermality, internal pressure gradients build up and core contraction slows to thermal timescale, with slow release of gravitational energy H-shell very T-sensitive – acts as thermostat:  if shell contracts, T rises,  grows, causing further T rise and raising thermal pressure – shell expands again  if shell expands, T drops → P thermal drop and contraction Hence T shell ~ constant => r shell ~ constant Effect driven by need for L shell to balance L surface

3. Consequence of constant shell radius Shell radius ‘wants’ to be constant But core inside it is contracting This requires the envelope to expand, to compensate – star becomes a giant L ~ constant (at L shell ), and L  R 2 T eff 4, so T eff drops as star expands – becomes red giant Expansion on thermal timescale, implies evolution across HR diagram very fast: accounts for Hertzsprung gap

4. Stars of lower mass S-C instability operates in stars with ~2 < M/M  < ~6 Lower-mass stars: isothermal core becomes degenerate before S-C limit reached, giving extra pressure support and preventing collapse – can be understood qualitatively using scaling arguments (see blackboard sketch):  Boyle’s law: P  +1/R 3  Self-gravity: P  Ω  -M 2 /R 4  Degeneracy: P   5/3  +M 5/3 /R 5 Core still contracts on thermal timescale, so thermostatic effect of shell still causes (slower) envelope expansion

5. Evolution to the giant branch Star evolves on thermal timescale of core Higher-mass stars: L roughly constant (Hertzsprung gap) Lower-mass stars: L increases, T eff still decreases When star reaches Hayashi line, it can’t cross it into ‘forbidden region’ Again need improved surface boundary conditions Star develops deep convective envelope (as in pre-MS) Unlike pre-MS star, has a nuclear source, so now moves up the Hayashi line: the red giant branch (RGB) (Handout 13)

6. Evolution up the giant branch Core shrinks, T rises until He can burn He ignition depends strongly on mass:  M > 2.3 M  : core still ideal gas, ignition occurs quietly, at centre; H-burning continues in shell; star stops climbing RGB  M < 2.3 M  : core has become degenerate, and ignition is explosive (see blackboard) – helium flash Post He-flash: T rises fast until P ion ~ P el, then P tot rises, core expands and cools, settles to steady burning Star survives explosion, but moves rapidly in HR diagram from top of RGB to horizontal branch – see blackboard sketch

7. He burning and after Steady core He burning, star in equilibrium, as on MS Timescale for He-burning much shorter than for H-burning, because burning rate much faster After He exhausted at centre (Y c = 0), all stars climb giant branch again, approaching it asymptotically from somewhat higher temperatures: Asymptotic Giant Branch (AGB) Detailed behaviour depends on mass (Handout 14) Shell burning continues on AGB, both He and H: double- shell source stars

8. Thermal pulses and mixing Shell burning thermally unstable → burning alternating between H and He shells (discovered numerically ~1965) Instability causes  thermal pulses of luminosity  mixing of processed material to surface (convective envelope outside H shell, plus convection between shells) Processed material seen in observations  Excess of C: ‘carbon stars’, with C/O ~ 2-5 (MS: ~0.5)  Isotope anomalies: 12 C/ 13 C ~ 10-20 (solar system ~90; CNO cycle in equilibrium ~4) Later evolution depends crucially on core mass

9. Post-He-burning – 1 (no WD remnant) Main Sequence mass > 8 M  Nuclear burning continues beyond C, mainly by addition of He nuclei to form O, Ne, Mg, Si etc, as far as Fe: limit of ‘free’ energy Core partially supported by degenerate electrons – some electrons in high-energy states may be captured by Ne or Mg nuclei Pressure drops, core cannot support itself, collapses catastrophically (timescale: 10s of milliseconds!) to nuclear densities, and bounces, leading to outward-travelling shock wave Shock also accelerated by pressure of neutrinos, produced in explosive nucleosynthesis generated by energy of collapse Leads to ejection of outer layers (~90% of mass of star) – Type II supernova (may leave compact core → NS or BH – see later)

10. Explosive nucleosynthesis (formation of elements heavier than iron) Very high densities favour neutronisation: e - + p + → n + (Normally, neutron is unstable, timescale ~900 s) Neutrino flux helps to accelerate shock Neutron flux allows rapid neutron addition to Fe and heavier elements, forming n-rich nuclei Addition very fast compared to  -decay timescale – elements produced called r-process elements (r for rapid) – seen in supernova remnants (AGB evolution: much smaller neutron flux available, n-addition occurs on timescale long compared to  -decay timescale – forms n-poor nuclei by s-process (s for slow) – s-process elements seen in atmospheres of red giants and supergiants)

11. Post-He-burning – 2 (produces WD) Main Sequence mass < 8 M  Neutrino processes cool centre, inhibiting C ignition (needs T ~ 5  10 8 K) Degenerate core:  pure helium (low initial mass)  He, C, O mixture (higher initial mass) On AGB, substantial mass loss by stellar winds (and possibly thermal pulses) – helps to prevent core heating to C ignition Finally, a “superwind” (observed, not understood) ejects entire outer envelope as coherent shell, revealing hot interior Hot remnant ionizes shell → planetary nebula Star then cools and fades → white dwarf star (Handout 15)