Lecture 17PHYS1005 – 2003/4 Detailed look at late stages of the Sun’s life: from Schröder et al 2001 (Astronomy & Geophysics Vol 42): –radius of Sun as it ascends RGB, then AGB (with inner planet orbits marked!)

Lecture 17PHYS1005 – 2003/4 but mass-loss in red-giant wind could be important: as is the likely temperature on Earth!

Lecture 17PHYS1005 – 2003/4 Lecture 17: Stellar Structure and Evolution – II Objectives: Understand differences in evolution of low and high M stars Importance of degeneracy pressure Understand the Helium Flash H-R diagram showing evolutionary tracks followed by both young and old clusters: Note the gap between the Main Sequence and RGB in young clusters Additional reading: Kaufmann (chap ), Zeilik (chap. 16)

Lecture 17PHYS1005 – 2003/4 Evolution of 5M O Star: on exhaustion of H in core (at 2) –  crisis point for high M stars –cores convective  well-mixed –  H runs out over large central volume at same time! –  must contract radically to ignite H shell –i.e. large change on thermal (short) timescale –  moves rapidly (2  3) to RGB explains Hertzsprung Gap in young clusters cf Low Mass stars: –cores are radiative  more stable  change much more gradual –  continuous and extended RGB in old clusters

Lecture 17PHYS1005 – 2003/4 Helium Flash and Degeneracy Pressure in low M stars ignition of He at tip of RGB is crisis point for low M stars due to new form of P which has been supporting the He core comes from Pauli Exclusion Principle: can estimate it as follows: –electron density of n per unit volume –  each electron occupies box of side –to avoid “overlap”, need de Broglie λ ~ size of box i.e. –therefore “degeneracy” energy –which is significant when E d ~ kT i.e. –N.B. low m  low n  electrons degenerate first! No two electrons within certain volume can occupy same quantum state which links v and n (m = electron mass)

Lecture 17PHYS1005 – 2003/4 Electron degeneracy pressure For case of ideal gas, where P = nkT and since n α ρ, then which is independent of T ! What happens when fusion begins in degenerate gas? –energy generated by fusion –  T rises –  fusion rate rises –but P stays the same  no expansion, no cooling ! –i.e. normal “safety valve” doesn’t work! –  disastrous runaway process until T very high Helium Flash ! L can rise to L O within ~ minutes

Lecture 17PHYS1005 – 2003/4 Speed of evolution: evolution speeds up with age, because –L is higher (and timescale α M / L) –higher neutrino losses –less fusion energy from heavier elements most stable nucleus is iron ( 56 Fe) H  Fe fusion converts 0.89% mass  energy, but H  He fusion converts 0.71% ! –so later phases give little in total Binding Energy (first 31 elements) Evolutionary model for Sun: