Lecture 17 PHYS1005 – 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 17 PHYS1005 – 2003/4

• but mass-loss in red-giant wind could be important:

• as is the likely temperature on Earth!

Lecture 17 PHYS1005 – 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. 21-22), Zeilik (chap. 16)

Lecture 17 PHYS1005 – 2003/4

Evolution of 5MO 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 (23) 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 17 PHYS1005 – 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 Ed ~ 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 17 PHYS1005 – 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 1010 LO within ~ minutes

Lecture 17 PHYS1005 – 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 (56Fe)• 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: