1. Death of a low mass star

Mass < 1-3 M

After Helium core burning on Horizontal Branch . . .

• inert carbon core

• volume of grape = 1 ton, i.e. dense

• intense shell burning:

  HeC

  HHe

• blows of outer layers

• formation of nebula

planetary nebula

+ ``naked'' hot core

white dwarf

Why white? ------ hot

Why dwarf? ------ small

recall:   L R² T⁴

2. Planetary nebula

- rich in carbon

enrich the ISM^* with dust

Why do they look like rings?

- actually shells

- projection effect

- longest path-length at edge

Fate:

nebula slowly disperses and mixes with ISM

^*ISM = interstellar medium

3. Fate of White Dwarf

Inert carbon core supported by electron degeneracy pressure

.............. forever!

cools and fades ................

``down and out on the HR diagram''

- predict many in solar neighborhood (<10pc)

- can't see 'em!

- recall: distance-limited vs. brightness-limited samples!

What's a 'clinker' ?

4. Degeneracy Pressure - revisited

Why important:

• Helium flash       (electron degeneracy   -   lecture 11)

• White Dwarfs     (electron degeneracy   -   this lecture)

• Neutron stars     (neutron degeneracy   -   lecture 13)

Why: exclusion principle

no two of the same particles can be in the same state and same place at the same time

Why insensitive to temperature:

- Number of states increases with energy of particle

- Temperature (T): measure of average particle speed

(see pp.73, 100-102, 502-504)

- Kinetic energy speed²

T is related to energy

E_thermal = kT

(k is another "magic" constant)

Definition:

Fermi Energy = top energy state of degenerate electrons

Degeneracy is lifted when E_thermal = kT is roughly equal to the Fermi Energy

When is this important?

5. The importance of star clusters - revisited

Times scales for different stages of stellar evolution ...

How can we check?

(i) Observe HR diagrams for clusters

(ii) Measure relative density of stars at different stages

(iii) Combine information for many clusters of different ages

assumption:

The number of stars as a function of mass is constant over a small range of mass

So what are those ``blue stragglers?''

(a) both radiate emission lines

(b) both are made of hot gas

(c) both have carbon

(d) both have at least one star inside them

(e) both are usually shaped like symmetric, evacuated shells

(a) it would never reach the Horizontal Branch

(b) core-bounce wouldn't occur

(c) there would be no Helium Flash

(d) shell-burning wouldn't occur

(e) in fact, it would never become a giant