1. On the Main Sequence Behaviour of a main sequence star
Stable hydrogen burning
Characterised by slow evolution
As the He concentration rises, the core slowly contracts and heats up
Power output slowly rises
eg, the sun is now somewhat hotter (5800 K rather than 5500 K) and 6% greater in radius than when it first formed (~5x109 years ago)
and therefore some 40% more luminous

2. Main Sequence Lifetime
The time a star spends on the main sequence can be estimated given:
mass-luminosity relationship for main sequence stars; L = M 7/2
Amount of hydrogen available µ M
in fact, a star will burn ~ 10% of the available hydrogen
Lifetime, t µ M/L
Hence t µ 1/M 5/2

3. Main Sequence Lifetime
Main Sequence lifetime of the sun estimated to be 1010 years
Hence t µ 1010/M 5/2 years

4. Beyond the Main Sequence
Events on exhaustion of core hydrogen
core contracts under gravity
no fusion power to support it
temperature and density rises
temperature and density also rise in a still hydrogen rich shell outside the core
Shell hydrogen fusion begins
Dormant core
Hydrogen burning shell

5. Beyond the Main Sequence
Helium “ash” from the shell falls into the core
Core mass increases, contraction continues
Temperatures and densities rise further
For a 1 solar mass star, this phase lasts ~ 1x108 years
Core radius shrinks to ~ 1/3 of original size
from ~ 25% to ~ 10% of the total radius for a sun-like star
Temperature rises to ~ 108 K

6. Beyond the Main Sequence
External appearance
Dramatic changes
Increased energy output from the core leads to expansion and cooling of outer layers
Luminosity increases markedly
The star has become a Red Giant

7. Beyond the Main Sequence
A 1 solar mass Red Giant
Not to scale!
Red Giant sun
dia. ~ 1AU
L ~ 2000
Dormant core + hydrogen burning shell
dia. ~ 2x Earth
MS sun
dia. ~ 0.01 AU

8. Beyond the Main Sequence
2,500
10-2 1
102
104
106
Luminosity (L¤)
40,000
20,000
10,000
5,000
Temperature (K)
Zero age
main sequence
Termination of core
hydrogen burning
1 M¤
2 M¤
3 M¤
5 M¤
9 M¤
15 M¤
Tracks on a Hertzprung Russel diagram for shell burning red giants

9. Helium Burning
Core temperatures and densities are now high enough for helium burning to commence via the triple alpha process
Start of helium burning depends on the mass of a star
High mass stars (>2 solar masses)
Helium burning begins gradually
Low mass stars
Helium ignites explosively in a “Helium Flash”

10. The Helium Flash
The Helium Flash occurs in low mass stars because of the properties of the core
To achieve helium ignition, the core density reaches levels where quantum effects become important
A degenerate electron gas forms
Degenerate gas pressure independent of temperature

11. The Helium Flash
On helium ignition, energy production restarts in the core
Core temperature rises
Pressure (and hence density) does not drop
in a normal gas this would slow down the reaction rate, preventing a runaway reaction
Helium burning rate continues to increase
recall large temperature dependence!

12. The Helium Flash
Eventually temperatures rise sufficiently to lift the electron degeneracy
The pressure can now drop, slowing the reaction
These events take place in a few seconds!
Stable helium burning now commences

13. The Helium Flash Consequences:
No leap in luminosity - energy absorbed internally
Lifting degeneracy and expanding the core
Hydrogen shell burning reduces
Temperature in this region drops
Total power output drops
Outer layers contract and heat up
Luminosity decreases

14. Helium Burning Stars
2,500
10-2 1
102
104
106
Luminosity (L¤)
40,000
20,000
10,000
5,000
Temperature (K)
Zero age
main sequence
Termination of core
hydrogen burning
1 M¤
2 M¤
Stars stably burn helium for ~ 20% of the original star’s main sequence lifetime
Low mass stars fall in a region roughly in the centre of the HR diagram - the Horizontal Branch
Horizontal Branch

15. Variable Stars Many helium burning stars are variable
Cepheid Variables
2,500
10-2 1
102
104
106
Luminosity (L¤)
40,000
20,000
10,000
5,000
Temperature (K)
Zero age
main sequence
Termination of core
hydrogen burning
1 M¤
2 M¤
9 M¤
Many helium burning stars are variable
A particular region on the HR disgram gives rise to periodic variable stars, Cepheids and RR Lyrae stars
Instability Strip
RR Lyrae Variables

16. Cepheid Variables Prototype, d Cephei
Luminosity varies by a factor of 2.3 over a 5.4 day period
Studies of the spectrum shows this is due to expansion and contraction of the star
The star’s temperature also changes
cooling on expansion, heating on contraction

17. Cepheid Variables

18. Cepheid Variables Direct relationship between period and luminosity:
Notice this gives us a standard candle for measuring stellar distances
(metal rich stars)
(metal poor stars)

19. Cepheid Variables Mechanism
Normally, oscillations of this type would be damped out.
A feasible mechanism would require:
the star to trap heat when compressed (increasing pressure and driving expansion)
the star to release heat when expanded (allowing contraction)

20. Cepheid Variables
Such a mechanism relies on ionisation of helium in a layer within the star:
Compressed helium: ionises and become opaque
Helium expands, cools and recombines: becomes transparent
Trapped radiation drives expansion
Radiation can escape - contraction occurs

21. Cepheid Variables Not all stars pulsate because either:
the star is too cool for an ionised helium layer to exist near the surface
occurs deeper, but convection disrupts it
in hot stars, the ionised helium layer is too close to the surface
insufficient density to trap radiation

22. RR Lyrae Variables Low mass stars on the horizontal branch
Periods typically shorter than one day
All roughly the same luminosity
Another standard candle

23. Post-Helium Burning
Core helium burning lasts for ~20% of the main sequence lifetime
What happens next?
Depends on the mass of the star
Next Lecture - The Deaths of Stars

24. The Death of a Low Mass Star
Evolution of a sun-like star post helium-flash
The star moves onto the horizontal branch of the Hertzprung-Russell diagram
Helium burning produces carbon and oxygen “ash”
Eventually, the helium concentration falls too low to sustain burning in the core

25. Post Core Helium Burning
Similar sequence of events to the end of hydrogen burning
Core contraction and heating
Degenerate carbon/oxygen core forms
Helium shell burning commences

26. Post Core Helium Burning
External Appearance
The star moves off the horizontal branch and ascends the red giant region again, becoming even larger and more luminous
The star is now an Asymptotic Giant and is on the Asymptotic Giant Branch

27. Asyomptotic Giants Location on the Hertzprung-Russell Diagram
Asymptotic Giant Branch
2,500
10-2 1
102
104
106
Luminosity (L¤)
40,000
20,000
10,000
5,000
Temperature (K)
Zero age
main sequence
Termination of core
hydrogen burning
1 M¤
2 M¤
Core helium burning ceases
Location on the Hertzprung-Russell Diagram

28. Asymptotic Giants Appearance and Structure Orbit of Mars
dia. ~ 1x Earth
AGB sun
dia. ~ 1.5AU
L ~ 10000
Helium burning shell
Degenerate C/O core
Dormant hydrogen shell

29. Asymptotic Giants Material Redistribution
Convection layers may reach to the core
Carbon and oxygen brought to the surface
In consequence, molecular absorption bands often seen in the spectra of AGB stars
Soot coccoons may also form around such carbon stars

30. Late Evolution As helium is consumed, the core contracts and heats up.
The hydrogen shell may re-ignite, producing more helium which re-fuels the temporarily depleted shell
Helium shell burning re-ignites in a helium shell flash, leading to a short-lived spike of luminosity - a Thermal Pulse
Luminosity rises by ~ 2

31. Late Evolution Such thermal pulses may occur a number of times:
3x105 years

32. Late Evolution AGB stars produce strong stellar winds
Typical mass loss ~ 10-4 solar masses per year
103 x a “normal” red giant
1010 x the sun
Combined with the thermal pulses, such winds drive off the outer layers of the star
As much as 40% of a star’s mass may be lost in this way

33. Late Evolution
A number of shells of material now surround the dying star
Central star in opaque cocoon
Concentric shells
Note: the phase shown here is very brief - ~ 1000 years
See for details

34. The Final Stages Ultimately, the hot carbon/oxygen core is exposed
Core surface temperature ~ 100,000K
Sufficient UV produced to ionise and excite the outer layers
The spectrum is now characterised by emission lines

35. Planetary Nebulae
The emitted gases now glow in the radiation of the exposed core, forming a Planetary Nebula
Exposed core
Fluorescing gas
Speed of gas ~ 10 kms-1
Diameter ~1 ly

36. Planetary Nebulae Planetary nebulae often appear as rings
actually spherical
looking through a greater depth of material at the edges
Core of “dead” star
Partner star

37. Planetary Nebulae
A disc of material around a star may allow a bipolar nebula to form

38. Planetary Nebulae The planetary nebula phase is relatively short lived
The nebulae in the previous slides are estimated to be only a few thousand years old
The material rapidly disperses, leaving the central core

39. White Dwarfs
Sun-like stars never achieve the core temperatures and densities to ignite carbon and oxygen
After the planetary nebula has dissipated, the hot core is left
Degenerate matter
Mass ~ 1 solar mass
about the size of the Earth
about 100,000 K surface temperature
<10-2 solar luminosities

40. White Dwarfs No further nuclear reactions take place
2,500
10-2 1
102
104
106
Luminosity (L¤)
40,000
20,000
10,000
5,000
Temperature (K)
No further nuclear reactions take place
Luminosity due to contained heat only
No further contraction takes place
Electron degeneracy pressure supports the star
Cooling occurs over many billions of years
Cooling curve of a 1/4 solar mass white dwarf

41. White Dwarfs Bizarre properties:
All as a consequence of the properties of degenerate matter
Higher mass white dwarfs are smaller
hence dimmer
Maximum mass ~1.4 solar masses
the Chandrasekhar Limit
These properties will be explored in a future lecture

42. The Death of a High Mass Star
High mass stars behave very differently
Higher core temperatures and densities imply burning beyond oxygen
Final stages often violent, leaving remnants even more bizarre than white dwarfs
To be discussed in the next lecture