1. POST-MAIN SEQUENCE EVOLUTION
THE END OF THE MAIN SEQUENCE
A star leaves the MS when it exhausts H at the core. During the MS, there is an excellent balance between P and gravity: HYDROSTATIC EQUILIBRIUM
When H is gone, the core is essentially all He and (at between 6 and 40 million K), far too cool to start nuclear fusion of He.
The structure must readjust since the H fusion, which had provided the energy and pressure, at the center.
Starter here next time: 10/15

2. SUBGIANT PHASE All H gone in core: He "ash" is too cold to "burn"
Pressure provided by energy from fusion in the core disappears.
The He core contracts -- gravity wins over pressure again.
Contraction heats the core.
Most of this heat is trapped, so core T rises.
Rising density and T imply core P rises pretty fast, so there is a contraction, NOT a collapse.
Starte here on 3/10

3. Hydrogen Burning Shell (Subgiant)

4. Thought Question
What happens when a star can no longer fuse hydrogen to helium in its core?
A. Core cools off
B. Core shrinks and heats up
C. Core expands and heats up
D. Helium fusion immediately begins

5. Thought Question
What happens when a star can no longer fuse hydrogen to helium in its core?
A. Core cools off
B. Core shrinks and heats up
C. Core expands and heats up
D. Helium fusion immediately begins

6. Subgiant, 2
Increased core T diffuses into the H BURNING SHELL -- the layer of H hot enough to fuse outside the inert He core.
This higher T causes a dramatic increase in L from that shell (both pp chains and CNO cycle fusion rates are VERY SENSITIVE to T)
Higher L in shell causes the inert H envelope to expand.
Work is done in producing this expansion, so the star's surface T declines (an expanding cloud of gas cools just as an opaque contracting one heats).
This corresponds to the star moving to the right and up on the H-R diagram and it enters the SUBGIANT phase.
Start here on 10/25

7. Life Track after Main Sequence
Observations of star clusters show that a star becomes larger, redder, and more luminous after its time on the main sequence is over

8. RED-GIANT PHASE
As the core continues to contract and heat up, T = 108 K is finally reached;
Then higher electric repulsion of Helium nuclei can be overcome
AND He CAN FUSE INTO CARBON: He  12C +  (the TRIPLE-ALPHA REACTION).
Really, 4He + 4He  8Be but Be-8 is unstable, so 3 He-4's are needed to come together nearly simultaneously.
This generates more energy, and both L and T in core increases.
Start here on 10/24

9. Helium Flash
For M < 2 M this occurs while the He core is degenerate; (yet more about this later when we discuss White Dwarfs)
As P doesn't rise with T for degenerate matter, the “thermostat” is broken
So the core temperature rises fast when He fusion begins: and the Luminosity from He goes up even faster: HELIUM FLASH
until thermal pressure is large again and expands core again, again dropping the core temperature
This causes a very fast expansion of the star's envelope, and a further cooling of its surface, yielding a RED GIANT (with size 100's of that of Sun on MS but lower Ts ).

10. Life Track after Helium Flash
Models show that a red giant should shrink and become less luminous after helium fusion begins in the core

11. THE HORIZONTAL BRANCH
He Flash ends quickly, once core pressure has grown, causing the core radius to rise, thus, yielding a decline in Tc to just about 108 K.
Now He burns smoothly in the core -- producing the He BURNING MAIN SEQUENCE -- which is visible on an H-R diagram as the HORIZONTAL BRANCH (lower L but higher Ts than during the He flash).
Stars are again in HYDROSTATIC EQUILIBRIUM throughout: the thermostat works again
These are still RGs, and on HB the higher masses are to the left part of the HB.
Most stars spend most of their POST-MS life on the HB, but this is typically < 10 % of their MS life.

12. Back up to the Red-Giant Branch on the H-R Diagram (Asymptotic Giant Branch)

13. Thought Question What happens when the star’s core runs out of helium?
A. The star explodes
B. Carbon fusion begins
C. The core cools off
D. Helium fuses in a shell around the core

14. Thought Question What happens when the star’s core runs out of helium?
A. The star explodes
B. Carbon fusion begins
C. The core cools off
D. Helium fuses in a shell around the core

15. AGB for Lower Mass Stars
Increased core T diffuses into the He BURNING SHELL -- the layer of He hot enough to fuse outside the inert C core.
This higher T causes a dramatic increase in L from that shell.
Higher L in shell causes the inert He envelope, as well as the H burning shell and inert H envelope to expand.
Work is done by the gas in producing this expansion, so the star's surface T declines by a bit.
Star is hotter inside and more luminous than before

16. Helium Burning Shell

17. Double Shell Burning
After core helium fusion stops, He fuses into carbon in a shell around the carbon core, and H fuses to He in a shell around the helium layer
This double-shell burning stage never reaches equilibrium—fusion rate periodically spikes upward in a series of thermal pulses
With each spike, convection dredges carbon up from core and transports it to surface

18. ON TO WHITE DWARFS
For stars with MS masses less than about 7 to 8 M : AGBs or Supergiants lose a good bit of mass, and some of these pulsations become so powerful that massive shells (of 0.1 to 0.2 M) are ejected.

19. End of Fusion
Fusion progresses no further in a low-mass star because the core temperature never grows hot enough for fusion of heavier elements (some He fuses to C to make oxygen)
Degeneracy pressure -- electrons fill up all quantum mechanically allowed energy levels --supports the white dwarf against gravity

20. Planetary Nebulae
Double-shell burning ends with a pulse (or pulses) that eject most of the H and He into space as a planetary nebula
The core left behind becomes a white dwarf

21. Ejected Shells = Planetary Nebulae

22. CENTRAL STARS OF PN
The cores of the RGs/SGs are very hot and excite the PN gas.
These Central Stars of PN have C or C+O cores, and He envelopes (All the H was expelled as winds or PN).

23. Dead Core Evolution
They are not massive enough to compress the C core to T > 7 x 108 K at which it could fuse, so these CSPN's just cool off and fade in power, slowly shrinking in size
BUT, when density of the core reaches 106 g/cm3 (or one ton / teaspoon!) the PAULI EXCLUSION PRINCIPLE takes over:
no 2 electrons can be in the same energy state;
this Quantum Mechanical effect provides a HUGE DEGENERACY PRESSURE that stops the continued contraction at a radius of about 1/100th of R (nearly the same as R ).

24. White Dwarfs Once it is held up by degeneracy pressure:
we call it a WHITE DWARF.
The MAXIMUM MASS electron degeneracy pressure can support is about 1.4 M-- the CHANDRASEKHAR LIMIT.
So 7-8 M stars on the MS leave WDs close to the Chandrasekhar limit
But the more common M stars leave WDs around M (the typical mass of a WD).

25. Observed White Dwarfs
Sirius B is a bound companion to the nearby very bright star Sirius (A): M=1.1 M R=5100 km
M4 the nearest globular cluster, about 16 pc across at 2100 pc distance
Nearly 100 WDs are seen in a small region

26. Size of a White Dwarf
White dwarfs with same mass as Sun are about same size as Earth
Higher mass white dwarfs are smaller!
(Higher density needed to support more mass)

27. Earth’s Fate
Errors on
Scale: 
10 1
Sun’s radius will grow to near current radius of Earth’s orbit

28. Earth’s Fate
Sun’s luminosity will rise to 1,000 times its current level—too hot for life on Earth
Life and Death of the Sun Applet

29. Summary for Low Mass Stars
What are the life stages of a low-mass star?
H fusion in core (main sequence)
H fusion in shell around contracting core (red giant)
He fusion in core (horizontal branch)
Double-shell burning (red giant)
How does a low-mass star die?
Ejection of H and He in a planetary nebula leaves behind an inert white dwarf

30. Asymptotic Giant Branch (for Massive Stars) Supergiants
Once the He in the core is all burned up, we reach the end of the He BURNING MAIN SEQUENCE.
As at the end of the He MS: Pressure provided by energy from fusion in the core disappears.
The Carbon core contracts -- gravity wins over pressure again.
Contraction heats the core; Most of this heat is trapped, so core T rises.
Rising density and T imply core P rises, so again there is a contraction, not a collapse.

31. Supergiants for Higher Mass Stars
For more massive stars the same thing happens, but the star starts way up on the H-R diagram, and it enters the SUPERGIANT phase.
The ESCAPE VELOCITY from such big stars gets low: Vesc = (2 G M / R)1/ as R increases while M stays the same.
They lose a lot of mass via winds.
Also, RGs and SGs are subject to opacity driven instabilities which cause the outer layers to expand and cool and contract and heat up.
This produces VARIABLE STARS if the atmosphere lies in the INSTABILITY STRIP.
Important classes of variable stars are the RR LYRAE (horizontal branch) and two types of CEPHEID VARIABLES (supergiants), since they are wonderful DISTANCE INDICATORS

32. Massive Star Post-MS Evolution
Stars starting the MS with more than ~8M are unlikely to leave behind WDs
Why? They leave cores w/ M > 1.4M : the Chandrasekhar limit.
Evolutionary History MS
H is exhausted in core
H shell burning starts, with modest increase in L and fast decrease in TS (fast move to right on H-R diagram)
He fusion starts (non-degenerately, so no flash)
Modest increase in L and core He burning -- a SUPERGIANT
He is exhausted in core
Start here on 10/14/09

33. Massive Post-MS Evolution, 2
So far, pretty similar to lower mass stars studied already, but
Now we feel the big difference: higher M means gravity can crush the C core until it reaches T > 7 x 108 K so
Carbon CAN ALSO FUSE
12C + 4He  16O + 
Some: 16O + 4He  20Ne + 
Also some: 12C + 12C  24Mg + 
This fuel produces less energy per mass so C is burnt quickly.
Loops in the H-R diagram.

34. Massive Post MS Evolution on H-R Diagram
Start here on 10/26

35. Massive Post-MS Evolution, 3
The more massive the star the more nuclear reactions will occur
Most such stars will have Oxygen cores that can also fuse, typically needs T > 1 x 109 K!
16O + 4He  20Ne + 
20Ne + 4He  24Mg + 
We’ll come back to this type of onion-layer model star when we talk about supernova explosions and neutron stars.
The elements cooked here are needed for life

36. Massive Stars Have Powerful Winds
HST picture of AG Carinae:
50 solar masses
Light echoes showing shells from
V838 Monocerotis

37. Binary Star Evolution Many stars are in binary or multiple systems
If the binary is close enough, evolution is affected
More massive stars still can be on MS while less massive has evolved off (like Algol)
Only possible if there is mass transfer through Lagrangian point (L1) between Roche lobes

38. Binary Evolution Depends on Separation
Detached, evolve separately
Semi-detached, one fills Roche lobe, dumping on other
Contact or common-envelope, both overflow: single star w/ two fusion cores

39. Binary Evolution: Algol Type
Start detached
More massive leaves MS, overflows Roche lobe
Now 2nd star is more massive but still on MS, so smaller!