Post Main-Sequence Evolution: The Red Giant Branch
- Back to Stellar Evolution
When we last saw the Sun it was evolving up the red
giant branch (also known as First Ascent Giant Branch) with
an ever-larger He core that is contracting and heating the
surrounding H-fusion shell.
- So where is this heading?
Eventually the core stops contracting for a Strange Reason .
You might expect the core to heat up to 108 K where He fusion
would start and produce the thermal pressure required to
balance gravity and then work in the thermostat mode. But, this is wrong
- The Red Giant core is supported by Electron Degeneracy.
This comes about because you can only squeeze electrons so close
together and no further because of the Pauli Exclusion
- The Red Giant core is made up of mostly ionized He so
it is a gas of nuclei and e-.
All subatomic particles have various properties characterized
by "quantum numbers". One is "spin". The quantum world gets
split into two flavors of particles according to their spin:
- "spin 1/2" particles are called Fermions (e- are Fermions).
- "spin 1" particles are called Bosons (neutrons and He nuclei are Bosons)
- Fermions all obey a law called the Pauli Exclusion Principle:
You can have at most 2 fermions occupying a volume of phase space density.
ΔxΔyΔzΔpxΔpyΔpz = Quantum Phase Space Volume
Here, the x, y, z refer to position and px etc. refer to momentum.
- At a given temperature (this means give the mean speed of
the e-), as the density goes up (packing those e- closer and
closer together), the e- gas starts to run out phase space
in which to put e-. The inability to increase the density
adds up to a form of supporting pressure called Electron Degeneracy Pressure.
- Electron Degeneracy Pressure is what balances gravity in the
RGB star core and EDP has a strange property in that it
is more-or-less independent of temperature.
- Remember the usual Gas Law:
This provides a saftey value:
- The Usual Gas Law as a Safety Value:
- Suppose the He fusion started in the core. This would release
some heat, the temperature and pressure would go up, the core
expands and cools off and the fusion rate decreases a little bit.
- Alternatively suppose the fusion rates go down. Then gravity
starts to compress the core, the Temperature goes up, fusion
rates go up and the core re-expands.
- But, because EDP is independent of temperature, when
He fusion starts, it is like a bomb going off.
- Core Temperature reaches 108K.
- A special form of He fusion starts where 3He Carbon
and there is an enormous release of energy and increase in the core temperature.
- Because the pressure in the core is due to e- degeneracy and is
T independent, the core does NOT expand and cool, but rather there is
a temperature runaway - this is the Helium Flash.
- Although it sounds exciting, the Helium Flash does not
add up to all that much. It runs for a few hours until the
temperature reaches 109 and at this temperature there is
lots of extra phase space available to the electrons and the
degeneracy is "lifted". The result is a small hiccup and
the internal structure now looks like a version of a main-sequence
star with core helium fusion. The new equilibrium puts
the star in a spot on the H-R Diagram called the "horizontal
Horizontal Branch Stars and Helium Fusion
There is a problem with 4He2 + 4He2
8Be4 because this reaction is endothermic. It does not
release energy, but rather requires energy for it to happen.
So, He and He atoms DO fuse to Be sometimes, but the Be decays
in ~10-12 seconds. So, you need to have the temperature
and density be high enough so that before this decay happens another
He collides with the Be to produce Carbon. This is called
the Triple Alpha reaction and it is the energy source for horizontal
- Horizontal Branch Stars have a structure that is analogous
to main-sequence stars.
- The fusion rates are running fast and the structure of
the HB stars changes relatively quickly. The carbon core starts
to shrink and release energy, the He fusion moves into
a shell (now we have a "double shell" source) and this
starts to look like the situation when a main-sequence star
became a Red Giant.
- This time, the star ascends the Asymptotic Giant
- For a 1 MSun star, it never gets hot enough to
fuse carbon together. Now the star is running out of fuel for good
- The triple-alpha reaction is extremely sensitive
to temperature: Triple-Alpha rate propto Temp30
which leads to instabilities called Helium shell flashes.