- We resume the evolution as the star ascends the giant branch.
The He core is contracting and gradually heating, but it is also getting
denser and more degenerate. A completely degenerate gas has a polytropic
equation of state, which means that the pressure is given by
P = K rho^gamma and has no temperature dependence. A discussion of the physics of degenerate gases is available in the full version of this tutorial.
When the temperature finally reaches enough for the ignition of the
He burning (via triple-alpha reactions; about 100 million degrees) the extra
energy released does not go into expansion, but rather increases the local
temperature. Due to the degeneracy, this simply causes the burning rate to
further increase, and we have a runaway! This is called the core helium
- There is another complication too. The high density of the
core enables various neutrino processes to remove energy from the core.
processes depend mostly on density, they are more efficient in the
very centre. Hence this region cools more than zones just outside the
centre. The result is that the maximum temperature in the star moves away
from the centre, and slightly outward in mass. The helium flash is ignited
at the point of maximum temperature, of course. Hence the flash begins in a
shell (in this spherically symmetric calculation!) somewhat displaced from
Here we show the maximum temperature within the star.
And below we see the mass where this maximum temperature occurs. Note that
it is initially in the centre, but finally moves somewhat away from the
In the full version of the tutorial we
show the central density and the density at the point of maximum
temperature. Note that they start to differ when the point of maximum
temperature moves away from the centre.
- Here we see the temperature
profiles during the ignition of the flash. This shows that the huge
energy deposition drives a convective zone which reaches almost all the
way to the H shell.
Note how the temperature of the whole core region decreases: this is because
the energy released by the flash is mostly used in changing the equation of
state of the core: it "lifts" the degeneracy and restores a more nearly
perfect-gas equation of state.
- A similar story is revealed in the
density profiles: the core expands
dramatically as a result of the energy input from the helium burning.
- The radius profiles also
show the expansion of the core. Note that this is a log plot!
- Of course, the luminosity profile is going to be impressive!
There is a small jump in L at the position of the H shell, but this is soon
dwarfed by the energy produced by the He flash.
Of course, the flash does not last long, as shown in the
- The He burning produces C-12. And the convection mixes the
C-12 throughout the convective region. The
C-12 profiles show this, but we must remember a couple of assumptions
that are unlikely to be true: that we can ignore dynamic terms in the
equation of motion, and that the mixing is instantaneous. Certainly for the
time-steps required during this calculation, these approximations are not
valid! But nevertheless we see stars in the next phase which look very much
like the models. This is encouraging, but we must remind ourselves that
these models must have limitations that we cannot yet determine.
- It takes more than one of these flashes to remove the
degeneracy on the core, and for the model to make its way to the Zero-Age
Note that the He luminosity reaches almost to 10^10 Lsun, but that the surface
value changes very little! Also see that the H luminosity drops to zero: the
expansion causes the H shell to be pushed outward and cool so much that the
H burning stops. The subsequent flashes are much weaker.
Below we show the convective regions in the star. There are a couple of
mini-flashes, but they also drive convective zones, Note that each
successive flash occurs closer to the centre than the one before it. Eventually the convective zone of the flash settles down to being the steadily burning helium core.