For these stars it never gets hot enough in the core to
have Carbon or Oxygen fusion to occur. So the ``central star''
of PN is not a star at all.
We are seeing the core of the AGB star composed of Carbon,
Oxygen with a small layer of Hydrogen and Helium.
Once the PN envelope has expanded away an dissipated
the AGB core sits at the top of the White Dwarf
sequence in the H-R Diagram.
The core is hot and therefore blue and small with a correspondingly
low luminosity.
What next? White dwarfs are alot like hot
embers. As they radiate away energy, they lose energy and
with no energy source to replace it, they cool off.
You might expect the WDs to shrink as they cool, but because
they are supported by degeneracy, they don't. They just
get cooler and cooler and fainter and fainter
till they are essentially lost to observations.
As they cool, there is a point at which the Carbon atoms
form a lattice with the still roaming around in their own quantum
phase space.
In the solar vicinity at least 15% of the mass in stars is
in WDs and the number is growing with time.
Because the Galaxy has a finite age, the oldest WDs have not
cooled to invisibility yet.
The temperature and luminosity of the coolest WD gives the
age of the Galactic disk - its around 10 Billion years old.
A last interesting fact about WDs and degeneracy.
e- degeneracy can only support so much mass. A WD supported by
e- degeneracy must have . This is called
the Chandrasekar Limit. What happens if a stellar core exceeds
this limit will come back to haunt you soon.