Understandings: Stellar evolution on HR diagrams; Red giants, white dwarfs, neutron stars and black holes
Applications and skills: Sketching and interpreting evolutionary paths of stars on an HR diagram; Describing the evolution of stars off the main sequence; Describing the evolution of stars off the main sequence; Describing the role of mass in stellar evolution
Utilization: An understanding of how similar stars to our Sun have aged and evolved assists in our predictions of our fate on Earth
The ultimate fate of a star also depends on the mass of the star. Low mass stars don't form red giants as they are completely convective (so the helium is spread throughout the star) and the core temperature is insufficient for helium burning, Larger stars (0.5 - 10 x the mass of the sun) do produce red giants with an inert core of helium (produced by a surrounding hydrogen burning shell) or carbon (if there is a helium burning shell). The most massive stars do not tend to swell with age as their outer layers get blow away during their lifetime, but their extreme temperatures enable them to fuse not just hydrogen to helium and helium to carbon, but carbon to neon and so on through oxygen and silicon all the way to iron. Iron will not fuse - it instead absorbs energy - and the resulting immediate cessation of nuclear fusion combined with the core collapse will lead to a supernova explosion.
As all nuclear fusion in a red giant ceases then much of its outer layers are blown away by the heat (and produce a planetary nebula). What remains is normally the exposed core of the star, a white dwarf. In a white dwarf the gravitational pull of the star is balanced by electron degeneracy. White dwarfs are very dense - the sun will form a white dwarf of about 0.6 solar masses, but its volume will be about that of the Earth. For a white dwarf of greater than 1.4 solar masses (the Chandrasekhar limit) electron capture results in the creation of a still denser neutron star - no larger than 10km in size. If the stellar remnant is great than about 3 solar masses (the Oppenheimer-Volkoff limit) then neutron degeneracy pressure is insufficient to prevent the collapse of the core into a singularity, a point of infinite density, surrounded by a black hole.
What is degeneracy pressure in white dwarf and neutron stars?
Oxford Physics: pp 657 - 659
Hamper HL (2014): p 551 - 553
Page 204 - 209