Stellar Remnants and Degeneracy Pressure

A forming star contracts under gravity until its core can sustain hydrogen fusion. During the main sequence, energy from fusion supports gas and radiation pressure against inward gravity. When core hydrogen is depleted, the core and outer layers evolve differently.

A Sun-like star expands into a red giant and later sheds outer layers as a planetary nebula, leaving a white dwarf. A sufficiently massive star can become a red supergiant and undergo core collapse and a supernova, leaving a neutron star or black hole depending on the surviving core. Distinguish initial stellar mass from final remnant mass.

A white dwarf is supported mainly by electron degeneracy pressure, a quantum effect associated with electrons being unable to occupy identical quantum states. Its support does not require continuing core hydrogen fusion. It can therefore cool and fade while remaining compact.

The Chandrasekhar limit is about 1.4 solar masses for a non-rotating white dwarf in the simple model. Above this remnant mass, electron degeneracy cannot provide the required support. It is not an initial-star mass boundary at which every star must follow exactly the same history.

A neutron star contains extremely dense neutron-rich matter and has a radius of order kilometres rather than a white dwarf’s planetary-scale radius. A black hole has an event horizon from within which signals cannot reach a distant observer. Do not describe the horizon as a material surface.

On an HR luminosity–temperature diagram, white dwarfs are hot but faint because their small areas limit total luminosity. Giants can be cool but very luminous because they have large radii. Neutron stars and black holes are not ordinary positions on the main sequence. The diagram’s temperature axis decreases to the right.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.