Stellar Death: White Dwarfs, Neutron Stars and Black Holes

A white dwarf's light and its support against gravity have different explanations. Stored heat supplies the light as the remnant cools. Degenerate electrons supply most of the pressure that supports its interior. Continued core fusion is not required.

Electrons cannot all occupy the same quantum state. When a dense electron gas is compressed, states with larger momenta must be occupied. The resulting pressure remains even at zero temperature. If density and composition are fixed, changing temperature has only a small effect while the electrons remain strongly degenerate.

A real white dwarf can still change its structure as it cools. Temperature independence in an idealized pressure law does not establish an exactly constant stellar radius. There is also a separate mass-radius relation: among cold white-dwarf models of the same composition, the more massive objects generally have smaller radii.

The Chandrasekhar limit is the approximate mass ceiling for electron-supported white dwarfs under specified assumptions. For a cold, nonrotating carbon-oxygen model, it is about 1.4 solar masses. This limit concerns the white dwarf's mass, not the birth mass of the original star. A star can lose much of its envelope before leaving a white dwarf. A core above the limit needs further physical analysis; the limit alone does not choose one outcome.

An iron-rich stellar core can remain supported by degenerate electrons after it stops gaining net energy from fusion. Burning in surrounding shells can keep adding material to it. Electron captures reduce the number of electrons, weakening their contribution to support. At high temperatures, breaking nuclei apart also absorbs energy.

Once the core becomes unstable, it collapses rapidly. The inner core becomes harder to compress near nuclear density, and a shock forms. That shock has to travel through infalling material. It can lose energy and stall, so an initial bounce is not enough to explain every successful explosion.

Neutrinos carry away much of the energy released during collapse. In many successful core-collapse supernova models, some neutrinos transfer energy to material behind the stalled shock. This heating helps material move outward. Other collapses can form black holes with little visible explosion.

When an explosion ejects outer layers, it carries elements produced during the star's life and during the explosion into surrounding gas. The compact remnant and the ejecta are different parts of the outcome. Matter has not all disappeared.

Heavy elements have more than one production and dispersal route. Stellar mass loss and neutron-star mergers also contribute. It is not accurate to assign every heavy atom to an ordinary core-collapse supernova.

Neutron stars contain matter compressed to densities comparable to, and in their interiors greater than, nuclear density. They are neutron-rich, but describing the entire star as pure neutrons leaves out other particles and the uncertain physics of its deepest layers. Nuclear interactions and degeneracy pressure both contribute to support.

A neutron star's maximum stable mass depends on the relation between pressure and density in this matter. Rotation also affects support. There is no exact universal boundary at 3 solar masses. For a definite exercise, use the maximum stated for its model and compare like quantities: retained remnant mass with the model's remnant-mass limit. A below-limit mass permits stability; it does not identify an object by itself.

A pulsar is observed through repeated pulses from a rotating neutron star. Its radiation beams sweep through space. A telescope detects pulses when a beam repeatedly crosses the direction of Earth. Some beams miss Earth, so those neutron stars are not observed as pulsars through those beams. Pulsar radiation can occur outside the radio band too.

Rotation supplies energy to many pulsars. As rotational energy is lost, the star can slow down and the interval between pulses can increase. The signal can be highly regular without being an unchanging clock. Measured masses and associations with supernova debris help test the neutron-star interpretation.

An event horizon is a boundary in spacetime. Events inside a black hole's horizon cannot send future-directed light signals to distant observers. This is a statement about possible light paths, not a claim that light slows down locally. Every local observer still measures light travelling at c.

A collapsing stellar remnant can form a black hole if it cannot maintain support. The star may previously have lost much of its mass. Its original birth mass therefore cannot be substituted for its retained compact-remnant mass in a support calculation.

Observations can reveal a black hole without receiving a signal sent from inside its horizon. A nearby star's orbit can reveal an unseen compact mass. Gas outside the horizon can heat up and emit radiation before falling in. Merging black holes can produce gravitational waves detectable far away. None of these observations requires light to escape from inside a horizon.

Stellar remnants are not the only black holes studied by astronomers. Supermassive black holes occur at the centers of many galaxies.

For an isolated black hole that has settled down, classical general relativity describes its external solution using mass, spin and electric charge. The stated conditions matter. This result does not reveal every detail of the original star or settle the uncertain physics of a proposed singularity.