Compare the internal structure of a white dwarf to that of a neutron star. What are the similarities? What are the differences?

Imagine a star that has lived a full life and is now in the twilight of its existence. This is the stage when a star becomes a white dwarf. Imagine a celestial object the size of Earth but with the mass of the Sun - incredibly dense and compact. The white dwarf is composed predominantly of electron-degenerate matter. This means the material of a white dwarf is so compressed that the electrons are stripped from their atoms, creating a dense core of atomic nuclei floating in a sea of electrons.

Electron degeneracy pressure, a concept rooted in the principles of quantum mechanics, acts as a counterbalance to gravity, preventing the white dwarf from collapsing. This principle is fundamental to understanding the longevity of white dwarfs as stable structures in the cosmos. Although they share this pressure with neutron stars, white dwarfs are less dense due to the type of particles exerting the degeneracy pressure - electrons as opposed to neutrons.

In the stellar world, neutron stars are the dense cores left behind after a supernova explosion. Consider these incredible objects no wider in diameter than a small city, yet they contain more mass than the Sun. Composed almost entirely of neutrons compressed to an unfathomable density, neutron stars are underpinned by neutron degeneracy pressure.

This pressure stems from quantum degeneracy, a principle asserting that no two fermions (particles like electrons and neutrons) can occupy the same quantum state. In the neutron star's dense core, this rule results in a form of pressure that halts further collapse. The gravity in a neutron star is so powerful that, if it were just slightly more massive, it would crush under its own weight into a black hole. Neutron stars mark the extreme boundary between matter as we know it and the unknown realms of black holes.

Electron degeneracy pressure is a concept vital for the structure of white dwarfs. It arises when the atoms of a dying star are squeezed under its own gravity, causing the electrons to be so closely packed that they resist further compression due to the principles of quantum mechanics.

According to the Pauli exclusion principle, no two electrons can occupy the same quantum state simultaneously. This principle results in a force that opposes the gravitational collapse of a white dwarf. Even when the nuclear fuel within the star is exhausted, this pressure ensures that the white dwarf remains in a state of equilibrium. Electron degeneracy pressure is the force that enables white dwarfs to exist and makes them stable against gravitational collapse for billions of years.

Quantum degeneracy is the physical phenomenon that becomes dominant in the life of stars at their most compact stages: the white dwarf and the neutron star. It's a state where particles, which follow the rules of quantum mechanics, are packed so densely that their quantum natures take precedence over their classical properties.

In quantum degeneracy, particles like electrons or neutrons are pushed into their smallest possible spaces. The Pauli exclusion principle prevents identical fermions (a type of particle that includes electrons and neutrons) from occupying the same quantum space. This leads to a form of pressure distinct from that exerted by a gas or plasma in less dense star matter. Quantum degeneracy is the underlying reason for the existence of white dwarfs and neutron stars, as it prevents them from collapsing further despite the tremendous gravitational forces at play.