White dwarfs are compact stellar remnants formed from Sun-like stars. Their distinctive properties arise from quantum mechanical effects that prevent further collapse, making them crucial objects in modern astrophysics.

White Dwarfs: Core Characteristics

White dwarfs represent the final evolutionary stage for low-mass and Sun-like stars once nuclear fusion has ceased. After exhausting hydrogen and helium in their cores, these stars expel their outer layers, leaving behind an exposed, hot core that cools gradually over billions of years. The resulting stellar remnant is exceptionally dense, extremely small, and governed by quantum physics rather than conventional thermal pressure.

White dwarfs typically possess:

• Masses comparable to the Sun’s but compressed into approximately the size of Earth.

• Densities on the order of 10910^9109 to 101010^{10}1010 kg m⁻³.

• Surface temperatures that may exceed 100 000 K when newly formed.

• Luminosities that decline steadily as they radiate residual thermal energy.

These characteristics arise because gravity has overcome all normal gas pressure, forcing matter into a highly compressed state dominated by electrons in a degenerate configuration.

Electron Degeneracy Pressure

A defining property of white dwarfs is that they are supported by electron degeneracy pressure rather than thermal pressure. This form of pressure originates from the Pauli exclusion principle, a fundamental law of quantum mechanics stating that no two electrons may occupy the same quantum state.

Electron degeneracy pressure is unique because, unlike thermal gas pressure, it does not depend on temperature. Even as a white dwarf cools, this pressure remains strong enough to counterbalance the inward pull of gravity. As a result, white dwarfs do not undergo further gravitational collapse unless specific physical limits are exceeded.

The electron degeneracy mechanism leads to several key consequences:

• Cooling does not reduce structural stability.

• Increases in mass cause the star to become smaller, as stronger gravity compresses the electron gas.

• There exists an upper mass threshold beyond which degeneracy pressure is insufficient.

The Chandrasekhar Mass Limit

The theoretical maximum mass for a white dwarf is known as the Chandrasekhar mass limit. This limit is central to understanding which stellar remnants become white dwarfs and which undergo further collapse into neutron stars or black holes.

At masses approaching this limit, electrons become relativistic, meaning their speeds approach the speed of light. Relativistic electrons provide less effective degeneracy pressure, weakening resistance to gravity. If the limit is surpassed, the white dwarf becomes unstable and collapses catastrophically.

Between these quantum mechanical and relativistic regimes, a white dwarf maintains equilibrium by balancing inward gravitational force with outward electron degeneracy pressure. This equilibrium behaves differently from normal stars and introduces counter-intuitive structural behaviour.

Physical Structure and Equation of State

The internal structure of a white dwarf is determined by its equation of state—the relationship between pressure and density in degenerate matter. In a typical white dwarf, electrons form a highly compressed Fermi gas, while nuclei form a crystalline lattice that contributes mass but little pressure.

EQUATION
—-----------------------------------------------------------------
Mass–radius relationship (White dwarf behaviour) = R∝M−1/3R \propto M^{-1/3}R∝M−1/3
R = Radius of the white dwarf (m)
M = Mass of the white dwarf (kg)
—-----------------------------------------------------------------

This inverse relationship demonstrates that more massive white dwarfs are smaller.

Graph illustrating the mass–radius relation for white dwarfs in both the relativistic and non-relativistic regimes, with the Chandrasekhar mass limit indicated. Source.

The cores of white dwarfs are typically composed of:

• Carbon and oxygen, for stars with initial masses similar to the Sun.

• Oxygen, neon, and magnesium, for progenitors at the upper limit of low-mass star formation.

The outer layers form a thin atmosphere of either hydrogen or helium, which affects spectral classification but contributes negligibly to overall mass.

Observational Properties

White dwarfs are observed primarily through their spectra, luminosity, and cooling behaviour.

Hubble image showing brilliant Sirius A with diffraction spikes and its faint white dwarf companion Sirius B, whose low luminosity requires overexposing the primary star to reveal it. Source.

Their small radii result in low luminosities despite high surface temperatures, placing them in the lower-left region of the Hertzsprung–Russell diagram.

Sparse Hertzsprung–Russell diagram highlighting the white dwarf sequence in the lower-left, demonstrating their high temperatures but low luminosities. Source.

Key observable features include:

• High surface gravity, causing broadened spectral lines.

• Continuous cooling, allowing astronomers to estimate ages of stellar populations.

• Absence of fusion, meaning luminosity arises solely from stored thermal energy.

Their predictable cooling curves make white dwarfs valuable cosmic chronometers in astrophysics.

Formation Pathway

White dwarfs are produced through the evolutionary processes of stars below the Chandrasekhar limit. The formation pathway generally follows:

• Expansion into a red giant after hydrogen depletion.

• Helium burning followed by shell burning stages.

• Ejection of outer layers to form a planetary nebula.

• Exposure of the hot, dense core, which becomes a white dwarf.

This process ensures that all Sun-like stars ultimately leave white dwarfs as their final remnants, provided no additional mass is added afterwards, such as in binary systems where accretion may push the star beyond the Chandrasekhar limit.