What Is a White Dwarf? A Dead Star Held Up by a Quantum Rule

A star spends most of its life fusing hydrogen into helium in its core, held in balance between gravity pulling inward and radiation pressure pushing outward. When the core hydrogen runs out the balance fails, the core contracts and heats while the outer layers expand enormously, producing a red giant. For a star of moderate mass, up to roughly eight times the sun, the core then becomes hot enough to fuse helium into carbon and oxygen, and there it stops, because the star never becomes hot enough to fuse carbon. The outer layers are shed over time, driven off by pulsations and radiation pressure, forming a planetary nebula, a shell of glowing gas that has nothing to do with planets and got its name from looking round through early telescopes. What remains is the exposed core: a ball of carbon and oxygen, extremely hot, roughly the size of the earth, containing a substantial fraction of the original star's mass, with no fuel left.

With fusion finished there is no radiation pressure, and gravity should crush the object. What prevents that is electron degeneracy pressure, which comes from the Pauli exclusion principle: no two electrons may occupy the same quantum state. Squeezing the material forces electrons into ever higher momentum states because the low ones are already filled, and the resulting pressure resists compression. It is entirely unlike ordinary gas pressure, since it does not depend on temperature at all, which is why a white dwarf can cool indefinitely without shrinking. It also produces a strange consequence: more massive white dwarfs are smaller, because greater gravity compresses the electrons further, so the mass and radius run in opposite directions. Subrahmanyan Chandrasekhar calculated in 1930, as a nineteen-year-old on a voyage to England, that degeneracy pressure has a limit, and that above roughly 1.4 solar masses it cannot hold, a result Arthur Eddington publicly ridiculed and which won Chandrasekhar a Nobel prize decades later.

A white dwarf's subsequent life is mostly a long cooling, and several consequences follow:

• •It begins extremely hot, up to a hundred thousand kelvin, and radiates that stored heat into space with no way to replace it, fading over billions of years
• •Cooling is slow enough that no white dwarf in the universe has yet cooled to a cold black dwarf, since the time required exceeds the current age of the universe
• •The interior is predicted to crystallise as it cools, with the carbon and oxygen freezing into a lattice, and observations of a pile-up in the numbers at particular brightnesses have been read as evidence that this is happening
• •Because their cooling is predictable, the faintest white dwarfs in a star cluster give an independent estimate of that cluster's age, which is used as a check on other methods
• •A thin atmosphere of hydrogen or helium sits above the dense interior, and gravity is so strong that heavier elements sink out of sight within days, so any metals detected in the atmosphere must have arrived recently
• •That last fact is how white dwarfs are used to study destroyed planetary systems, since the metals come from asteroids and planetary debris falling in, giving a direct chemical analysis of rocky bodies around other stars

A white dwarf in a binary system can draw material from its companion, and the consequences depend on how much arrives. A modest accumulation of hydrogen on the surface can ignite in a runaway fusion event, brightening the star enormously for weeks without destroying it, which is a nova, and a system can do this repeatedly. If instead the white dwarf's total mass is pushed towards the Chandrasekhar limit, either by steady accretion or by merging with another white dwarf, degeneracy pressure fails, carbon fusion ignites throughout the star almost simultaneously, and the entire object is destroyed in a type one-a supernova. Because the explosion happens at a characteristic mass, these events have a consistent intrinsic brightness, which makes them standard candles for measuring cosmic distances. That property is what allowed two teams in 1998 to measure the expansion history of the universe and find it accelerating, the discovery that established dark energy and won the 2011 Nobel prize in physics.

A white dwarf is the exposed carbon and oxygen core left when a star of up to about eight solar masses sheds its outer layers, packing something near the sun's mass into an earth-sized object. It is held up by electron degeneracy pressure, which does not depend on temperature, so it cools without shrinking, and which fails above about 1.4 solar masses. Heavy elements sink out of its atmosphere within days, so detected metals reveal recently swallowed planetary debris, and exploding white dwarfs measured the accelerating universe.