Illustrated Physics
physics, drawn
Concept

White dwarf — where it appears

The cooling core left when a star like the Sun has used up its fuel: about a solar mass packed into a body the size of the Earth. It is held up by the pressure of degenerate electrons, which cannot support more than about 1.4 solar masses.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Cold matter, and the mass above which nothing holds it up. The radius of a cold, degenerate star against its mass, obtained by integrating the equations of hydrostatic support outward from 11 different central densities with the exact degenerate equation of state, and nothing else. Heavier means smaller — the opposite of every ordinary object, and the direct consequence of a pressure that comes from counting states rather than from heat. The curve turns over and runs into a vertical asymptote at 1.452 solar masses, against 1.456 from the limiting polytrope, whose own constant 2.0182 is integrated here as well. That is Chandrasekhar's limit. It exists because the electrons become relativistic: once they are, the pressure goes as the four-thirds power of the density, and for that exponent alone the mass of a self-gravitating ball is independent of its radius — so squeezing it harder produces no more support and there is exactly one mass such a star can have. The horizontal line is the Earth's radius, which the curve crosses near a solar mass: a white dwarf of the Sun's mass is the size of a planet, and the ones close to the limit are a few thousand kilometres across. What the model leaves out is what actually happens at the top: at those densities electrons begin to be captured onto nuclei, which removes the very pressure holding the star up, so the collapse starts slightly below the line rather than at it.

The mass no cold matter can hold up

A white dwarf gets smaller as it gets heavier, which no ordinary object does. Follow that curve upward and the radius reaches zero at 1.46 solar masses — because once the electrons are relativistic the pressure goes as the four-thirds power of the density, and for that exponent alone the mass of a self-gravitating ball does not depend on its radius at all.

astrophysics · Self-gravity The redshift of a white dwarf weighs it. The gravitational redshift at the surface of a cold white dwarf, expressed as the velocity that would give the same Doppler shift, against the star's mass; computed from the radius each mass is forced to have. The Sun's surface redshift is 636 m/s. A white dwarf of 0.6 solar masses shifts its light by 30.1 km/s, one of 1.0 by 77.6, of 1.2 by 128 and of 1.35 by 223. Because the radius is not free, the curve is single-valued and steepening: a measured shift returns one mass. The cold model puts Sirius B, at 1.018 solar masses, at 80.8 km/s; its measured mass and radius together give 80.0.

The redshift that weighs a dead star

Light leaving the surface of an ordinary star is reddened by gravity, but the shift alone says little, because a star's radius is free and the shift depends on mass over radius. A white dwarf has no free radius. Degenerate electrons fix its size from its mass, so one measured line shift returns one mass — and the gauge grows sharper the closer the star is to collapse. The first measurement of it, in 1925, was hailed as a confirmation of general relativity and was wrong by a factor of four, in agreement with a forecast that was wrong by the same factor.

astrophysics · Gravitational redshift

Named alongside it

The objects these essays reach for when they reach for this one.

Chandrasekhar limitDegeneracy pressureCompactnessExclusionGravitational redshiftHydrostatic equilibriumMass radius relationNeutron starPolytropeRelativistic electronsSelf-gravitySpectral line

All concepts