White Dwarf Cooling Simulator: Thermal Evolution of Stellar Remnants

simulator intermediate ~10 min
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T ≈ 12,400 K — a DA white dwarf cooling for 1 Gyr

A 0.6 M☉ white dwarf that started at 100,000 K has cooled to about 12,400 K after 1 billion years, with luminosity roughly 0.0013 L☉ — still visible but fading steadily.

Formula

L = (4πR²)σT⁴ (Stefan-Boltzmann luminosity)
L ∝ M × T_c^(7/2) (Mestel cooling law)
Γ = Z²e² / (a_i k_B T) ≈ 175 (crystallization criterion)

Stellar Embers

When a star below about 8 solar masses exhausts its nuclear fuel, it sheds its outer layers as a planetary nebula, leaving behind a hot, dense core — the white dwarf. About the size of Earth but with the mass of the Sun, white dwarfs are supported not by fusion but by the quantum mechanical pressure of degenerate electrons. With no energy source, they simply cool and fade, like embers pulled from a fire.

Mestel's Cooling Theory

In 1952, Leon Mestel derived the foundational theory of white dwarf cooling. The degenerate interior has enormous thermal conductivity, making it nearly isothermal. The thin non-degenerate envelope acts as an insulating blanket, controlling the rate of energy loss. The result: luminosity drops as a power law in time, L ∝ t^(−7/5), meaning white dwarfs dim rapidly at first, then increasingly slowly over billions of years.

Crystallization and Phase Transitions

As the interior cools below about 6,000 K, the carbon and oxygen ions begin crystallizing into a solid lattice — the white dwarf literally freezes from the inside out. This phase transition releases latent heat and gravitational energy from chemical fractionation (heavier oxygen sinks toward the center). In 2019, the Gaia spacecraft detected a pile-up of white dwarfs at specific luminosities, beautifully confirming the crystallization delay predicted decades earlier.

Cosmic Chronometers

Because white dwarfs cool predictably, the coolest ones in a stellar population set a minimum age for that population. This technique — white dwarf cosmochronology — provides independent age estimates for the Milky Way disk, open clusters, and globular clusters. The faintest white dwarfs in the solar neighborhood have temperatures around 3,500 K and luminosities below 10⁻⁵ L☉, corresponding to cooling ages of 10-12 billion years.

FAQ

What is a white dwarf?

A white dwarf is the remnant core of a low- to intermediate-mass star (< 8 M☉) after it has exhausted nuclear fuel and shed its envelope. Supported by electron degeneracy pressure rather than fusion, it slowly cools and fades over billions of years. Most are composed of carbon and oxygen with thin hydrogen or helium envelopes.

How do white dwarfs cool?

White dwarfs cool by radiating stored thermal energy from their ions. The degenerate electron gas conducts heat efficiently to the surface, where a thin non-degenerate envelope acts as an insulating blanket. Mestel's theory predicts luminosity drops as L ∝ t^(−7/5). Crystallization releases latent heat that temporarily slows cooling.

What is white dwarf crystallization?

As a white dwarf cools below ~6,000 K, the carbon-oxygen ions in its interior begin to solidify into a crystalline lattice, starting at the center. This phase transition releases latent heat and gravitational energy from oxygen sedimentation, temporarily slowing the cooling rate — an effect observed by Gaia in 2019.

Can white dwarfs be used to date stellar populations?

Yes. Because white dwarfs cool predictably, the faintest (coolest) white dwarfs in a cluster set a lower limit on the cluster's age. This white dwarf cosmochronology provides independent age estimates for the Galactic disk (~8-10 Gyr) and globular clusters (~12-13 Gyr).

Sources

Embed

<iframe src="https://homo-deus.com/lab/stellar-evolution/white-dwarf-cooling/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub