---
title: "White Dwarf Cooling and Crystallization Interactive Lab | Sandbox Physics"
description: "How does freezing slow the cooling of a white dwarf? A white dwarf shines by losing stored heat."
canonical_url: "https://sandboxphysics.com/labs/white-dwarf-crystallization/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/white-dwarf-crystallization/"
last_modified: "2026-11-04"
---

AC31 · Heat inside a stellar remnant

# White Dwarf Cooling and Crystallization

**How does freezing slow the cooling of a white dwarf?** A white dwarf shines by losing stored heat. Freezing releases latent heat, and changes in composition can release more energy. That extra supply slows cooling, so brightness gives an age only after the star’s mass, atmosphere and interior physics are specified.

Drag a probe through a partially crystallized core. Watch a shell release latent heat, then compare a published cooling plateau with the same-mass reference.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The controlled view evolves an isothermal pure-carbon OCP core on four discrete native MESA density geometries, with Debye and degenerate-electron heat capacities, explicit latent heat and a declared Kramers-envelope luminosity. Its independent model clock is uncalibrated and gives very long ages; it is not a stellar age estimate. The displayed phase colours are schematic, and core temperature is not photospheric effective temperature. It omits structural relaxation, a solved atmosphere, residual burning, neutrinos, C/O separation and neon transport. The separate published STELUM view has three 1.00-solar-mass standard-composition cases, with about one-gigayear author smoothing; only supplied surface quantities are shown. It has no radial front or solid-fraction data. No mass/composition interpolation or Galactic population-age inference is provided.

Selected independent clock

## A crystal core grows

The section fits the selected core to the view; its actual outer radius is $7.19\times10^{8}\,\mathrm{cm}$

Source total mass $0.608\,M_\odot$

Probe material **Liquid** $\rho=9.89\times10^{5}\,\mathrm{g\,cm^{-3}}$ $\Gamma=151$

### Core temperature along the model clock

$T/(10^6\,\mathrm K)$ $t/(10^9\,\mathrm{yr})$

Scaled core temperature; the gold line marks the selected time in this demo interval.

### Stored heat and latent heat leave as light

$E/(10^{46}\,\mathrm{erg})$ $t/(10^9\,\mathrm{yr})$

Scaled energy. Green: sensible heat lost. Blue: latent heat released. Gold: photons emitted.

Latent heat released **$6.61\times10^{45}\,\mathrm{erg}$**

Photon energy emitted **$4.46\times10^{46}\,\mathrm{erg}$**

Sensible heat capacity

Ionic contribution **$2.34\times10^{40}\,\mathrm{erg\,K^{-1}}$**

Electron contribution **$4.1\times10^{38}\,\mathrm{erg\,K^{-1}}$**

These are sensible-energy derivatives; latent release is counted separately. At an exact cell melting temperature, the stored derivative uses the solid-side branch.

Physics tutorial

## Watch stored heat leave a freezing core

**Background** A white dwarf can remain supported by degenerate electrons while losing thermal energy. Its dense ionic material can freeze at a very high temperature, releasing latent heat along the way.

**Why it matters** The cooling light can become a clock only after the mass, envelope and internal energy sources have been specified. This controlled core lets us follow each heat term before comparing a separate published surface sequence.

Start with the essentials

- **Focus question**: Why does the core temperature pause while the star still radiates?
- **One-sentence intuition**: During freezing, released latent energy can supply the outgoing luminosity without the same drop in sensible energy.

### Core mathematical model

#### The controlled thermal energy

$$
E(T,\{f_i\})=U_{\rm sens}(T)+\sum_i(1-f_i)q_i
$$

Each $f_i$ is the solid fraction of one mass shell; $q_i$ is its declared latent reservoir. The sensible branch contains ionic and electron heat capacities.

#### Heat leaving the model

$$
\frac{dE}{dt}=-L(T),\qquad L\propto T^{7/2}
$$

The luminosity comes from the stated Kramers-envelope approximation. This is a model core temperature, not the photospheric effective temperature.

#### A shell freezes at its own temperature

$$
\Gamma_i=\frac{Z^2e^2}{a_i k_BT},\qquad a_i=\left(\frac3{4\pi n_i}\right)^{1/3}
$$

The pure-carbon one-component model freezes at the declared coupling threshold. Denser shells have higher freezing temperatures.

### Common difficulties

#### Support versus heat

**Typical misconception** Degenerate pressure means the electrons supply all the thermal energy.

**Better mental model** Pressure support and heat capacity answer different questions. The controlled calculation includes ion and electron thermal terms separately.

#### Radius versus mass

**Typical misconception** A front halfway out contains half the core mass.

**Better mental model** Mass also depends on the radial density profile. The displayed solid mass is integrated over shells, not inferred from the coloured radius.

#### One clock for all views

**Typical misconception** The long controlled-model time can be appended to a published cooling age.

**Better mental model** The models use different physics and origins. The visible uncalibrated elapsed time is not a stellar-age measurement, and the native sequences retain their own clocks.

### Run the experiment

1. 01

   #### Cross the phase boundary

   Drag the gold probe from the warm liquid into the blue solid.

   **What to observe:** The phase, density and temperature all belong to the selected radial shell and the same saved time.

2. 02

   #### Catch a shell releasing latent heat

   Choose Latent plateau, then compare temperature, released latent energy and radiated energy.

   **What to observe:** The shell can continue supplying light while its temperature remains fixed during the phase change.

3. 03

   #### Visit the cold tail

   Choose Debye tail, open Sensible heat capacity and compare the ionic and electron terms.

   **What to observe:** The solid ionic heat capacity falls at low temperature. The electron term is computed separately rather than silently discarded.

4. 04

   #### Change the calculation, and read its clock

   Open the published plateau, then compare STD, partial and full distillation in the advanced case selector.

   **What to observe:** These are supplied surface sequences with a native origin and about one-gigayear smoothing. They contain no internal front. The controlled core keeps its own uncalibrated clock.

Physical conclusion

Read the front, probe, thermal reservoirs and time as one state. Then ask which additional physics is needed before that model clock can become a stellar age.

## Related experiments and articles

The heat and clocks of white dwarfs · Reading path

### The heat and clocks of white dwarfs

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why white dwarfs cool so slowly**](https://sandboxphysics.com/stories/white-dwarf-cooling/why-white-dwarfs-cool-slowly/)
2. [Article **Where a dead star keeps its heat**](https://sandboxphysics.com/stories/white-dwarf-cooling/degenerate-support-and-stored-heat/)
3. [Article **How crystallization slows white dwarf cooling**](https://sandboxphysics.com/stories/white-dwarf-cooling/latent-heat-and-white-dwarf-cooling/)
4. [Article **Inferring a cooling age from brightness**](https://sandboxphysics.com/stories/white-dwarf-cooling/cooling-clocks-and-age-likelihoods/)
5. [Article **Compare white dwarf cooling models with original Gaia data**](https://sandboxphysics.com/stories/white-dwarf-cooling/mesa-gaia-cooling-model-comparison/)
6. [Article **Why crystals can float inside a white dwarf**](https://sandboxphysics.com/stories/white-dwarf-cooling/white-dwarf-phase-separation-distillation/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)