Why does oxygen crystallize before carbon?

The Coulomb coupling of an ion species scales as Gamma_i = Gamma_e * Z_i^(5/3). Oxygen has Z=8 versus carbon's Z=6, so at any given temperature oxygen's Gamma is roughly 1.4-1.6x higher, crossing the crystallization threshold (Gamma about 175) first while nearby carbon is still liquid.

Why does this matter for how white dwarfs cool?

Sinking oxygen-rich crystal releases gravitational potential energy in addition to ordinary latent heat of freezing. Together they act as an extra heat source that slows the star's fade, an effect used to explain the pile-up of white dwarfs Gaia observes at intermediate luminosities.

Carbon-Oxygen Phase Separation in a Crystallizing White Dwarf

Core Cooling

Core temperature T_c 2.20 × 10⁷ K

Cooling speed 1.0×

Composition

Oxygen mass fraction X_O 0.50

Live Readouts

Γ (oxygen)

—

Γ (carbon)

—

Crystallized

O enrich. (solid/liq.)

1.00×

Latent heat (rel.)

0.0

Grav. release (rel.)

0.0

How it works

As a white dwarf's carbon-oxygen core cools, the ions stop behaving like a gas and lock into a crystal lattice once the Coulomb coupling parameter crosses a critical value:

Γ_i = Γ_e · Z_i^(5/3),   Γ_e = e² / (a_e · k_B · T_c)
crystallizes when Γ_i ≈ 175

Because Γ scales with Z^5/3, the higher-charge oxygen ions (Z=8) reach the crystallization threshold at a higher temperature than carbon (Z=6) — oxygen freezes first while carbon is still liquid.

Rayleigh fractionation (partition coeff. k_D ≈ 1.3):
X_liquid(f) = X₀ · (1−f)^(k_D−1)
X_solid(f)  = k_D · X_liquid(f)

Core temperature slider — drag it down to cool the core and watch the crystallization front rise from the bottom of the cell.
Auto-cool — lets the temperature drift down on its own at the chosen speed, like billions of years compressed into seconds.
Oxygen fraction — sets the initial C/O mix; a higher X_O means more of the lattice-forming, higher-Γ species.
Phase separation ON/OFF — with it on, newly frozen oxygen is captured preferentially into the solid and the lighter carbon-enriched liquid is left buoyant above the front, exactly the fractionation process (Bildsten & Hall 1998) invoked to explain the extra cooling delay Gaia observes in the white dwarf luminosity function. Turn it off to see plain, unfractionated freezing for comparison.

The sinking of denser oxygen-rich solid releases gravitational potential energy on top of ordinary latent heat, and both act as an extra heat source that slows the star's fade — this is the leading explanation for the observed "pile-up" of white dwarfs at intermediate luminosity in Gaia's H-R diagram.

Oxygen ion (liquid) Oxygen ion (crystal) Carbon ion (liquid) Carbon ion (crystal)

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