When a carbon–oxygen white dwarf rich enough in 22Ne crystallizes, the solid phase is depleted in 22Ne and is buoyant: crystals float up and melt while 22Ne-rich liquid sinks, and the resulting release of gravitational energy can halt the star's cooling for up to ~10 Gyr. This distillation mechanism, implemented by Bédard, Blouin & Cheng (2024) in the STELUM stellar-evolution code, explains the Q-branch overdensity of ultramassive white dwarfs discovered by Gaia, but its central physics is underdetermined: C–O–Ne phase diagrams fix only the onset and final compositions, so the composition trajectory of the crystal-forming region is inserted by hand as a linear function of the carbon coupling parameter, and the behavior at the critical 22Ne buoyancy threshold — self-termination versus instability-driven restart and possible 22Ne-rich shell formation — is unknown. The duration and mass dependence of the distillation cooling delay, and hence crystallized-white-dwarf ages, remain model-dependent. The trajectory and termination questions remain open — restated as open by Salaris et al. (2024) — with only partial progress along adjacent strands (formation channels of 22Ne-rich white dwarfs, the distilled fraction, cluster-level observational tests).

Background

White dwarfs are the dense, electron-degenerate remnants of stars below roughly eight solar masses. Lacking a nuclear energy source, they cool over billions of years, and their cooling times serve as cosmic clocks (white-dwarf cosmochronology) for dating the Galactic disk, star clusters, and companion stars. The interior of a carbon–oxygen (C–O) white dwarf is a Coulomb plasma of 12C and 16O ions with a few percent by mass of 22Ne — produced from nitrogen during the progenitor's helium burning — plus heavier neutron-rich impurities in merger products. As the star cools, the Coulomb coupling parameter Γ (the ratio of electrostatic to thermal energy, Γ = ⟨Z^{5/3}⟩e²/(a_e k_B T), where a_e is the mean inter-electron spacing) rises, and the core crystallizes from the center outward once Γ exceeds a critical value Γ_cr ≈ 200.

Crystallization delays the cooling in two ways. First, ordinary phase separation (fractionation): the solid retains oxygen preferentially, so the growing crystal core becomes oxygen-rich and the overlying liquid carbon-enriched, releasing gravitational energy. Second — the subject here — 22Ne distillation: Monte Carlo phase-diagram calculations by Blouin, Daligault & Saumon (2021) showed that when the 22Ne abundance of the liquid exceeds a threshold (a number fraction of order 1–2%, depending on Γ), the coexisting solid is so strongly depleted in 22Ne that it is lighter than the liquid. The crystals are then buoyant: they float up and melt while displacing 22Ne-rich liquid downward, so the central 'crystal-forming' region stays liquid and is progressively enriched in 12C and 22Ne at the expense of the whole core. The gravitational energy released is large enough to interrupt the cooling for several billion years. An analogous distillation was predicted for 56Fe in oxygen–neon white dwarfs by Caplan, Blouin & Freeman (2023).

Observationally, Gaia's color–magnitude diagrams revealed the 'Q branch': a striking overdensity of ultramassive (~1.1–1.3 solar mass) white dwarfs along the crystallization sequence, requiring cooling delays of up to ~10 Gyr in about 6% of them — far beyond what ordinary fractionation or gravitational settling of 22Ne can provide. Bédard, Blouin & Cheng (2024) showed, with the STELUM stellar-evolution code, that 22Ne distillation in C–O white dwarfs formed by stellar mergers (which homogenize the core and enrich it in neutron-rich impurities; see also Shen, Blouin & Breivik 2023 on the merger origin of Q-branch objects) interrupts the cooling for billions of years and reproduces the Q branch and its delay distribution.

Their implementation, however, had to bridge two gaps in the underlying physics with prescriptions. (i) Trajectory: C–O–Ne phase diagrams specify only the state at the onset of distillation (where the solid first becomes buoyant) and the terminal state, in which the central liquid reaches a composition of number fractions x_C = 0.8, x_O = 0, x_Ne = 0.2 (a 22Ne mass fraction ≈ 0.318) at a value Γ_C = 208 of the carbon-ion coupling parameter (the Coulomb coupling parameter Γ evaluated for carbon); the compositional path followed in between is unknown and was taken to vary linearly with Γ_C. (ii) Termination: distillation requires the liquid 22Ne abundance to stay above the buoyancy threshold; when the outermost crystal-forming layer is driven to that threshold, it is unclear whether distillation stops permanently, or whether the continued 22Ne depletion of newly formed solid re-enriches the overlying liquid and restarts distillation — an unstable stopping state — possibly building 22Ne-rich shells around the distilled core. The adopted numerical expedients (freezing the inner 22Ne-rich core, about 25% of the stellar mass, in place at the end of distillation, and artificially slowing the crystallization front to preserve convergence) inherit this uncertainty. Because the rate of gravitational-energy release, the total delay, and its dependence on stellar mass and 22Ne content are all shaped by the trajectory and termination behavior, these two gaps are the central open physics of distillation-driven cooling delays.

Problem Statement

Bédard, Blouin & Cheng (2024) pose, as the central unresolved physics of their 22Ne-distillation mechanism for white-dwarf cooling delays, the microscopic-to-macroscopic mapping of distillation and its late-time behavior. The problem is to determine, from first principles or convincingly constrain:

  1. The composition trajectory actually followed by the crystal-forming region during distillation — the functions x_C(Γ_C), x_O(Γ_C), x_Ne(Γ_C) linking the beginning state (onset of crystal buoyancy, fixed by the C–O–Ne phase diagram) to the terminal state (Γ_C = 208; number fractions x_C = 0.8, x_O = 0, x_Ne = 0.2, i.e. X(22Ne) ≈ 0.318) — in place of the ad hoc linear-in-Γ_C interpolation.

  2. The physical behavior when the 22Ne abundance of the liquid in the outermost crystal-forming layer reaches the critical buoyancy threshold: does distillation self-terminate because the solid is no longer buoyant, or does the continued 22Ne depletion of the crystallizing solid re-enrich the overlying liquid and restart distillation (oscillatorily or continuously), possibly building 22Ne-rich shells around the distilled core?

  3. The consequences of (1) and (2) for the duration and mass/abundance dependence of the distillation cooling delay, and correspondingly for the fidelity of the numerical expedients adopted at the end of distillation (freezing the inner 22Ne-rich ~25% of the stellar mass in place; artificially slowing the crystallization front) and for the use of crystallized white dwarfs as chronometers.

The same source frames companion uncertainties belonging to the same overarching objective of a complete, predictive theory of distillation cooling delays: tighter empirical or theoretical constraints on the initial 22Ne abundance and helium-envelope mass of candidate merger remnants; the secondary effects of omitted physics (rotation, magnetic fields, convective mixing in DQ-type, carbon-atmosphere white dwarfs); and the conclusive observational identification of distillation operating in other mass ranges, such as lower-mass C–O white dwarfs where delays of order 1 Gyr are predicted. An answer to the core problem need not resolve these companion strands, but progress on them alone does not close the core: without the trajectory and the termination dynamics, the predicted delay remains prescription-dependent.

References

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