Neon Cluster Formation and Phase Separation during White Dwarf Cooling

Recent observations of Galactic white dwarfs (WDs) with Gaia suggest there is a population of massive crystallizing WDs exhibiting anomalous cooling— the Q branch. While single-particle $^{22}$Ne sedimentation has long been considered a possible heat source, recent work suggests that $^{22}$Ne must separate into clusters, enhancing diffusion, in order for sedimentation to provide heating on the observed timescale. We show definitively that $^{22}$Ne cannot separate to form clusters in C/O WDs using molecular dynamics simulations, and we further present a general C/O/Ne phase diagram showing that strong $^{22}$Ne enrichment is not achievable for $^{22}$Ne abundance $>30$\%. We conclude that the anomalous heating cannot be due to $^{22}$Ne cluster sedimentation and that Q branch WDs may have an unusual composition, possibly rich with heavier elements.