2025ApJ...994...19M

Carbon-deficient giants (CDGs) are a rare and chemically peculiar class of stars whose origins remain under active investigation. We present an asteroseismic analysis of the entire known CDG population, selecting 129 stars observed by Kepler, K2, and TESS to obtain seismic constraints. We detect solar-like oscillations in 43 CDGs. By measuring ${\nu }_{{\rm{\max }}}$ and applying seismic scaling relations, we determine precise masses for these stars, finding that 79% are low mass (M ≲ 2 M_⊙). The luminosity distribution is bimodal, and the CDGs separate into three chemically and evolutionarily distinct groups, characterized by clear trends in sodium and CNO abundances, α-element enhancement, and kinematics. We find that two of these groups are only distinguished by their initial α-element abundances, thus effectively reducing the number of groups to two. Lithium enrichment is common across all groups, linking CDGs to lithium-rich giants and suggesting a shared evolutionary origin. We find that the spectroscopic $\mathrm{log}g$ is systematically offset from seismic values. Group 1 CDG patterns are most consistent with formation through core He-flash mixing, while the more massive and more chemically processed Groups 2 and 2α likely formed through mergers involving helium white dwarfs, possibly in hierarchical triples. Pollution from asymptotic giant branch stars appears very unlikely, given the unchanged [C+N+O] abundance across all groups.