Potassium abundances in extremely metal poor stars: Implications for nucleosynthesis in the final stages of massive star evolution

We present a potassium (K) abundance analysis in extremely metal-poor (EMP) stars based on high-resolution ($R\sim 60000$) spectra obtained with the High Dispersion Spectrograph on the Subaru Telescope, covering the K I resonance lines at 766 and 769 nm. One-dimensional local thermodynamic equilibrium (LTE) abundances of K and other elements, including Na, Mg, Ca, Ti, Cr, and Ni, were derived using spectral synthesis. Non-local thermodynamic equilibrium (NLTE) corrections were applied to the K abundances by interpolating a precomputed grid of corrections based on stellar parameters and the LTE K abundance. We detected K I lines in seven stars with [Fe/H]$< -3.0$ and derived upper limits for other stars in the same metallicity regime, making this sample well-suited for investigating the nucleosynthesis origins of K in the early universe. We found that the [K/Fe] and [K/Ca] ratios of the seven stars are enhanced relative to the solar value, with a scatter of approximately 0.1 dex, as small as the typical measurement uncertainty. Under the assumption that each star formed from gas purely enriched by a single or a few massive stars' supernovae, the small scatter in [K/Fe] and [K/Ca], contrasted with the $\sim$0.7 dex scatter in [Na/Mg] ratios (after NLTE correction), suggests that the production of K in massive stars or their supernovae is independent of the processes that drive Na/Mg variation. These findings demonstrate that K abundances in EMP stars, and their correlations with other elemental abundances, can serve as sensitive tracers of the physical mechanisms governing the final evolutionary stages of massive stars and their supernova explosions.