Phosphorus abundances and multi-element co-enrichment in nearby FGK stars

The distribution of bio-essential elements is key to assessing the chemical `fertility' for life in a galactic context. Among these, phosphorus plays a central role in biomolecules, but it is relatively scarce and difficult to measure in stellar spectra. We aim to characterise phosphorus abundances in nearby FGK stars and quantify how P co-varies with other bio-related elements in different Galactic disk populations. We analysed phosphorus abundances for 233 FGK stars in the solar neighbourhood from the Hypatia Catalog. We studied P/Fe as a function of Fe/H and other elemental abundances, separating thin- and thick-disk stars. We used non-parametric tests and bootstrap resampling to derive median trends, confidence intervals, correlation coefficients, and residual correlations at fixed Fe/H . We also investigated molar ratios involving P relevant to planetary mineralogy. We find a P/Fe -- Fe/H trend broadly similar to that of α elements, supporting a dominant origin in core-collapse supernovae, with some deviations that suggest additional nucleosynthetic channels. Phosphorus shows strong positive correlations with several CHNOPS, α, and Fe-peak elements, especially in the thin disk, where stars with higher phosphorus abundances are enriched in multiple bio-essential and rock-forming species. These co-enrichment patterns remain significant in residual analyses at fixed Fe/H , indicating that they are not a trivial by-product of global metallicity. Thin-disk stars also exhibit higher abundances than thick-disk stars for many elements. The molar P/Mg and P/Si ratios of the Sun are representative of the local stellar population, whereas the relatively elevated solar P/O may have favoured phosphorus bioavailability on Earth. Our study provides a systematic and statistically robust view of how P co-varies with other CHNOPS and α elements in the solar neighbourhood. The results reveal a genuine multi-element co-enrichment pattern beyond metallicity effects and support the use of phosphorus as a tracer of the chemical fertility of galactic environments.