Chemical abundance patterns – fingerprints of nucleosynthesis in the first stars

The interstellar medium of low-metallicity systems undergoing star formation will show chemical abundance in-homogeneities due to supernova events enriching the medium on a local scale. If the star formation timescale is shorter than the timescale of mixing of the interstellar matter, the inhomogeneities are reflected in the surface abundances of low-mass stars and thereby detailed information on the nucleosynthesis in the first generations of supernovae is preserved. Characteristic patterns and substructures are therefore expected to be found, apart from the large scatter behaviour, in the distributions of stars when displayed in diagrams relating different element abundance ratios. These patterns emerge from specific variations with progenitor stellar mass of the supernova yields and it is demonstrated that the patterns are insensitive to the initial mass function (IMF) even though the relative density of stars within the patterns may vary. An analytical theory of the formation of patterns is presented and it is shown that from a statistical point of view the abundance ratios can trace the different nucleosynthesis sites even when mixing of the interstellar medium occurs. Using these results, it should be possible to empirically determine supernova yields from the information on relative abundance ratios of a large, homogeneous sample of extremely metal-poor Galactic halo stars.