The chemical composition of extremely metal-poor stars (EMP stars; [Fe/H]<~ -3) is a unique tracer of early nucleosynthesis in the Galaxy. As such stars are rare, we wish to find classes of luminous stars which can be studied at high resolution. We aim to determine the detailed chemical composition of the two EMP stars CS30317-056 and CS22881-039, originally thought to be red horizontal-branch (RHB) stars, and compare it to earlier results for EMP stars as well as to nucleosynthesis yields from various supernova (SN) models. In the analysis, we discovered that our targets are in fact the two most metal-poor RR Lyrae stars known. Our detailed abundance analysis, taking into account the variability of the stars, is based on VLT/UVES spectra (R~ 43000) and 1D LTE OSMARCS model atmospheres and synthetic spectra. For comparison with SN models we also estimate NLTE corrections for a number of elements. We derive LTE abundances for the 16 elements O, Na, Mg, Al, Si, S, Ca, Sc, Ti, Cr, Mn, Fe, Co, Ni, Sr and Ba, in good agreement with earlier values for EMP dwarf, giant and RHB stars. Li and C are not detected in either star. NLTE abundance corrections are newly calculated for O and Mg and taken from the literature for other elements. The resulting abundance pattern is best matched by model yields for supernova explosions with high energy and/or significant asphericity effects. Our results indicate that, except for Li and C, the surface composition of EMP RR Lyr stars is not significantly affected by mass loss, mixing or diffusion processes; hence, EMP RR Lyr stars should also be useful tracers of the chemical evolution of the early Galactic halo. The observed abundance ratios indicate that these stars were born from an ISM polluted by energetic, massive (25 - 40M*) and/or aspherical supernovae, but the NLTE corrections for Sc and certain other elements do play a role in the choice of model.
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