We have determined the oxygen abundance of HE0107-5240 from UV-OH lines detected in VLT/UVES spectra. Using a plane-parallel LTE model atmosphere, we derive [O/Fe] = +2.4, and a similar analysis of CD -38 245 yields [O/Fe] = +1.0. We estimate systematic errors due to 3D effects to be in the order of 0.3 to 0.4 dex. That is, our derived O abundances are likely overestimates: effects from thermal inhomogeneities due to convection may require that the abundances should be reduced by 0.3-0.4 dex or even more. Radial velocity data for HE0107-5240 based on high-resolution spectra show that over a time span of 373 days the radial velocity was constant at 44.5 km/s, with a 1 sigma scatter of the measurements of 0.5 km/s. However, it can not yet be ruled out that HE0107-5240 is a very long period and/or low amplitude binary. These results provide new constraints on scenarios for the origin of the abundance pattern of HE0107-5240. In particular, it seems unlikely that the large overabundances of CNO have been produced in a medium-mass AGB star which later evolved to a white dwarf. The oxygen abundance of HE0107-5240 is significantly smaller than the prediction of Umeda & Nomoto (2003) from calculated yields of a ~25 solar mass Population III star exploding as a supernova of low explosion energy (E_exp = 3 x 10^50 erg) with mixing and fallback. The scenario of Limongi et al. (2003), involving two Population III supernovae, predicts an oxygen abundance of [O/Fe] = +4.1 for HE0107-5240, in strong contradiction with the observed value. In conclusion, none of the above mentioned scenarios, in their present realizations, can satisfactorly explain the abundance pattern of HE0107-5240.
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