Pop III i-process nucleosynthesis and the elemental abundances of SMSS J0313-6708 and the most iron-poor stars

We have investigated a highly energetic H-ingestion event during shell He burning leading to H-burning luminosities of log (L_H/L_⊙) ∼ 13 in a 45 M_⊙ Pop III massive stellar model. In order to track the nucleosynthesis which may occur in such an event, we run a series of single-zone nucleosynthesis models for typical conditions found in the stellar evolution model. Such nucleosynthesis conditions may lead to i-process neutron densities of up to ∼10¹³ cm^-3. The resulting simulation abundance pattern, where Mg comes from He burning and Ca from the i process, agrees with the general observed pattern of the most iron-poor star currently known, SMSS J031300.36-670839.3. However, Na is also efficiently produced in these i-process conditions, and the prediction exceeds observations by ∼2.5 dex. While this probably rules out this model for SMSS J031300.36-670839.3, the typical i-process signature of combined He burning and i process of higher than solar [Na/Mg], [Mg/Al], and low [Ca/Mg] is reproducing abundance features of the two next most iron-poor stars HE 1017-5240 and HE 1327-2326 very well. The i process does not reach Fe which would have to come from a low level of additional enrichment. i process in hyper-metal-poor or Pop III massive stars may be able to explain certain abundance patterns observed in some of the most metal-poor CEMP-no stars.