Some ancient, dim, metal-poor stars may have formed in the ashes of the first supernovae (SNe). If their chemical abundances can be reconciled with the elemental yields of specific Population III (Pop III) explosions, they could reveal the properties of primordial stars. But multidimensional simulations of such explosions are required to predict their yields because dynamical instabilities can dredge material up from deep in the ejecta that would otherwise be predicted to fall back on to the central remnant and be lost in one-dimensional (1D) models. We have performed two-dimensional (2D) numerical simulations of two low-energy Pop III SNe, a 12.4 Msun explosion and a 60 Msun explosion, and find that they produce elemental yields that are a good fit to those measured in the most iron-poor star discovered to date, SMSS J031300.36-670839.3 (J031300). Fallback on to the compact remnant in these weak explosions accounts for the lack of measurable iron in J031300 and its low iron-group abundances in general. Our 2D explosions produce higher abundances of heavy elements (atomic number Z > 20) than their 1D counterparts due to dredge-up by fluid instabilities. Since almost no Ni is ejected by these weak SNe, their low luminosities will prevent their detection in the near-infrared with the James Webb Space Telescope and future 30-m telescopes on the ground. The only evidence that they ever occurred will be in the fossil abundance record.
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