Expected star-to-star scatter in [Si/Fe] for core collapse SNe. The top panel shows the expected maximum range in [Si/Fe] for stars enriched by single Type II SNe. The solid curve denotes the probability density function (PDF) assuming SN yields by Nomoto et al. (2006), while the dashed curve (SN mass range 10 ≤ m/ℳ⊙ ≤ 40) and the dotted curve (10 ≤ m/ℳ⊙ ≤ 100) denote the PDFs assuming yields by Heger & Woosley (2008). Each PDF is convolved with a Gaussian (σ = 0.14) to account for the observational uncertainty in [Si/Fe]. The corresponding 1-σ dispersions are shown as solid (σ = 0.33), dashed (σ = 0.23), and dotted (σ = 0.27) thin lines, centered at the respective mean of each distribution. The grey thin line at [Si/Fe] = 0.53 denotes the observational star-to-star scatter (σ = 0.22) below [Fe/H] = −3. The bottom panel shows the full (convolved) distribution of model stars (small black dots) in the [Fe/H] – [Si/Fe] plane. The observations are shown as red dots (upper limits are shown as triangles), for comparison. The star-to-star scatter below [Fe/H] = −3 in the simulation is σ ≃ 0.23. Note the small number of EMP stars below [Si/Fe] ~ 0. These stars have been partly enriched by electron capture SNe in the mass range 8 ≤ m/ℳ⊙ ≤ 10, which produce very small amounts of Si. The SN II (Fe-core collapse) yields are taken from Nomoto et al. (2006), while the electron capture SN yields are taken from Wanajo et al. (2009).
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