True PISN descendant: implications for the mass distribution of the first stars

The initial mass function (IMF) of the first Pop III stars remains a persistent mystery. Their predicted massive nature implies the existence of stars exploding as pair-instability supernovae (PISN), but no observational evidence had been found. Now, the LAMOST survey claims to have discovered a pure PISN descendant, J1010+2358, at ${\rm [Fe/H]}= -2.4$. Here we confirm that a massive 250-260 ${\rm M_\odot}$ PISN is needed to reproduce the abundance pattern of J1010+2358. However, the PISN contribution can be as low as 10%, since key elements are missing to discriminate between scenarios. We investigate the implications of this discovery for the Pop III IMF, by statistical comparison with the predictions of our cosmological galaxy formation model, NEFERTITI. First, we show that the non-detection of mono-enriched PISN descendants at ${\rm [Fe/H]}<-2.5$ allows us to exclude: (i) a flat IMF at a 90% confidence level; and (ii) a Larson type IMF with characteristic mass $m_{\rm ch}/{\rm M_\odot} > 191.16x - 132.44$, where x is the slope, at a 75% confidence level. Secondly, we show that if J1010+2358 has only inherited <70% of its metals from a massive PISN, no further constraints can be put on the Pop III IMF. If, instead, J1010+2358 will be confirmed to be a nearly pure (>90%) PISN descendant, it will offer strong and complementary constraints on the Pop III IMF, excluding the steepest and bottom-heaviest IMFs: $m_{\rm ch}/{\rm M_\odot} < 143.21x - 225.94$. Our work shows that even a single detection of a pure PISN descendant can be crucial to our understanding of the mass distribution of the first stars.