Probing the existence of very massive first stars

We present a novel approach aimed at identifying the key chemical elements to search for the (missing) descendants of very massive first stars exploding as pair instability supernovae (PISN). Our simple and general method consists in a parametric study accounting for the unknowns related to early cosmic star formation and metal-enrichment. Our approach allow us to define the most likely [Fe/H] and abundance ratios of long-lived stars born in interstellar media polluted by the nucleosynthetic products of PISN at a {> } 90{{ per cent}}, 70{{ per cent}}, and 50{{ per cent}} level. In agreement with previous works, we show that the descendants of very massive first stars can be most likely found at [Fe/H] ≈ -2. Further, we demonstrate that to search for an underabundance of [(N, Cu, Zn)/Fe] < 0 is the key to identify these rare descendants. The `killing elements' N, Zn, and Cu are not produced by PISN, so that their sub-Solar abundance with respect to iron persists in environments polluted by further generations of normal core-collapse supernovae up to a 50{{ per cent}} level. We show that the star BD+80° 245, which has [Fe/H] = -2.2, [N/Fe] = -0.79, [Cu/Fe] = -0.75, and [Zn/Fe] = -0.12 can be the smoking gun of the chemical imprint from very massive first stars. To this end we acquired new spectra for BD+80° 245 and re-analysed those available from the literature accounting for non-local thermodynamic equilibrium corrections for Cu. We discuss how to find more of these missing descendants in ongoing and future surveys to tightly constrain the mass distribution of the first stars.