Nucleosynthesis Constraints on the Energy Growth Timescale of a Core-collapse Supernova Explosion

Details of the explosion mechanism of core-collapse supernovae (CCSNe) are not yet fully understood. There is an increasing number of numerical examples by ab-initio core-collapse simulations leading to an explosion. Most, if not all, of the ab-initio core-collapse simulations represent a `slow' explosion in which the observed explosion energy ($\sim 10^{51}$ ergs) is reached in a timescale of $\gtrsim1$ second. It is, however, unclear whether such a slow explosion is consistent with observations. In this work, by performing nuclear reaction network calculations for a range of the explosion timescale $t_{\rm grow}$, from the rapid to slow models, we aim at providing nucleosynthetic diagnostics on the explosion timescale. We employ one-dimensional hydrodynamic and nucleosynthesis simulations above the proto-neutron star core, by parameterizing the nature of the explosion mechanism by $t_{\rm grow}$. The results are then compared to various observational constraints; the masses of $^{56}$Ni derived for typical CCSNe, the masses of $^{57}$Ni and $^{44}$Ti observed for SN 1987A, and the abundance patterns observed in extremely metal-poor stars. We find that these observational constraints are consistent with the `rapid' explosion ($t_{\rm grow} \lesssim 250$ ms), and especially the best match is found for a nearly instantaneous explosion ($t_{\rm grow} \lesssim 50$ ms). Our finding places a strong constraint on the explosion mechanism; the slow mechanism ($t_{\rm grow} \gtrsim 1000$ ms) would not satisfy these constraints, and the ab-inito simulations will need to realize a rapid explosion.