Updating the $^{56}$Ni Problem in Core-collapse Supernova Explosion

Details of the core-collapse supernova (CCSN) explosion mechanism still need to be fully understood. There is an increasing number of successful examples of reproducing explosions in multidimensional hydrodynamic simulations, but subsequent studies pointed out that the growth rates of the explosion energy $\dot{E}_\mathrm{expl}$ of these simulations are insufficient to produce enough $^{56}$Ni to match observations. This issue is known as the `$^{56}$Ni problem' in CCSNe. Recently, however, some studies have suggested that this $^{56}$Ni problem is derived from the simplicity of the explosion model. In response, we investigate the effect of the explosion energy growth rate $\dot{E}_\mathrm{expl}$ on the behavior of nucleosynthesis in CCSNe in a more realistic model. We employ the 1D Lagrangian hydrodynamic code, in which we take neutrino heating and cooling terms into account with the light-bulb approximation. We reiterate that, consistent with previous rebuttal studies, there is the $^{56}$Ni problem: Although $^{56}$Ni is synthesized to almost the same mass coordinate independent of $\dot{E}_\mathrm{expl}$, some of the innermost material in the low-$\dot{E}_\mathrm{expl}$ model failed to escape, leading to a shift in the innermost mass coordinate of the ejecta to the outer positions. Comparing our results with observations, we find that while modern slow explosions can, in principle, reproduce observations of standard Type II SNe, this is not possible with stripped-envelope SNe. Our finding places a strong constraint on the explosion mechanism. There are significant differences in the progenitor structures and the explosion mechanism between Type II and stripped-envelope SNe.