Impacts of hydrogen envelope on supernova fallback and the resulting compact remnant masses

Abstract

Fallback in core-collapse supernovae plays a central role in setting compact-remnant masses and may produce late-time emission. In hydrogen rich progenitors, the reverse shock arising at the hydrogen-helium interface has the potential to dramatically enhance fallback, yet its overall impact across a broad explosion-energy range has not been systematically quantified. Using one-dimensional hydrodynamic simulations for metal-poor progenitors with $M_{\rm ZAMS}=18$-$28\,M_\odot$ and models with and without hydrogen envelopes, we explore fallback over explosion energies of $10^{48}$-$10^{52}\,{\rm erg}$. We find a robust and universal mass-transition behaviour: when the explosion energy reaches only $2$-$3$ times the binding energy of the hydrogen envelope, the reverse shock returns to the centre and sharply increases the remnant mass by $\gtrsim 2\,M_\odot$. Above this threshold, the reverse shock escapes and hydrogen-rich and stripped-envelope progenitors yield nearly identical remnant masses. By normalizing the results with the envelope binding energy, we show that all progenitor models converge to a common fallback relation. We further provide a simple analytic prescription that connects explosion energy, hydrogen-envelope binding energy, and final compact-remnant mass. This relation provides an important link between progenitor properties and compact-remnant masses, and is useful for population-synthesis and galactic chemical-evolution studies.