Electron-capture Supernova Candidates from Light Curves: Implications for Their Progenitors and Explosion Properties

Core-collapse supernovae are explosions of massive stars. While most massive stars end as iron-core-collapse supernovae, less massive stars are expected to explode as electron-capture supernovae (ECSNe), defining the low-mass boundary of core-collapse supernovae. ECSNe were proposed $\sim 40$ years ago, and first-principles simulations predict their successful explosions with low energies of $\sim {10}^{50}$~erg. Nevertheless, only one convincing candidate, SN~2018zd, has been proposed other than SN~1054, the progenitor of the Crab Nebula. We search for ECSN candidates among Type~II SNe from the literature and a public Zwicky Transient Facility sample, using a color-based diagnostic, selecting ten candidates with blue colors at the middle of the plateau. We classify three as $\mathit{\text{gold}}$, for which a spectrum around the middle of the plateau disfavors strong circumstellar-medium interaction that would make the SN bluer, and seven as $\mathit{\text{silver}}$ without such spectra. Comparing the observed multicolor light curves with radiation-hydrodynamical models, we infer the explosion energies, $(0.4-1.7)\times {10}^{50}$~erg for the $\mathit{\text{gold}}\mathit{\text{candidates}}$ and $(0.4-2.7)\times {10}^{50}$~erg including the $\mathit{\text{silver}}\mathit{\text{candidates}}$, consistent with first-principles predictions and the mass-loss rates, $3\times {10}^{-3}-3\times {10}^{-2}{M}_{\odot }{\mathrm{y}\mathrm{r}}^{-1}$ for the $\mathit{\text{gold}}\mathit{\text{candidates}}$, which remain similar when the $\mathit{\text{silver}}\mathit{\text{candidates}}$ are included, higher than those expected for the early super-asymptotic-giant-branch phase. The ECSN occurrence ratios among SNe~II are inferred as $3.0_{-2.9}^{+10.6}$ and $15.7_{-12.7}^{+17.3}\mathrm{\%}$ from the $\mathit{\text{gold}}$ and $\mathit{\text{silver}}\mathit{\text{candidates}}$, respectively, which we interpret as lower and upper limits. To robustly identify ECSNe and refine this ratio, spectroscopic follow-ups of ECSN candidates around the middle of the plateau are essential.