Euclid detectability of pair instability supernovae in binary population synthesis models consistent with merging binary black holes

We infer the expected detection number of pair instability supernovae (PISNe) during the operation of the Euclid space telescope based on binary population models. Our models reproduce the global maximum of the rate at the primary BH mass of $\sim 9-10$ $M_\odot$, and the overall gradient of the primary BH mass distribution in the binary BH merger rate consistent with recent observations. We consider different PISN conditions depending on the $^{12}$C$(\alpha, \gamma)^{16}$O reaction rate. The fiducial and $3\sigma$ models adopt the standard and $3\sigma$-smaller reaction rate, respectively. Our fiducial model predicts that Euclid detects several hydrogen-poor PISNe. For the $3\sigma$ model, detection of $\sim 1$ hydrogen-poor PISN by Euclid is expected if the stellar mass distribution extends to $M_{\max} = 600 M_\odot$, but the expected number becomes significantly smaller if $M_{\max} = 300 M_\odot$. We may be able to distinguish the fiducial and $3\sigma$ models by the observed PISN rate. This will help us to constrain the origin of binary BHs and the reaction rate, although there remains degeneracy between $M_{\max}$ and the reaction rate. PISN ejecta mass estimates from light curves and spectra obtained by follow-up observations would be important to disentangle the degeneracy.