  Core collapse of massive stars leads to different fates for various physical
factors, which gives different spectra of the emitted neutrinos. We focus on
the supernova relic neutrinos (SRNs) as a probe to investigate the stellar
collapse fate. We present the SRN fluxes and event rate spectra at a detector
for three resultant states after stellar core collapse, the typical mass
neutron star, the higher mass neutron star, or the failed supernova forming a
black hole, based on different nuclear equations of state. Then possible SRN
fluxes are formed as mixtures of the three components. We also show the
expected sensitivities at the next-generation water-based Cherenkov detectors,
SK-Gd and Hyper-Kamiokande, as constraining the mixture fractions. This study
provides a practical example of extracting astrophysical constraints through
SRN measurement.
