Search for supernova neutrinos and constraint on the galactic star formation rate with the KamLAND data

We present the results of a search for core-collapse supernova neutrinos, using long-term KamLAND data from 2002 March 9 to 2020 April 25. We focus on the electron antineutrinos emitted from supernovae in the energy range of 1.8--111 MeV. Supernovae will make a neutrino event cluster with the duration of $\sim$10 s in the KamLAND data. We find no neutrino clusters and give the upper limit on the supernova rate as to be 0.15 yr$^{-1}$ with a 90% confidence level. The detectable range, which corresponds to a >95% detection probability, is 40--59 kpc and 65--81 kpc for core-collapse supernovae and failed core-collapse supernovae, respectively. This paper proposes to convert the supernova rate obtained by the neutrino observation to the Galactic star formation rate. Assuming a modified Salpeter-type initial mass function, the upper limit on the Galactic star formation rate is <(17.5--22.7) $M_{\odot} \mathrm{yr}^{-1}$ with a 90% confidence level.