We investigate the flux and event rate of supernova relic neutrinos ( SRNs ) and discuss their implications for the cosmic star formation rate .
Since SRNs are diffuse neutrino background emitted from past core-collapse supernova explosions , they contain fruitful information on the supernova rate in the past and present universe , as well as on the supernova neutrino spectrum itself .
As reference models , we adopt the supernova rate model based on recent observations and the supernova neutrino spectrum numerically calculated by several groups .
In the detection energy range E _ { e } > 10 MeV , which will possibly be a background-free region in the near future , the SRN event rate is found to be 1–2 yr ^ { -1 } at a water Cerenkov detector with a fiducial volume of 22.5 kton , depending on the adopted neutrino spectrum .
We also simulate the expected signal with one set of the reference models by using the Monte Carlo method and then analyze these pseudodata with several free parameters , obtaining the distribution of the best-fit values for them .
In particular , we use a parameterization such that R _ { SN } ( z ) = R _ { SN } ^ { 0 } ( 1 + z ) ^ { \alpha } , where R _ { SN } ( z ) is the comoving supernova rate density at redshift z and R _ { SN } ^ { 0 } and \alpha are free parameters , assuming that the supernova neutrino spectrum and luminosity are well understood by way of a future Galactic supernova neutrino burst or the future development of numerical supernova simulations .
The obtained 1 \sigma errors for these two parameters are found to be \delta \alpha / \langle \alpha \rangle = 30 \%~ { } ( 7.8 \% ) and \delta R _ { SN } ^ { 0 } / \langle R _ { SN } ^ { 0 } \rangle = 28 \%~ { } ( 7.7 \% ) for a detector with an effective volume of 22.5 kton \times 5 yr ( 440 kton \times 5 yr ) , where one of the parameters is fixed .
On the other hand , if we fix neither of the values for these two parameters , the expected errors become rather large , \delta \alpha / \langle \alpha \rangle = 37 \% and \delta R _ { SN } ^ { 0 } / \langle R _ { SN } ^ { 0 } \rangle = 55 \% , even with an effective volume of 440 kton \times 5 yr .