Constraints on the origin of the ultra-high energy cosmic-rays using
  cosmic diffuse neutrino flux limits: An analytical approach
  Astrophysical neutrinos are expected to be produced in the interactions of
ultra-high energy cosmic-rays with surrounding photons. The fluxes of the
astrophysical neutrinos are highly dependent on the characteristics of the
cosmic-ray sources, such as their cosmological distributions. We study possible
constraints on the properties of cosmic-ray sources in a model-independent way
using experimentally obtained diffuse neutrino flux above 100 PeV. The
semi-analytic formula is derived to estimate the cosmogenic neutrino fluxes as
functions of source evolution parameter and source extension in redshift. The
obtained formula converts the upper-limits on the neutrino fluxes into the
constraints on the cosmic-ray sources. It is found that the recently obtained
upper-limit on the cosmogenic neutrinos by IceCube constrains the scenarios
with strongly evolving ultra-high energy cosmic-ray sources, and the future
limits from an 1 km^3 scale detector are able to further constrain the
ultra-high energy cosmic-rays sources with evolutions comparable to the cosmic
star formation rate.
