Sterile neutrinos in astrophysical neutrino flavor

In this paper, we study the effect of active-neutrino-sterile-neutrino mixing in the expected high-energy astrophysical neutrino flavor content. Non-unitarity in the measurement of the three-active neutrinos can be due to the existence of sterile neutrino states. We introduce the concept of the four-flavor tetrahedron in order to visualize the lack of unitarity in the astrophysical neutrino three-flavor triangle. We demonstrate that active-sterile neutrino mixings modify the allowed region of the astrophysical flavor ratio from the standard case. However, a projection of the four-flavor tetrahedron has restrictions of phase space similar to the three-flavor triangle. On the other hand, the initial presence of astrophysical sterile neutrinos drastically changes the scenario, and it allows an apparent unitarity violation in the three-flavor triangle space. Using current global fit constraints including the non-unitarity case, we also illustrate the allowed astrophysical neutrino flavor ratios. Thus, the measurement of the high-energy astrophyscal neutrino flavor content allows us to explore sterile neutrinos independently of the sterile neutrino mass scale. These are topics of investigation for current and future neutrino telescopes.