Measuring the spectra of high energy neutrinos with a kilometer-scale neutrino telescope

We investigate the potential of a future kilometer-scale neutrino telescope, such as the proposed IceCube detector in the South Pole, to measure and disentangle the yet unknown components of the cosmic neutrino flux, the prompt atmospheric neutrinos coming from the decay of charmed particles and the extra-galactic neutrinos in the 10 TeV to 1 EeV energy range. Assuming a power law type spectra, $d{\phi }_{\nu }{/dE}_{\nu }\sim \alpha E_{\nu }^{\beta },$ we quantify the discriminating power of the IceCube detector and discuss how well we can determine magnitude $\left(\alpha \right)$ as well as slope $\left(\beta \right)$ of these two components of the high energy neutrino spectrum, taking into account the background coming from the conventional atmospheric neutrinos.