The spectrum and flavor composition of the astrophysical neutrinos in IceCube

We fit the energy distribution of the IceCube starting events by a model which involves four parameters in the neutrino spectrum, namely three normalizations $n_e,n_\mu,n_\tau$ and a common power-law index $\gamma$, with a fixed background simulated by IceCube. It is found that the best fit index is $\gamma = 2.7$ with $\chi^2_{\rm min} = 32.3/24\,{\rm dof}$. As for the two parameter model involving a democratic normalization and an index, the best fit is at $\gamma = 2.8$ with $\chi^2_{\rm min} = 33.9/26\,{\rm dof}$. The flavored model and the democratic model do not have much difference in the quality of the (energy-spectrum) fit. The standard $1:1:1$ composition is not disfavored by the current data.