In a new paper with Markus Ahlers, we introduce a method to infer the flavor composition of high-energy astrophysical neutrinos at their sources, based on measurements of the flavor composition at Earth:

Inferring the flavor of high-energy astrophysical neutrinos at their sources
Mauricio Bustamante, Markus Ahlers

To do this, we effectively revert the effect of flavor oscillations, while taking into account uncertainties in the neutrino mixing parameters.

We apply the method to flavor measurements published by IceCube, and to projections for the near-future IceCube upgrade and the more distant IceCube-Gen2.

In the illustrative, physically motivated case where there is no production of tau neutrinos at the sources, we can recover the fraction of electron neutrinos produced at the sources:

Presently (“IceCube 2015”), we find that neutrino production by the decay of high-energy pions is compatible with the flavor and oscillation data, with a slight preference for sources harboring strong magnetic fields which make intermediate muons lose energy by synchrotron radiation.  In the future, the IceCube ugprade and IceCube-Gen2 have the potential to single out the neutrino production mechanism