Astrophysical Neutrinos: Flavor Ratios Depend on Energy

Electromagnetic (and adiabatic) energy losses of π's and μ's modify the flavor ratio (measured at Earth) of neutrinos produced by π decay in astrophysical sources, ${{Φ}}_{{{ν}}ₑ}{:}{{Φ}}_{{{ν}}_{{μ}}}{:}{{Φ}}_{{{ν}}_{{τ}}}$, from $1{:}1{:}1$ at low energy to $1{:}1.8{:}1.8$ at high energy. The transition occurs over 1--2 decades of ${ν}$ energy, and is correlated with a modification of the neutrino spectrum. For ${γ}$-ray bursts, e.g., the transition is expected at ${~}100 TeV$ and may be detected by km-scale ${ν}$ telescopes. Measurements of the transition energy and energy width will provide unique probes of the physics of the sources. ${π}$ and ${μ}$ energy losses also affect the ratio of ${{{ν}}}ₑ$ flux to total ${ν}$ flux, which may be measured at the $W$ resonance (6.3 PeV): It is modified from $1/6$ ($1/15$) at low energy to $1/9$ (practically 0) at high energy for neutrinos produced in $pp$ ($p{γ}$) interactions.