The flavor composition of ultra-high-energy cosmic neutrinos: measurement forecasts for in-ice radio-based EeV neutrino telescopes

In-ice radio-detection is a promising technique to discover and characterize ultra-high-energy (UHE) neutrinos, with energies above 100 PeV, adopted by present - ARA, ARIANNA, and RNO-G - and planned - IceCube-Gen2. So far, their ability to measure neutrino flavor has remained unexplored. We show and quantify how the neutrino flavor can be measured with in-ice radio detectors using two complementary detection channels. The first channel, sensitive to $\nu_e$, identifies them via their charged-current interactions, whose radio emission is elongated in time due to the Landau-Pomeranchuk-Migdal effect. The second channel, sensitive to $\nu_\mu$ and $\nu_\tau$, identifies events made up of multiple showers generated by the muons and taus they generate. We show this in state-of-the-art forecasts geared at IceCube-Gen2, for representative choices of the UHE neutrino flux. This newfound sensitivity could allow us to infer the UHE neutrino flavor composition at their sources - and thus the neutrino production mechanism - and to probe UHE neutrino physics.