Modeling the South Polar ice refractive index profile for ultra-high energy neutrino (UHEN) detectors

Current polar experiments seek measurement of UHEN via detection of radio waves created in neutrino-ice collision. At the lowest end of the detectable neutrino energy range (100 PeV), experiment sensitivity is limited by ray bending in the upper 150m of ice, where the densification process leads to a refractive index variable with depth. We develop an in-situ index of refraction profile using the transit time of radio signals broadcast from an englacial transmitter to 2-5 km distant radio-frequency receivers deployed at depths up to 200 m. Maxwell's equations admit two ray propagation solutions, corresponding to a direct path (D) and also a refracted path (R); the direct vs. refracting (dt(D,R)) timing differences measured by the Askaryan Radio Array (ARA) astrophysics neutrino observatory provide powerful calibration information. Measurements of the timing differences between D and R ray paths from deep pulser (DP) signals to all five of the ARA stations provide constraints on the index of refraction profile near South Pole. A DP source which was lowered into a borehole and illuminates most stations over a transmit depth range of 700-1200m was used in our calibration. We constrain the refractive index profile by simulating D and R ray paths via ray tracing and comparing them to measured dt(D,R) signals in the 5 stations. Previous Antarctic ice density data is used as a basis for n(z), and assumed to follow an exponential ansatz. We demonstrate that our data strongly favors a multi-phase densification model familiar to glaciologists rather than a simple exponential scale height model