Analytic Aperture Calculation and Scaling Laws for Radio Detection of Lunar-Target UHE Neutrinos

TL;DR

This paper derives analytic formulas and scaling laws for the radio detection aperture of ultra-high-energy neutrinos hitting the Moon, improving understanding of detection capabilities and informing future observational strategies.

Contribution

It provides the first closed-form analytic expressions for the lunar neutrino detection aperture, validated against simulations, and explores how observational parameters influence detection prospects.

Findings

Analytic aperture expressions agree with Monte Carlo simulations.

Downward neutrinos dominate at low frequencies, upward at high frequencies.

Detection of GZK neutrinos requires large radio arrays and long exposure times.

Abstract

We derive analytic expressions, and approximate them in closed form, for the effective detection aperture for Cerenkov radio emission from ultra-high-energy neutrinos striking the Moon. The resulting apertures are in good agreement with recent Monte Carlo simulations and support the conclusion of James & Protheroe (2009)that neutrino flux upper limits derived from the GLUE search (Gorham et al.2004) were too low by an order of magnitude. We also use our analytic expressions to derive scaling laws for the aperture as a function of observational and lunar parameters. We find that at low frequencies downward-directed neutrinos always dominate, but at higher frequencies, the contribution from upward-directed neutrinos becomes increasingly important, especially at low neutrino energies. Detecting neutrinos from Earth near the GZK regime will likely require radio telescope arrays with extremely large collecting area and hundreds of hour of exposure time. Higher energy neutrinos are most easily detected using lower frequencies. Lunar surface roughness is a decisive factor for obtaining detections at higher frequencies and higher energies.