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