Analytic Aperture Calculation and Scaling Laws for Radio Detection of Lunar-Target Ultra-High-Energy Neutrinos

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 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 lower neutrino energies. Detecting neutrinos from Earth near the GZK regime will likely require radio telescope arrays with extremely large collecting area (A e ∼ 10 6 m 2 ) and hundreds of hours 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 (ν ∼ > 300 MHz) and higher energies (E ∼ > 10 21 eV).

Radio Cherenkov signals from the Moon: Neutrinos and cosmic rays

“…For the higher frequencies, the downward signals that emerge from the smooth surface approximation (ds) are smaller than the downward signals accounting for surface roughness. This comes from f 0 ∆ 0 ∼ 0.01 − 0.1 which is small compared to the solid angle characterizing the surface roughness, σ 0 0.2, as discussed by Gayley et al [27]. In Fig.…”

“…[27]. The effective aperture A M (E ν ) combines the neutrino interaction probability, effective area (A) and effective solid angle,…”

“…With flux attenuation, the integral over h in the evaluation of the effective aperture results in a factor of | sin α|L CR , where α is the angle of the incident cosmic ray with respect to the horizontal, as in Ref. [27]. This modification of eq.…”

“…In Section III, we evaluate the event rates using the standard model neutrino nucleon cross section and for some rescaled cross sections, all using the approximate analytic GMJ expression of Ref. [27]. The dependence of the event rate on detection characteristics, namely the radio frequency and minimum detectable electric field, is shown.…”

A lunar radio experiment with the Parkes radio telescope for the LUNASKA project

“…Further away on the limb, a radially aligned pulse more closely matches one or the other polarisation of the beam, which results in greater limb coverage: 20%, calculated as for the limb beam. These limb coverage values are suitable for inclusion in particle aperture models such as that of Gayley et al [39]. The limb coverage for both beams is shown in Fig.…”