Study of the acoustic signature of UHE neutrino interactions in water and ice

The production of acoustic signals from the interactions of ultra-high energy (UHE) cosmic ray neutrinos in water and ice has been studied. A new computationally fast and efficient method of deriving the signal is presented. This method allows the implementation of up to date parameterisations of acoustic attenuation in sea water and ice that now includes the effects of complex attenuation, where appropriate. The methods presented here have been used to compute and study the properties of the acoustic signals which would be expected from such interactions. A matrix method of parameterising the signals, which includes the expected fluctuations, is also presented. These methods are used to generate the expected signals that would be detected in acoustic UHE neutrino telescopes.

💡 Research Summary

The paper presents a comprehensive study of the acoustic signatures generated by ultra‑high‑energy (UHE) cosmic‑ray neutrino interactions in water and ice, with a focus on developing a fast, accurate computational framework suitable for large‑scale detector simulations. The authors begin by motivating acoustic detection as an attractive complement to optical and radio techniques: acoustic attenuation lengths in seawater (≈3–4 km at 10–25 kHz) and in polar ice (≈8–10 km) are orders of magnitude larger than optical scattering lengths, allowing instrumented volumes of tens to hundreds of cubic kilometres.

The core of the work is a reformulation of the thermo‑acoustic mechanism. Instead of directly integrating the pressure source term, the authors introduce the velocity potential Φ, related to pressure by p = −ρ ∂Φ/∂t and to particle velocity by v = ∇Φ. The wave equation for Φ is solved using Green’s functions, yielding an expression where Φ at an observer is a sum over contributions from infinitesimal volume elements of the particle cascade. By sampling the cascade energy density with Monte‑Carlo points proportional to deposited energy, the flight‑time distribution to a given sensor becomes a simple histogram, and Φ(t) is obtained essentially as a scaled histogram of these times. The pressure pulse follows by differentiating Φ(t). This approach reduces the computational cost dramatically while preserving the essential physics: in the far‑field the pressure pulse is proportional to the line‑of‑sight derivative of the energy deposition, and only the projection of the cascade onto the observer direction matters.

The authors then address acoustic attenuation, which in realistic media is both frequency‑dependent and, in seawater, complex (i.e., it introduces a phase shift). For seawater they adopt the Ainslie‑McColm parameterisation of the magnitude of attenuation and augment it with the complex phase derived from Lieb‑erman’s chemical‑relaxation theory. The resulting attenuation coefficient a(ω) = e^{−k(ω)r} includes two high‑pass filters (boric acid and MgSO₄) with cut‑off frequencies around 1 kHz and 100 kHz, respectively, plus a real pure‑water term. The model depends on temperature, salinity, depth, and pH, allowing site‑specific predictions (e.g., Mediterranean conditions). In ice, the dominant mechanisms are proton‑reorientation absorption and Rayleigh‑type scattering from grain boundaries; the authors use Price’s formulation for absorption and a k⁴ scattering term, yielding an almost flat absorption length of ≈10 km up to ~25 kHz, after which scattering becomes significant.

Attenuation is applied in the frequency domain (multiplication by a(ω)) and transformed back to the time domain, which is equivalent to convolving the unattenuated pulse with the medium’s impulse response. For a Gaussian source and Gaussian attenuation (as in distilled water) the convolution yields another Gaussian, and analytic expressions for the pressure pulse are derived, confirming earlier results (e.g., from Askaryan’s work) but obtained via a different route.

A novel contribution is the matrix method for signal parameterisation. The stochastic nature of the cascade (fluctuations in energy deposition and geometry) is encoded in a covariance matrix constructed from many Monte‑Carlo realizations. Sampling this matrix produces synthetic waveforms that incorporate realistic event‑by‑event variations without the need to run a full cascade simulation each time. This dramatically speeds up the generation of large signal libraries for detector response studies.

Simulation results show that a 1 J energy deposition in a Gaussian cascade produces a bipolar pressure pulse whose amplitude scales as 1/σ₀² (σ₀ being the projected standard deviation along the line of sight) and falls off as 1/ sin²θ for off‑axis observers. The peak amplitude is largest when the observer lies in the plane of the cascade’s longest axis. Complex attenuation in seawater introduces a small (~0.005 %) increase in phase velocity, leading to a modest advance of high‑frequency components for a 1 km propagation distance. The authors also compare several attenuation models (Ainslie‑McColm, Francois‑Garrison, and Mediterranean‑specific fits) and illustrate their impact on signal shape.

Overall, the paper delivers a robust, computationally efficient toolkit for predicting acoustic signals from UHE neutrino interactions, incorporating up‑to‑date complex attenuation models for both seawater and polar ice, and providing a statistical framework for signal fluctuations. These results are directly applicable to the design, optimisation, and data‑analysis pipelines of future acoustic neutrino telescopes such as those envisioned for the deep ocean or the South‑Pole ice. Future work should focus on experimental validation of the complex phase term in seawater, refinement of ice scattering parameters, and integration of the matrix signal library into full detector simulations.