[Paper Review] Coherent radio emission from the cosmic ray air shower sudden death

B. Revenu, Vincent Marin|arXiv (Cornell University)|Jul 22, 2013

Astrophysics and Cosmic Phenomena2 references4 citations

TL;DR

This paper proposes that the sudden deceleration of secondary electrons and positrons when they reach the ground generates a coherent radio signal at frequencies below 20 MHz, detectable via simple antennas. Simulations show this 'sudden death' signal is linearly proportional to primary energy, scales as 1/distance, and enables precise timing and estimation of the atmospheric depth of maximum electric field production ($X_{ ext{max}}^{ ext{prod}}$), offering a new method to infer primary cosmic ray properties.

ABSTRACT

We describe the characteristics of a new radio signal, generated by the secondary electrons and positrons of the shower front when they reach the ground. The very fast deceleration of these particles induces the coherent emission of an electric field at frequencies smaller than 20 MHz. We show, using simulations with the code SELFAS, that this sudden death signal should be detectable with a simple dedicated antenna and could provide many informations on the shower, in particular the nature of the primary cosmic ray. We also show that this signal permits to estimate the atmospheric depth of maximum of electric field emission X_{max}^{prod}, which occurs max well before the atmospheric depth corresponding to the maximum number of secondary particles in the shower (Xmax). Observation of this signal should be considered for the design of future radio experiments.

Motivation & Objective

• To identify and characterize a new coherent radio emission mechanism associated with the termination of cosmic ray air showers at ground level.
• To explain the observed anomalously high low-frequency radio signals (below 20 MHz) in previous experiments that cannot be accounted for by standard geomagnetic or Askaryan mechanisms.
• To demonstrate that the sudden death of shower particles at ground level produces a detectable, coherent signal sensitive to the full electromagnetic shower component.
• To show that this signal enables precise timing and estimation of $X_{ ext{max}}^{ ext{prod}}$, the atmospheric depth of maximum electric field production, which precedes $X_{ ext{max}}$ (maximum particle density).

Proposed method

• Simulations using the SELFAS code to model the electromagnetic fields generated by secondary electrons and positrons during their final deceleration at ground level.
• Analysis of the power spectral density (PSD) of the electric field signal in both horizontal (EW) and vertical polarizations across varying core distances and shower geometries.
• Calculation of the lateral distribution function (LDF) of the sudden death pulse (SDP), comparing it to the prompt pulse (PP) from shower development in the atmosphere.
• Use of geometric and kinematic models to relate the time delay of the SDP signal to the distance from the shower core, enabling core reconstruction via time-of-flight triangulation.
• Derivation of the polarization direction of the SDP as proportional to the vector $\boldsymbol{\beta} - (\mathbf{n} \cdot \boldsymbol{\beta})\mathbf{n}$, where $\mathbf{n}$ is the unit vector from core to observer and $\boldsymbol{\beta}$ is the shower axis direction.
• Estimation of $X_{ ext{max}}^\text{prod}$ by identifying the atmospheric depth corresponding to the peak of the electric field emission rate during the final particle deceleration.

Experimental results

Research questions

• RQ1 What causes the anomalously strong low-frequency radio signals (below 20 MHz) observed in past air shower experiments, which exceed predictions from standard geomagnetic and Askaryan mechanisms?
• RQ2 Can the sudden deceleration of secondary electrons and positrons at ground level produce a coherent radio emission that is detectable and distinct from the prompt shower signal?
• RQ3 How does the amplitude and coherence of the sudden death pulse (SDP) scale with primary energy, core distance, and shower geometry?
• RQ4 Can the SDP signal be used to determine the atmospheric depth $X_{ ext{max}}^\text{prod}$ of maximum electric field production, and how does it relate to the longitudinal shower profile?
• RQ5 What is the polarization and timing structure of the SDP, and can it be used to reconstruct the shower core position and primary particle properties?

Key findings

• The sudden death signal (SDP) is coherent up to approximately 20 MHz, independent of core distance, unlike the prompt pulse (PP), which loses coherence at higher frequencies depending on observer distance.
• The SDP amplitude is approximately 15 μV/m at 100 m from the shower core for a vertical 1 EeV proton shower, scaling linearly with primary energy and decreasing as 1/distance.
• The lateral distribution function (LDF) of the SDP is less steep than that of the prompt pulse, explaining why low-frequency experiments detect showers at larger core distances.
• The SDP is polarized along the vector $\boldsymbol{\beta} - (\mathbf{n} \cdot \boldsymbol{\beta})\mathbf{n}$, enabling directional reconstruction of the shower axis.
• The SDP arrives at the observer with a time delay of $d/c$ relative to the core impact time, allowing precise core localization via time-of-flight triangulation using multiple detectors.
• The SDP enables estimation of $X_{\text{max}}^{\text{prod}}$, the atmospheric depth of maximum electric field production, which occurs near the inflection point of the longitudinal shower profile and precedes $X_{\text{max}}$ (maximum particle density).