X-rays Emission: a novel tool to detect Extensive Air Showers

TL;DR

This work introduces a theoretical and computational framework to assess the detectability of Extensive Air Showers via geo-synchrotron X-ray emission observed from high-altitude platforms. It derives a differential photon yield $\frac{dN_\gamma}{dX\,d\epsilon}$ for an ensemble of gyrating shower electrons under incoherent emission, incorporating atmospheric propagation and a CORSIKA-informed electron distribution. Using a Monte Carlo approach, the authors compute photon fluxes, footprints on the detector plane, and the acceptance for a 1 m radius, 70° FoV detector at altitudes of 20–30 km, predicting roughly $\mathcal{O}(10)$ events per month. The results suggest a promising complementary channel for PeV cosmic-ray detection and provide a practical framework to guide balloon/sub-orbital experiments, while highlighting backgrounds and the need for refined modeling of young showers and hybrid triggering strategies.

Abstract

We investigate the feasibility of detecting extensive air showers via their geo-synchrotron X-ray emission from high-altitude platforms. Starting from first principles, we derive a differential expression for the number of emitted photons per unit grammage and photon energy for an ensemble of gyrating shower electrons. The calculation uses noted parameterizations of the electron state variable distributions in the shower to establish a scale for the photon footprint and, further, takes into account the propagation of emitted photons in the atmosphere. The computed fluxes at the position of the detector are used to estimate the detector acceptance and event rate using a bootstrap Monte Carlo procedure. For a 1 m radius and 70° half-aperture circular detector at an altitude between 20 to 30 km viewing the Earth's limb, we find acceptances at the 1 $\mathrm{m^2 sr}$ level and integral event rates of roughly 10 per month. These results indicate that X-ray geo-synchrotron emission is a promising, complimentary channel for high-altitude indirect cosmic ray detection in the PeV regime.

Figures (12)

• Figure 1: (Left) Longitudinal profile for a 100PeV proton-induced shower as obtained from averaging the output of 0 CORSIKA simulations (see text for details). The dashed, dotted, and dash-dotted lines show the contribution of electrons, hadrons, and muons to the all-charged particle content of the shower, respectively. In this work, we consider the synchrotron emission from electrons only as they are the dominant component of charged-particles in the shower, and emission from other species is suppressed by their larger mass. (Right) Examples of the grammage-length relation for three showers developing horizontally in the atmosphere ($\theta_\text{V} = \qty{90}{\degree}$) as observed from three different altitudes. The vertical dashed lines show the instant at which $s = 0.4$, and the vertical dotted lines show the position of the detector.
• Figure 2: Contour plot of the transmission factors from the point of emission to the position of a detector at $z = \qty{36}{km}$, computed according to Eq. \ref{['eq:attenuation_factor']}, for photons in the 1030keV energy band (left) and for photons in the 0.54.0MeV energy band (right).
• Figure 3: Comparison of the RMS provided by different models (as labeled) of the Angular Distribution function of high energy electrons in an 100 PeV EAS
• Figure 4: (Left) Geometry conventions used in this work to correlate distances from the point of first interaction (or $\tau$ lepton decay) to altitudes and accumulated grammages. All slant-depths are computed with reference to the CR atmospheric entry or $\tau$ Earth exit points (pink points in the diagram), offset by the slant-depth at the point of decay or first interaction (green points in the diagram). Eq. \ref{['eq:master_formula']} is solved by integrating numerically along the green portions of the tracks shown in the diagram. The track geometry is entirely defined by the height of the detector, $h$, and the viewing angle, $\theta$ ($\theta'$). See the text and cummings2021modeling1cummings2021modeling2 for further details. (Right) Diagram illustrating the effect of considering the electron deviation due to the geomagnetic field and the propagation of the photons along the instantaneous direction of the electron at the point of emission on the extent of the photon footprint area on the detection plane.
• Figure 5: Number of photons across all photon energy bands (10E4keV) arriving at the position of a detector at several altitudes for below-the-limb events (left) and above-the-limb events (right) from 100PeV proton-induced EAS. The proton track geometry is characterized by its viewing angle (i.e., the off-nadir angle at the position of the detector) as described in § \ref{['sec:atmosphere']}. The vertical dotted lines correspond the viewing angle of the Earth's limb at the respective altitude.