Cosmic rays in the transition energy region ($10^{15}$–$10^{18}$ eV) remain a puzzle: their sources and composition are not precisely known. Direct measurements are impossible due to the low flux, so we detect extensive air showers, cascades of particles in the atmosphere. The main uncertainty lies in the choice of hadronic interaction model in simulations. Rare anomalous events, such as double showers, could provide independent information, but until now they have been impossible to isolate. This work stands apart: the nearest neighbors focus on reconstructing the energy and radio signals of ordinary showers, as well as fast radio bursts, but no one has attempted to directly detect double bumps. SKA-Low, with its dense antenna array and wide frequency band, makes this possible for the first time.
Showers were simulated in CORSIKA with CoREAS radio emission for primary protons and helium at an energy of $10^{15}$ eV and a zenith angle of 60°. For the analysis, the SMIET package was used, which divides the atmosphere into layers of 5 g/cm² and allows the contribution of each layer to the radio signal to be computed separately. First, a two-point-source model was built at the locations of the sub-shower maxima: it links the frequency of the interference notch to the difference in arrival times of the signals. Then, for full reconstruction, a brute-force method was applied: parameters (depths and particle numbers at the maxima) were scanned, and for each set a synthetic double shower was quickly generated via SMIET and its fluence compared to the reference using the root-mean-square deviation.
The two-point-source model accurately reproduces the positions of the first interference notches in the spectra. For nine simulated double showers, it provided estimates of the depths of the maxima with uncertainties ranging from 15 to 66 g/cm² relative to a fit with a double Gaisser–Hillas function. Full brute-force reconstruction over four parameters (Xmax1, Xmax2, Nmax1, Nmax2) showed that the global RMS minimum is often offset from the true values, but fixing two parameters improves accuracy: deviations in depths range from 6 to 164 g/cm², and the ratios of particle numbers lie between 0.61 and 1.21. Thus, even a simple model allows rough parameter estimation, and the SMIET approach provides a basis for further refinement.
This work demonstrates for the first time that the characteristic radio fingerprint of double showers can be used to recover their longitudinal profile. Unlike neighboring studies that focus on ordinary showers or other sources, here a concrete path is proposed to isolate rare anomalous events. This opens the possibility of testing hadronic interaction models by measuring the distance between peaks, and obtaining an independent estimate of mass composition, especially for helium, where the leading particle often carries 25% of the primary energy.
The next step will be to add realistic noise (galactic, instrumental) and use the full configuration of the SKA-Low antenna array, which is an order of magnitude denser than in the current simulation. This will test how robustly the notches stand out in the spectra under real conditions. Plans also include expanding the SMIET template library for different atmospheres and energies, so the method can be applied to data from future observations.
The method will impact ultra-high-energy cosmic-ray physics and radio astronomy: SKA-Low could serve a dual purpose, detecting both astrophysical sources and cosmic rays.
Test the robustness of the reconstruction when adding noise and using the full antenna array; expand the SMIET template library for various conditions.
In cosmic-ray physics, the problem of choosing the hadronic interaction model at ultra-high energies remains unsolved. Double showers provide direct access to the path length of the leading particle, which is sensitive to details of these models. Furthermore, they offer a new way to determine mass composition that does not depend on calibration from ordinary showers.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors build a two-point-source model for double air showers, estimate the depths of shower maxima from interference dips, and apply a brute-force method with fast signal synthesis (SMIET) to reconstruct parameters on simulated events.
Where its strength is
This work shows for the first time that the characteristic radio fingerprint of double air showers (multiple pulses and interference dips) can be used to reconstruct their longitudinal profile, paving the way for detecting such events with SKA-Low.
Where it could go next
Worth trying
Why this may matter
Detecting double air showers would provide an independent test of hadronic interaction models and refine the mass composition of cosmic rays in the transition energy region.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.53, against a usual 0.64. It looks like few have drilled nearby.
The frequency of the interference notch in the spectrum of a double shower is related to the distance between the two sub-showers: the farther apart the maxima, the lower the frequency of the first notch. For a typical event at $10^{15}$ eV, the notch falls within the SKA-Low band around 100 MHz.
The idea of using interference of signals from separated sources echoes the principle of radio interferometry described in Carl Sagan's novel 'Contact', where the protagonist analyzes a signal coming from different directions to pick out a weak source against the noise.