Radio Morphing: Fast computation of inclined air shower radio emission

TL;DR

Radio Morphing delivers a fast, semi-analytical method to simulate radio emission from inclined cosmic-ray air showers by morphing from a small set of ZHAireS reference showers. It combines a scaling step (to match energy, composition, $X_{ m max}$, and geomagnetic conditions) with an interpolation/extrapolation stage to predict signals at arbitrary observer positions and along the shower axis, while incorporating fluctuations and density/ refractive-index effects. Across thousands of tests, the method achieves mean amplitude biases on the order of a few percent and timing accuracies of a few nanoseconds, with computation times reduced by over four orders of magnitude relative to full Monte Carlo simulations. These capabilities enable rapid, large-scale detector studies for next-generation radio arrays (e.g., GRAND, SKA, and the Pierre Auger Observatory upgrade), with open-source code and planned refinements for azimuthal biases, magnetic-field scaling, and additional primaries such as neutrinos.

Abstract

The preparation of next-generation large-scale radio experiments requires running a fast and efficient number of simulations to explore multiple detector configurations over vast areas and develop novel methods for the reconstruction of air shower parameters. While Monte Carlo simulations are accurate and reliable tools, they are too computationally expensive to explore the full parameter space of these new detectors within a reasonable timescale. We introduce a new version of Radio Morphing, a semi-analytical tool designed to simulate the radio emission of any cosmic-ray induced air shower with zenith angle $θ>60^{\circ}$, at any desired antenna position, from the simulation data of a few reference showers at given positions. We present the latest performances of Radio Morphing which now provides simulation of air shower radio signals with average relative differences on the peak amplitude below $17\%$ on raw traces, below $15\%$ with a $3σ$ trigger threshold, below $13\%$ in the $[50-200]\,\rm MHz$ band, and even below $\sim 10\%$ in the $[30-80]\,\rm MHz$ band. These results are combined with a computation time reduced by more than four orders of magnitude, compared to standard Monte Carlo simulations.

Figures (9)

• Figure 1: Sketch of the Radio Morphing procedure. The electric field from a reference ZHAireS simulation with parameters [$E_{\rm ref}, \theta_{\rm ref}, \varphi_{\rm ref}, D_{\rm xmax}$] (blue "reference plane") is scaled towards a shower with [$E_{\rm target}, \theta_{\rm target}, \varphi_{\rm target}, D_{\rm xmax}$] (red "scaled plane"). The resulting signal is then interpolated within the plane and extrapolated along the shower axis to infer the radio-emission at any position.
• Figure 2: ( Top) Lateral distribution functions (LDFs) for two showers with the same arrival directions ($\theta= 75^{\circ},\, \varphi=90^{\circ}$), but different primary energies ($E_r = 3.98\, \rm EeV,\, E_t = 1.0\, \rm EeV$) without any energy scaling ( top left) and with the energy scaling procedure ( top right). The $\omega$ angle corresponds to the angular deviation from the shower axis, taken from $X_{\rm max}$ as shown in Fig. \ref{['fig:sketch_rm']}. ( Bottom) LDFs for two showers with the same primary energy and zenith angle ($E=3.98\, \rm EeV, \theta= 75^{\circ}$), but different azimuth angles ($\varphi_r = 90^{\circ},\, \varphi_t= 0^{\circ}$), with ( left) and without ( right) applying the scaling procedure.
• Figure 3: ( Left) Average geomagnetic electric field amplitude dependency with air-density (black crosses), from ZHAireS simulations. Results are fitted with a broken power law (red line), using $\phi_{0} = 1010$, $\gamma_{1} = -1.0047$, $\gamma_{2} = 0.2222$, $\rho_{\rm break} = 3.5\times 10^{-4}$, $\beta = 2.5$ and $\rho_{0} = 1.87\times 10^{-6}$. ( Right) Average charge excess electric field amplitude dependency with air-density from ZHAireS simulations. Results are fitted with a simple power law, using $b = 1.195$. Both plots are normalized by their maximal value.
• Figure 4: Example of shower-to-shower fluctuations. LDFs generated with Radio Morphing for three showers with the same input parameters ($E=3.98\, \rm EeV$, $\theta=75^{\circ}$, $\varphi=180^{\circ}$) but different random seed.
• Figure 5: ( Left) Relative differences $\delta$ on the electric field peak amplitude between ZHAireS and Radio Morphing simulations as a function of the shower energy. Crosses show the mean value of $\delta$ while the shaded area corresponds to its standard deviation. ( Right) Distribution of $\delta$ at the antenna level for showers with three different azimuth angles.