Advanced techniques of searching for flares of ultra-high-energy photons from point sources

TL;DR

This work develops two enhanced, unbinned likelihood–based analyses for detecting direction-time clustering of ultra-high-energy air showers as evidence for neutral UHE photons from point sources. By integrating a photon tag based on the $S_4$ observable into both a multiplet and a stacking approach, the study demonstrates improved sensitivity and the ability to identify multiple flares, even with limited event counts. Monte Carlo tests quantify discovery potentials and show that stacking with the $S_4$ tag lowers the required signal fraction significantly, suggesting practical improvements in photon flux limits and source searches. The methods are implemented in the UHECluster package to enable robust, scalable analysis of UHECR data from large observatories such as Auger.

Abstract

Astrophysical flares are one of the possible prominent source classes of ultra-high-energy (UHE, $E > 10^{17}$ eV) cosmic rays, which can be detected by recording clusters of extensive air showers in arrays of detectors. The search for sources of neutral particles offers distinct advantages over searching for sources of charged particles, as the former traverse cosmic distances undeflected by magnetic fields. While no cosmic-ray photons exceeding $10^{17}$ eV have been definitively detected, identifying the clustering of events in cosmic-ray data would provide compelling evidence for their existence. We compare two analysis methods for detecting direction-time clustering in UHE extensive air showers: an approach in which one examines multiplets, and the stacking method, in which one analyzes sets of doublets that are not necessarily consecutive, thus making it sensitive to multiple flares. Both techniques combine time-clustering algorithms with unbinned likelihood study. Background events (initiated by hadrons) can be more efficiently distinguished from photon-induced events (signals) by using a photon tag that employs probability distribution functions to classify each event as more likely to be initiated by either a photon or a hadron. We demonstrate that these methods can effectively distinguish between events initiated by photons and those initiated by hadrons (background), and can accurately reproduce both the number of photon events within flares and their duration. We calculate the discovery potentials, i.e., the number of events required to identify a photon flare. The methods discussed can be used to search for cosmic ray sources and/or improve limits on the fluxes of UHE photons.

Figures (4)

• Figure 1: Probability distribution functions of the variable $\log S_4$, derived from simulations of extensive air showers initiated by photons (considered as the signal, shown in red) and protons (considered as the background, shown in dashed blue) universe8110579. These functions are used as the $S_4$ photon tag.
• Figure 2: Plots showing the results obtained for the multiplet (Braun BRAUN2010175) method with (square points) and without (circular points) application of the $S_4$ photon tag. The analyses were performed for flares of three different lengths: 1, 10, and 30 days. The plots on the left show the estimator $n_s$ (top) and the fraction of reconstructed to true flare duration for different numbers of injected signal events (bottom). The shown values (points) and their error bars are calculated as the mean and the width of the corresponding distribution obtained from multiple maps, respectively. The plots for the different flare durations are shifted slightly to avoid the visual overlap and facilitate easier comparison. The plots on the right show the $TS$ (top) and the statistical confidence level of the obtained results (bottom). The bottom right plot also shows the minimum number of events required to detect direction-time clusters at the $5\sigma$ confidence level, which is called the discovery threshold (see Section \ref{['sec:discovery']} for its exact definition). Discovery thresholds are obtained from the crossing between colored lines representing different simulated cases and the horizontal dashed black line (5$\sigma$ confidence level). The ranges of injected signal events are chosen differently for each analysis to capture the corresponding discovery threshold values, which are shown in the plot legend.
• Figure 3: Distributions of $n_s$ (left) and $\Delta T$ (right) obtained from Monte Carlo simulations for the stacking method, applied to a triple-flare scenario (comprising three distinct flares of ten, ten, and twenty days duration) with $N_s = 20$ injected signal events. Each plot features a box highlighting the most common value, the peak of the distribution. The parameters of the flares are accurately reconstructed: the number of signal events is estimated as $n_s = 21$, and the combined flare duration is $\Delta T = 40$ days.
• Figure 4: Discovery thresholds for the stacking method, both with and without using the $S_4$ photon tag, are shown as a function of the $\rm{S/B}$ threshold. Results are presented for both single and multiple flares of varying lengths. These results are compared with the multiplet (Braun) method BRAUN2010175 and the time-integrated method BRAUN2008299 (star-shaped points), which employs direction-only clustering without time information, both without (filled markers) and with (hollow markers) application of the $S_4$ photon tag. In these cases, no pre-selection $\rm{S/B}$ threshold is applied. The single flares shown here are of three scenarios: a one-day flare (blue line), a ten-day flare (red lines), and a thirty-day flare (black line). The multiple flares are shown as dashed and dotted lines. All the results have been obtained for $\Delta T_{\rm{data}} = 3150$ days and 595 background events within a 12$^{\circ}$ x 12$^{\circ}$ sky region.