Atmospheric pion, kaon, and muon fluxes for sub-orbital experiments

TL;DR

The study addresses atmospheric backgrounds for sub-orbital detectors by computing angular- and energy-resolved fluxes of $\pi^{\pm}$, $K^{\pm}$, and $\mu^{\pm}$ reaching altitudes 0, 18, and 33 km for $E>10$ GeV using 1-D cascade equations implemented in MCEq, with a Gaisser-Hillas H3a primary spectrum, US Standard Atmosphere, and Sibyll 2.3c hadronic interactions. It shows how fluxes depend on altitude and telescope orientation, shaped by decay vs interaction dynamics and muon energy losses, with critical energies $E_c^{\pi} \approx 110$ GeV and $E_c^{K} \approx 850$ GeV governing the energy response. The results quantify backgrounds for balloon experiments like EUSO-SPB2 and guide trigger and veto strategies, providing ionizing-particle rate estimates for representative detector configurations. Despite the 1-D approximation, the work highlights significant backgrounds and the role of geometry, urging future 3-D studies to refine background models in sub-orbital missions.

Abstract

Cosmic rays interacting with the Earth's atmosphere generate extensive air showers, which produce Cherenkov, fluorescence and radio emissions. These emissions are key signatures for detection by ground-based, sub-orbital, and satellite-based telescopes aiming to study high energy cosmic ray and neutrino events. However, detectors operating at ground and balloon altitudes are also exposed to a background of atmospheric charged particles, primarily pions, kaons, and muons, that can mimic or obscure the signals from astrophysical sources. In this work, we use coupled cascade equations to calculate the atmospheric pion, kaon and muon fluxes reaching detectors at various altitudes. Our analysis focuses on energies above 10 GeV, where the influence of the Earth's magnetic field on particle trajectories is minimal. We provide angular and energy-resolved flux estimates and discuss their relevance as background for extensive air shower detection. Our results are potentially relevant for interpreting data from current and future balloon-borne experiments such as EUSO-SPB2 and for refining trigger and veto strategies in Cherenkov and fluorescence telescopes.

Figures (8)

• Figure 1: Detector (shown as black box) at altitude H$_{0}$ (not to scale). In red is the particle trajectory to the detector's surface which makes angle $\alpha$ as shown in the figure ($\alpha=180^\circ$ for down-going particles incident on the detector). The cosmic ray nucleons (e.g., $p$) interact in the atmosphere to create pions and kaons which may decay to muons.
• Figure 2: Altitude as a function of atmospheric column depth $X$ for particle trajectories incident from an infinite distance, for trajectories from above and along the detector horizon for $H_0=0$ km (left) and from above, along and below the detector horizon for $H_0= 33$ km (right). The atmospheric density is approximated by the US Standard Atmosphere Heck:1998vt.
• Figure 3: Variation in the meson ($\pi^{\pm} + K^{\pm}$) flux scaled by $E_{\rm meson}^{2.7}$ as a function of $E_{\rm meson}$ for different detector altitude locations. It is shown for three different $\alpha$ angles. Curves for altitudes $H_0=0,\ 18$ km and $\alpha=90^\circ$ is not shown in the plot because there is a negligible meson flux at the detector. The meson fluxes for $H_0=18$ km and $\alpha=135^\circ$ and $180^\circ$ are nearly equal.
• Figure 4: Variation in the muon flux scaled by $E_\mu^{2.7}$ as a function $E_\mu$ for different detector altitude locations. Left: Three different $\alpha$ angles with horizontal ($\alpha=90^\circ$), downward-going ($\alpha=135^\circ$) and vertical ($\alpha=180^\circ$) trajectories. Right: Upward-going trajectory flux for 18 km and 33 km case.
• Figure 5: Fraction of mesons (left) and muons (right) reaching detector located at 0 km and 33 km of altitude. The fractions are shown for two trajectories $\alpha=90^{\circ}, 180^\circ$. In the left plot, labels Pions and Kaons represent: $\phi_{CR \to \pi^{\pm}}/(\phi_{CR \to \pi^{\pm}} + \phi_{CR \to K^{\pm}})$ and $\phi_{CR \to K^{\pm}}/(\phi_{CR \to \pi^{\pm}} + \phi_{CR \to K^{\pm}})$, respectively. Curve for altitude $H_0=0$ km and $\alpha=90^\circ$ is not shown because the flux is negligible. For the right plot, the labels represent: $\phi_{\pi^{\pm} \to \mu^{\pm}}/(\phi_{K^{\pm} \to \mu^{\pm}} + \phi_{\pi^{\pm} \to \mu^{\pm}})$ and $\phi_{K^{\pm} \to \mu^{\pm}}/(\phi_{K^{\pm} \to \mu^{\pm}} + \phi_{\pi^{\pm} \to \mu^{\pm}})$. The plots are generated using MCEq package. Note the different $x$-axis scales in the two panels.