High-Altitude Horizontal Air Showers (HAHAs)

• HAHAs are extensive air showers from ultra-high-energy cosmic rays traversing nearly horizontal paths in the high-altitude, low-density atmosphere.
• They exhibit distinctive longitudinal development and multi-modal emission signatures, including geomagnetic radio and synchrotron X-ray/gamma-ray outputs.
• HAHAs require specialized detection strategies with horizon-pointing instruments like balloon-borne and mountain-top arrays to capture their fleeting signals.

High-Altitude Horizontal Air Showers (HAHAs) are a class of extensive air showers (EAS) initiated by ultra-high-energy cosmic rays or neutrinos traversing the atmosphere along nearly tangential (zenith $\theta \sim 84^\circ$–$96^\circ$) paths. In contrast to vertical or conventional inclined EAS, HAHAs develop entirely within the atmosphere at high altitudes, often never intersecting the ground. This geometry leads to unique phenomenology in the shower’s longitudinal development, electromagnetic and radio emission, X- and gamma-ray signatures, and detection strategies. HAHAs are accessible primarily to high-altitude balloon platforms, mountain-top radio arrays, and future satellite missions, and have become central to the design of next-generation cosmic-ray and neutrino observatories.

1. Fundamental Geometry and Longitudinal Development

HAHAs are defined as EAS whose axis is nearly parallel to the Earth’s surface, typically corresponding to zenith angles $\theta > 84^\circ$ and often extending just above the geometric horizon (for a balloon at $h\sim 36$ km, $\theta_\mathrm{hor}\simeq 96^\circ$) (Tueros et al., 1 Apr 2024, Tueros et al., 20 Sep 2024, Battisti, 15 Nov 2025). The minimum impact parameter $b$ (distance of closest approach to the ground) is generally of order tens to hundreds of km, depending on altitude and zenith. The shower slant depth $X(s)$ encountered before reaching the detector is reduced compared to downward showers, given by

$X(s) = \int_0^s \rho[h(s')]\, ds',$

where the atmospheric density $\rho(h)$ drops rapidly with altitude. For instance, at 33 km, typical local densities are $\rho \sim 10^{-3}\,\mathrm{kg\,m}^{-3}$ and accumulated $X_s \lesssim 100\,\mathrm{g\,cm}^{-2}$, an order of magnitude lower than that for vertical EAS.

Shower longitudinal profiles, when characterized as a function of $X$, can be parametrized by traditional Gaisser–Hillas functions. Simulations confirm that profiles collapse onto standard curves ($N(X)$ vs. $X$) typical of EAS, but with geometrical shower lengths elongated to $O(100)$ km due to the lower air density (Tueros et al., 1 Apr 2024). The classical elongation rate $$d\langle X_\mathrm{max} \rangle/d\log E \simeq 55\,\mathrm{g/cm}^2$$ and fluctuations $\sigma(X_\mathrm{max})$ match expectations from downward-going cascades. However, because $X_\mathrm{max}$ maps to $$\Delta d_\mathrm{max} = \Delta X_\mathrm{max}/\rho(h)$$ at much lower $\rho$, the fluctuations in shower–detector separation become tens of kilometers, driving substantial event-to-event variability in electromagnetic signatures (Tueros et al., 1 Apr 2024).

A unique implication of HAHA geometry is the narrow angular phase space for full shower development: only for $92^\circ \lesssim \theta \lesssim 96^\circ$ can showers reach $X_\mathrm{max}$ before intersecting a balloon-borne detector at $h\sim 30$–36 km (Tueros et al., 1 Apr 2024). This restricts the instantaneous geometric acceptance and emphasizes the importance of horizon-pointing detectors.

2. Electromagnetic and Radio Emission Mechanisms

The dominant emission processes in HAHAs mirror those in standard EAS but exhibit distinctive features due to reduced density, extreme geometry, and enhanced Lorentz forces:

• Geomagnetic Emission: Time-varying transverse currents induced by lateral separation of $e^+e^-$ pairs under the Earth's magnetic field $\vec{B}$. The macroscopic field at observer position $\vec{r}$ is commonly parameterized as:

$$\vec{E}(\vec{r},t) \simeq E_0 \cdot \left(\frac{E_0}{10^{17}\,\mathrm{eV}}\right)\sin \alpha \cdot f(R) \cdot g(t-t_0),$$

with lateral falloff $f(R)$ typically exponential or NKG-type; $\sin\alpha$ is the geomagnetic angle (Kambeitz, 2015, Collaboration et al., 2022).

• Askaryan (Charge-Excess) Emission: Coherent Cherenkov-like emission from net negative charge buildup in the shower front. For HAHAs, the Askaryan contribution is suppressed in low-density conditions and is typically subdominant ($\lesssim$10\% of $E_\mathrm{geomagnetic}$) (Tueros et al., 20 Sep 2024, Collaboration et al., 2022).
• Synchrotron X-ray/Gamma-Ray Emission: At early shower ages $s \lesssim 0.2$, a large fraction of high-energy ($E_e \gtrsim 1$ TeV) $e^\pm$ generate synchrotron X-rays and $\gamma$-rays in $\sim 50\,\mu$T geomagnetic fields (Battisti, 15 Nov 2025, Saavedra et al., 3 Nov 2025). The typical photon energy is $$E_\mathrm{sync} \sim 10\,\mathrm{keV}(B/50\,\mu\mathrm{T})(E_e/1\,\mathrm{TeV})^2$$.
• Cherenkov Emission: In high-altitude, horizontal geometries, only the muon component ($E_\mu \gtrsim 120$ GeV for survival over $\sim 800$ km) near the detector produces detectable Cherenkov light. Rayleigh scattering attenuates electron-induced UV Cherenkov almost entirely over long slant paths (Królik et al., 2019).

The pulse width and time-compression effects are amplified in HAHAs: for observers near the Cherenkov angle $\psi_\mathrm{C}$, radio pulses are $\sim1$–$5$ ns wide, with coherence up to 1 GHz, broadening rapidly for off-axis or off-plane observers (Tueros et al., 20 Sep 2024). The frequency spectrum $|E(f)| \sim A\,\exp[\gamma(f-f_0)]$ and the radio lateral distribution function (LDF) are both modified by the shower geometry, as well as by atmospheric refractive gradients and integrated geomagnetic path length.

3. Asymmetries and Footprint Structure

Unique to HAHAs are pronounced refractive and magnetic asymmetries in the radio footprint, which must be accounted for in both experiment design and data analysis (Tueros et al., 20 Sep 2024):

• Refractive Displacement: Due to the vertical index-of-refraction gradient $n(h)$, the Cherenkov angle $\psi_\mathrm{C}$ and coherent emission ring are vertically displaced. Observers above and below the shower axis sample radio emission traversing different $n(h)$ profiles, causing the LDF peak to shift by several kilometers vertically—a kilometer-scale effect confirmed by ZHAireS-RASPASS simulations (Tueros et al., 20 Sep 2024).
• Coherence Modulation: Over $O(100\;\mathrm{km})$ path lengths, the transverse spread of the shower (especially along $\vec{v}\times\vec{B}$) broadens arrival-time distributions, reducing coherence for observers in the magnetic plane and imprinting a twofold azimuthal asymmetry on the LDF and spectrum.
• Lateral Distribution and Scaling: The radio LDF for HAHAs can be modeled as:

$$E(R) = E_0\, (R/R_0)^{-\eta}\, \exp(-R/R_\mathrm{cut}),$$

with $\eta \simeq 1.3$ and $R_\mathrm{cut} \simeq 1.2$ km measured for ground-based horizontal showers ($\theta=62^\circ$–$80^\circ$) (Kambeitz, 2015). At higher altitude, the footprint area decreases due to the lower refractive index and narrower Cherenkov cone, requiring correspondingly denser detector packing.

• Cherenkov and Muon Contributions: For balloon experiments, the detectable UV Cherenkov signal is limited to muons above threshold, as the electromagnetic component’s Cherenkov is attenuated by atmospheric scattering. The photon density from muon Cherenkov in $E_0=10^{17}$–$10^{18}$ eV showers is $\sim3$–$10$ ph/m$^2$ for detectors within $\sim$4 km of the core, consistent with proposed thresholds for EUSO-SPB2 detection (Królik et al., 2019).

4. Detection Methods and Major Experiments

A range of methodologies have been developed for detecting HAHAs, leveraging their multi-modal signatures:

• Ground-Based and Mountain-Top Radio Arrays: Arrays such as TAROGE-M (Mt. Melbourne, Antarctica, $H=2700$ m) deploy log-periodic dipole antennas oriented to maximize horizon coverage and reconstruct near-horizontal events with $\sim0.3^\circ$ angular resolution in the 180–450 MHz band. The event selection exploits polarization (dominantly $\vec{v}\times\vec{B}$), time-of-arrival consistency, and spectral coherence (Collaboration et al., 2022). Measured rates and energy/zenith distributions confirm consistency with simulated expectations.
• High-Altitude Arrays (AERA, Horizon-T): The Auger Engineering Radio Array at 1400 m (AERA) and Horizon-T at 3340 m are optimized for $62^\circ \leq \theta \leq 85^\circ$, combining radio, scintillator, and optical (Vavilov–Čerenkov) detectors for event reconstruction and cross-calibration (Kambeitz, 2015, Beisembaev et al., 2016). Dense station spacing and multi-band instrumentation are essential given the extended radio footprint and need for directional discrimination.
• Balloon and Space-Borne Instruments: ANITA (36 km), PUEO, POEMMA-Balloon with Radio (PBR, 33 km), and EUSO-SPB2 leverage their altitude for synoptic horizon views. Triggers utilize both RF and X-ray/gamma-ray channels—the latter now feasible following demonstration of geo-synchrotron X-ray emission detection from air showers at early development stages (Saavedra et al., 3 Nov 2025, Battisti, 15 Nov 2025).
• X-ray and Gamma-Ray Detectors: The PBR X-$\gamma$ instrument employs scintillating crystals (NaI(Tl), CsI(Tl)) coupled to SiPMs, anti-coincidence vetoes, and FPGA-driven trigger logic. Energy coverage (10 keV–4 MeV), spectral calibration, and coincidence capability with fluorescence and Cherenkov imagers aim to search for the predicted X-ray flashes from very young HAHA stages (Battisti, 15 Nov 2025).

5. Signal Analysis, Sensitivity, and Event Rates

A robust detection campaign for HAHAs requires precise modeling of signal expectations and systematics:

• Signal Simulations: Full 3D time-dependent Monte Carlo simulations (e.g., ZHAireS-RASPASS) incorporate realistic atmospheric profiles, geomagnetic effects, and microscopic tracking of charged particles for radio and X-ray emission (Tueros et al., 1 Apr 2024, Tueros et al., 20 Sep 2024, Saavedra et al., 3 Nov 2025). Measured parameters match expectations: LDF shapes, field amplitudes, and spectral slopes are validated in data and simulation, guiding energy and angle reconstruction strategies.
• Sensitivity and Acceptance: Effective acceptance depends sensitively on detector altitude, geometry, threshold, and the narrow $\theta$ window for full development. For PBR, an event rate of $O(10)$ HAHAs per two-week campaign is expected for $E>10^{17}$ eV; for a 1 m$^2$ X-ray detector at $h=30$ km, $O(10)$ events/month are projected in the PeV regime (Battisti, 15 Nov 2025, Saavedra et al., 3 Nov 2025). For TAROGE-M, event rates and reconstructed fluxes match other EeV-scale experiments (Collaboration et al., 2022).
• Backgrounds and Suppression: Coincidence triggering (across radio, X-ray, and optical), polarization filtering, spectral slope and time-coincidence cuts suppress both anthropogenic and natural backgrounds to below accidental rates of $<1$ per $10^6$ s for multi-channel events (Battisti, 15 Nov 2025).
• Uncertainties: Systematic uncertainties arise from geometry (shower–detector distance fluctuations), antenna calibration ($\pm2$ dB), gain and threshold stabilities, and Monte Carlo model limitations (with up to $\sim20$\% uncertainty in reconstructed $E_0$ from coherence asymmetry). Lateral spread and X-ray footprint scale as $1/\rho(z)$, so footprint sizes range from $\sim1$–$100$ m$^2$ as altitude increases (Saavedra et al., 3 Nov 2025).

6. Implications for Ultra-High-Energy Cosmic Ray and Neutrino Astronomy

HAHAs provide a unique observational window for high-energy astrophysics:

• Cosmic Ray Composition and Spectrum: The ability of HAHAs to probe early shower development, particularly through X-ray and early radio emission, allows cross-checks of universality in shower evolution, particle spectra, and hadronic models under extreme atmospheric conditions (Tueros et al., 1 Apr 2024, Battisti, 15 Nov 2025).
• Tau Neutrino Searches: Earth-skimming tau neutrinos producing upward-going HAHAs are accessible to horizon-viewing arrays on high mountains or balloons. The radio technique enables sensitivities competitive with balloon and in-ice neutrino experiments, as demonstrated by TAROGE-M and ANITA (Collaboration et al., 2022).
• Combined Modalities and Multi-Messenger Potential: Coordinated observation across radio, X-ray/gamma, Cherenkov, and fluorescence bands optimizes event identification, suppresses backgrounds, and enables detailed reconstruction of primary parameters and physics beyond the Standard Model (Battisti, 15 Nov 2025).
• Future Scaling: Further deployment of multi-station high-altitude radio arrays (e.g., expanded TAROGE-M networks, POEMMA satellites) and optimization of X-ray camera size and geometry could boost exposure to HAHAs and rare Earth-emergent events to transformative levels.

7. Experimental Advances, Challenges, and Prospects

Table: Representative HAHA Detection Platforms

Platform	Altitude (m)	Principal Channels	Event Rate (per month)
TAROGE-M	2700	Radio	$>4$, $\sim$25 days (Collaboration et al., 2022)
AERA	1400	Radio, Surface	6/yr/km$^2$ > $10^{17}$ eV (Kambeitz, 2015)
Horizon-T	3340	Charged, Čerenkov	$O(1$/hr) > $10^{17}$ eV (Beisembaev et al., 2016)
ANITA	36\,000	Radio	7 events/50 days > $10^{18}$ eV (Tueros et al., 1 Apr 2024)
PBR X-$\gamma$	33\,000	X-ray, $\gamma$, Radio	$O(10)$/2 weeks > $10^{17}$ eV (Battisti, 15 Nov 2025)
EUSO-SPB2	38\,000	Čerenkov (muons)	$O(100)$/100 days > $10^{17}$ eV (Królik et al., 2019)

Detection of HAHAs at high altitude leverages unique environments (low noise, strong $B$, large horizon) and benefits from modular, scalable architectures, as in TAROGE-M (Collaboration et al., 2022), and from hybrid/multi-channel strategies, as emphasized by balloon-borne missions (Battisti, 15 Nov 2025, Saavedra et al., 3 Nov 2025). Critical challenges include the narrow geometric acceptance window, necessity for dense or overlapping apertures at high altitude, and systematic control of triggering/energy-reconstruction ambiguities due to coherence and refractive asymmetries.

A plausible implication is that ongoing advances in instrument synchronization, real-time directionality, and multi-wavelength coincidence will enable correspondingly higher-purity HAHA samples and expand the search parameter space for both cosmic-ray composition studies and ultra-high-energy neutrino signals. Continued development of dedicated Monte Carlo tools (e.g., ZHAireS-RASPASS) and calibration campaigns remain essential for exploiting HAHA observables in the next generation of particle-astrophysics observatories (Tueros et al., 20 Sep 2024, Saavedra et al., 3 Nov 2025).