Cosmogenic Cascade Emission in High-Energy Astrophysics

• Cosmogenic cascade emission is electromagnetic radiation produced when VHE gamma rays trigger pair production and inverse Compton scattering in diffuse photon fields.
• Its spectral features and angular signatures are shaped by extragalactic backgrounds, IGMF strength, and source evolution, often exhibiting a universal power-law behavior.
• Numerical simulations using Monte Carlo codes help constrain UHECR source models, probe cosmic-ray composition, and inform dark matter searches through cascade emission analysis.

Cosmogenic cascade emission refers to the electromagnetic (EM) radiation produced by the development of EM cascades as high-energy photons or cosmic-ray primaries propagate through diffuse photon backgrounds in extragalactic space. These cascades are triggered by gamma–gamma ($\gamma\gamma$) pair production and subsequent inverse Compton (IC) scattering, redistributing VHE (very-high-energy, $>$100 GeV) gamma-ray energy down to the GeV–TeV regime. The observable signatures of cosmogenic cascades are fundamentally shaped by the properties of the extragalactic backgrounds, the intergalactic magnetic field (IGMF), the source population, and astrophysical propagation effects.

1. Physical Principles and Cascade Processes

Cosmogenic electromagnetic cascades are initiated when VHE gamma rays ($E_\gamma \gtrsim 100$ GeV) or secondary neutral particles from ultra-high-energy cosmic rays (UHECRs) interact with background photons from the extragalactic background light (EBL) and the cosmic microwave background (CMB). The primary process is $\gamma\gamma \to e^+e^-$, where the Breit–Wheeler cross section governs the pair-production rate: $$\sigma_{\gamma\gamma}(s) = \frac{3}{16}\sigma_T(1-\beta^2)\left[(3-\beta^4)\ln\left(\frac{1+\beta}{1-\beta}\right)-2\beta(2-\beta^2)\right]$$ with $s=2E_\gamma \epsilon (1-\cos\theta)$ and $\beta = \sqrt{1-4m_e^2c^4/s}$.

The resulting leptons ($e^\pm$) upscatter ambient CMB and, to a lesser extent, EBL photons via IC scattering, generating secondary gamma rays with: $$E_\text{IC} \simeq \frac{4}{3}\gamma_e^2 \epsilon_\text{CMB}, \quad \gamma_e \simeq \frac{E_e}{m_e c^2}$$ If these secondary gamma rays remain above the pair-production threshold on the EBL, the process iterates, building a multi-generation cascade. In addition, protons and heavier nuclei inject energy through Bethe–Heitler pair production ($p+\gamma\to p+e^+e^-$) and photo-pion production ($p+\gamma\to\pi^0, \pi^+$), further feeding the cascade channel (Ahlers et al., 2011, Uryson, 2023).

The development and “stall” of the cascade set the spectral energy distribution (SED) shape observed at Earth, with universal power-law behavior ($dN/dE \propto E^{-\gamma}$ with $\gamma \simeq 1.5$–2) below the energy at which the cascade can no longer proceed due to the transparency of the background (Fang et al., 13 Feb 2025, Uryson, 2022).

2. Role of the Extragalactic Magnetic Field

The IGMF influences both the angular and temporal spread of cascade emission, as well as the cascade’s energy deposition pathways. For a lepton of energy $E_e$, the typical IC cooling length is

$$D_\text{IC} \approx \frac{3m_e^2 c^3}{4 \sigma_T u_\text{CMB} E_e}$$

and the deflection angle under a field $B$ is

$\delta \simeq D_\text{IC} \frac{e B}{E_e}$

Regimes:

• Strong field ($B > 10^{-7}$ G): Synchrotron losses dominate, suppressing the EM cascade.
• Moderate field ($10^{-12} < B < 10^{-7}$ G): Lepton trajectories are significantly deflected, resulting in isotropized, extended halos with angular size $\sim0.1$–$1^\circ$.
• Weak field ($B < 10^{-14}$ G): Cascade is only mildly broadened; the emission remains essentially beam-like (Alonso et al., 2015, Collaboration et al., 2017).

For $B \leq 10^{-12}$ G, as typical in voids or filaments, the intensity and spectrum of cascade gamma rays at energies $E \leq 10^{17}$ eV are insensitive to the precise value of the IGMF. Only for $B \gtrsim 10^{-6}$ G (clusters, galaxies) does synchrotron radiative cooling modify the spectrum via a pronounced dip between $10^7$ and $10^9$ eV (Uryson, 2023, Uryson, 2022).

$B$ [G]	Spectral Coincidence with $10^{-12}$ G	Energy Range [eV]	Astrophysical Site
$10^{-12}$	Yes	$\leq 10^{17}$	Voids, filaments
$10^{-9}$	Yes	$\leq 10^{17}$	Filaments, sheets
$10^{-6}$	No (synchrotron dip visible)	$10^{7}$–$10^{9}$	Clusters, galaxies

This near-independence allows robust prediction of the cascade component of the extragalactic gamma-ray background (EGB), critical for constraining dark matter and exotic physics via gamma-ray observations.

3. Cascade Emission as a Probe of Cosmic Accelerators

Cosmogenic cascade signatures provide critical constraints on the nature of UHECR sources and their intergalactic propagation. The diffuse and point-source contributions of cascades are particularly sensitive to:

• Source composition (proton-rich vs. heavy nuclei): Pure-proton models maximize photon output; admixture of He or heavier nuclei suppresses the cascade yield (Berezinsky et al., 2016, Ahlers et al., 2011).
• Source evolution and redshift distribution: Positive source evolution ($m$ in $Q_p(E,z)\propto(1+z)^m$) enhances cascade flux, especially if sources exist up to high $z$. For instance, interpreting the $120$ PeV KM3-230213A neutrino as cosmogenic requires integrating source populations at least to $z\sim 6$ and allowing a $\gtrsim 5$–10% proton component (collaboration, 27 Oct 2025).
• Spectral index and maximum energy: Cascade intensity at $E\lesssim 1$ TeV tightly constrains the injection spectral index $\gamma_g$ and $E_{p,\max}$—harder, high-$E_{\max}$ models produce more photons in the Fermi window and risk overshooting IGRB bounds (Berezinsky et al., 2016).

Cosmogenic cascades from individual nearby UHECR sources with $L\sim10^{42}$ erg/s at $d\sim10-20$ Mpc are detectable with imaging atmospheric Cherenkov telescopes such as H.E.S.S., VERITAS, MAGIC, and CTA, provided the local source density is low ($\mathcal{H}_0 \lesssim 10^{-5}$ Mpc$^{-3}$) and the IGMF is weak $B<10^{-14}$ G.

4. Numerical Simulation and Observational Signatures

State-of-the-art modeling of cosmogenic cascades uses Monte Carlo codes (such as ELMAG, CRPropa, TransportCR) that simulate all relevant interaction processes: pair production, IC upscattering, synchrotron losses, and magnetic deflections. Key components:

• Injection of primary particles with physically motivated spectra (e.g. $dN/dE \propto E^{-\Gamma}$, typically $\Gamma \simeq 2$ for blazars).
• Realistic EBL and CMB photon fields (Franceschini et al. 2008, Domínguez et al. 2011).
• Magnetic field strength and coherence length.
• Instrument response functions: sensitivity $S(E)$, effective area $A_\mathrm{eff}(E)$, and PSF, tailored to next-generation arrays such as CTA and to legacy arrays such as VERITAS (Alonso et al., 2015, Acharyya et al., 8 Nov 2025).

Simulated observable imprints include:

• Extended or broadened angular emission (“halos”) around point sources, with FWHM $\theta_\text{ext} \sim 0.1^\circ$–$0.5^\circ$ depending on $B$.
• Universal power-law spectral profiles ($dN/dE \propto E^{-3/2}$ to $E^{-2}$) below the pair-production cutoff, with prominent spectral features (“humps”) in the 10–100 GeV range for certain blazar subpopulations (0912.3794, Venters, 2010).
• Time-delayed “echoes” following transient events, with delays $\Delta t(E) \sim 1$ yr$(B/10^{-15}~\mathrm{G})^2(E/1~\mathrm{TeV})^{-2}$ (Fang et al., 13 Feb 2025, Fitoussi et al., 2017).

Non-observation of extended emission in deep VERITAS exposures constrains the allowed IGMF to $5.5\times10^{-15} < B < 7.4\times10^{-14}$ G at 95% CL for blazars such as 1ES 1218+304, under specific intrinsic spectrum and EBL model assumptions (Collaboration et al., 2017).

5. Implications for Gamma-Ray and Neutrino Backgrounds

Cosmogenic cascade emission sets an irreducible component of the extragalactic gamma-ray background (EGB), with crucial implications for multi-messenger astrophysics:

• At $E\sim 10^7$–$10^9$ eV, the cosmogenic cascade flux is nearly universal and B-independent (to $\lesssim 30\%$), contributing $\sim10$–20% of the Fermi-LAT measured EGB for fiducial UHECR emissivity (Uryson, 2022, Uryson, 2023).
• Observed EGB spectra in the Fermi ($\sim20$ MeV–820 GeV), CTA, and SWGO windows must account for cascade emission when constraining blazars, star-forming galaxies, and dark matter models (0912.3794, 0912.3794).
• The tightest constraints on pure-proton UHECR models arise from the IGRB at $E\sim600$–800 GeV: next-generation instruments such as CTA are expected to shrink the allowed parameter space further unless UHECRs have lower $z_{\max}$, softer spectra, or significant He admixture (Berezinsky et al., 2016).
• Joint gamma–neutrino analyses remove major systematics in dark matter searches and UHECR source modeling. The quasi-universality of the cascade emission at sub-TeV energies makes it possible to robustly distinguish new-physics contributions from the “guaranteed” cosmogenic foreground.

6. Cascade Emission in Blazar and UHECR Source Populations

The integrated effect of cosmogenic cascades is sensitive to the luminosity functions, spectral index distributions, and evolution of blazar populations and UHECR sources. In the context of blazars:

• BL Lacs (harder spectra, weaker luminosity evolution) inject more energy in VHE photons, producing prominent cascade enhancements in the Fermi band (~$30$–$100$ GeV). Thus, BL Lacs are expected to dominate the high-energy EGB above $\sim 20$ GeV once cascades are included, whereas FSRQs dominate below $\sim10$ GeV (0912.3794, Venters, 2010).
• The amplitude and location of the cascade “hump” are indicators of both the EBL density (especially near-IR/optical) and blazar evolution, allowing Fermi and CTA EGB measurements to probe cosmic star formation and the high-$z$ universe (Acharyya et al., 8 Nov 2025, 0912.3794).

For UHECR-driven cascades, the cascade photon flux provides a more robust, composition-insensitive signature than the associated cosmogenic neutrino flux, due to the near universality of seed pair injection, the dominance of the Bethe–Heitler channel at low energies, and the loss of memory of the primary cosmic-ray species in the cascade process (Ahlers et al., 2011, Uryson, 2022).

7. Observational Prospects and Future Directions

The upcoming generation of gamma-ray observatories (CTA, SWGO, LHAASO) and neutrino detectors (IceCube-Gen2, KM3NeT, RNO-G) are expected to decisively test cosmogenic-cascade scenarios through:

• Detection or upper limits on extended gamma-ray emission from selected blazar fields, constraining IGMF to the $10^{-16}$–$10^{-14}$ G window (Alonso et al., 2015, Collaboration et al., 2017).
• Precision spectral measurements in the $0.1$–$1$ TeV window, directly probing UHECR composition and source evolution (Berezinsky et al., 2016, Acharyya et al., 8 Nov 2025).
• Stacked, time-resolved searches for gamma-ray cascade “echoes” and photon/neutrino spatial and temporal coincidences with high-energy neutrino events (such as those from TXS 0506+056 and KM3-230213A) (Fang et al., 13 Feb 2025, collaboration, 27 Oct 2025).
• Use of the well-predicted cascade component as a robust background for dark matter and exotic particle searches, reducing model uncertainties in indirect detection studies (Uryson, 2022, Uryson, 2023).

A plausible implication is that any residual EGB excess above predicted astrophysical (including cascade) components is a credible signature for non-standard sources such as decaying or annihilating dark matter. Conversely, a failure to detect predicted cascade features will impose new lower or upper bounds on the IGMF, EBL density, and cosmic-ray source composition.

---

Cosmogenic cascade emission thus constitutes a critical intersection of high-energy astrophysics, cosmic magnetism, and particle physics, encoding joint information on the origins of cosmic rays, photon backgrounds, and the structure of the intergalactic medium. The current and next decades are anticipated to yield decisive empirical advances on all these fronts.