On gamma rays as predictors of UHECR flux in AGNs

Technical Summary: On $\gamma$ rays as predictors of UHECR flux in AGNs

Problem Statement
Active Galactic Nuclei (AGNs) are primary candidates for the sources of Ultra-High-Energy Cosmic Rays (UHECRs). However, recent phenomenological models that use the observed very-high-energy (VHE) $\gamma$-ray flux as a direct proxy for UHECR luminosity ($L_{CR}$) fail to reproduce experimental data from the Pierre Auger Observatory. Specifically, these models struggle to simultaneously fit the energy spectrum, the mass composition, and the arrival direction map. A critical failure point is the overestimation of the contribution from the blazar Markarian 421 (Mkn 421), which creates a predicted hotspot and dipole direction inconsistent with observations. Furthermore, these models often produce a "spurious" dipole direction and a poor fit to the spectral shape, particularly when mixing different AGN classes (e.g., radio galaxies and blazars) in the same analysis.

Methodology
The authors propose that the discrepancy arises from an implicit assumption in previous works: that UHECR emission is beamed in the same manner as $\gamma$-ray emission from relativistic jets. The paper argues that while $\gamma$-rays are subject to strong Doppler boosting ($D^4$) due to relativistic motion in "blobs" within the jet, UHECRs likely undergo isotropization (decollimation) before escaping the source environment.

The study proceeds through the following steps:

1. Theoretical Review: The authors review acceleration mechanisms in AGN jets (shocks, reconnection, shear acceleration) and the propagation of particles through jet lobes. They argue that magnetic fields in the lobes and the source cocoon scatter UHECRs, effectively isotropizing their emission even if they originate in relativistic flows.
2. Proxy Correction: Instead of using the observed $\gamma$-ray luminosity ($L^{obs}_{\gamma}$), the authors propose using the intrinsic $\gamma$-ray luminosity ($L^{int}_{\gamma}$) or the radiative jet power as the proxy for $L_{CR}$. This involves correcting the observed flux by the Doppler factor ($D$) to the power of $q$, where $L^{int}_{\gamma} = D^{-q}L^{obs}_{\gamma}$. Two scenarios are tested: $q=4$ (assuming $L_{CR} \propto L^{int}_{\gamma}$) and $q=2$ (assuming $L_{CR} \propto$ radiative jet power).
3. Simulation and Fitting: Using the CRPropa3 framework, the authors perform 1-D propagation simulations for five primary nuclei (H, He, N, Si, Fe) across a grid of energies and distances. They compare the simulated flux against Pierre Auger data (spectrum and $X_{max}$ moments) and arrival direction maps.
4. Comparative Analysis: Three cases are compared:
   • Case (a): Using $L^{obs}_{\gamma}$ as the proxy (standard approach).
   • Case (b): Using $D^{-2}L^{obs}_{\gamma}$ as the proxy.
   • Case (c): Using $D^{-4}L^{obs}_{\gamma}$ as the proxy.

Key Contributions and Results

• Suppression of Blazar Dominance: The correction significantly reduces the weight of highly beamed blazars (like Mkn 421) relative to radio galaxies (like Cen A, M87, and Fornax A). In the standard model, Mkn 421 dominates the flux; in the corrected models, its contribution is suppressed by 2 to 5 orders of magnitude, rendering it negligible.
• Improved Spectral and Composition Fit: The combined fit of the energy spectrum and composition data improves significantly when using the intrinsic luminosity proxies. The reduced chi-squared ($\chi^2/NDF$) decreases from 4.6 (using $L^{obs}_{\gamma}$) to 3.1 (using $D^{-2}L^{obs}_{\gamma}$). This improvement is attributed to a more realistic relative contribution of nearby sources versus distant sources, avoiding the spectral distortions caused by the over-contribution of distant, highly beamed sources.
• Resolution of Dipole Tension: The tension between the modeled and observed dipole directions is reduced. For the Auger field of view at energies $E > 8$ EeV, the discrepancy drops from 5.9$\sigma$ to 3.5$\sigma$. For $E > 32$ EeV, the tension reduces from 2.1$\sigma$ to 1.1$\sigma$.
• Hotspot Realignment: The predicted arrival direction maps shift from being dominated by Mkn 421 to showing hotspots around Cen A, Fornax A, M87, and specific distant blazars (Mkn 180, 1ES2344+514). These new hotspots align more closely with the two hotspots reported by the Pierre Auger Observatory and the one reported by the Telescope Array.

Significance and Claims
The paper claims to offer a solution to the contradictions found in previous AGN-based UHECR source models by decoupling the beaming assumptions of $\gamma$-rays and UHECRs. The authors assert that:

1. The association between $\gamma$-rays and UHECRs is weak but non-zero; while $\gamma$-rays trace particle acceleration regions, UHECRs are likely isotropized by magnetic fields in the source lobes before escaping.
2. Using the observed $\gamma$-ray flux as a proxy implicitly assumes UHECRs are beamed, an assumption the authors argue is physically unlikely for UHECRs escaping complex magnetic environments.
3. Correcting for Doppler boosting ($L^{int}_{\gamma}$ or radiative jet power) provides a more robust proxy that reconciles the spectrum, composition, and arrival direction data from the Pierre Auger Observatory.

The authors conclude that while their model is a simplified combined fit (not accounting for full $X_{max}$ distributions or detailed magnetic field deflections), the results strengthen the hypothesis of AGNs as UHECR sources and provide a more consistent framework for interpreting multi-messenger data from different AGN classes. They note that future work must address the energy-dependent decollimation and the specific effects of regular galactic and extragalactic magnetic fields.