UHECRs Propagation and their Multimessengers: Upper limits and the Impact of the Extragalactic Magnetic Field

TL;DR

This work develops a multimessenger framework to constrain UHECR sources by linking cosmogenic gamma-ray and neutrino fluxes to the underlying cosmic-ray luminosity, incorporating propagation through both extragalactic and Galactic magnetic fields. Using CRPropa3, the authors perform 1D and 4D simulations with mixed nuclear compositions, exploring how $L_{\mathrm{CR}}$ maps to observable $I_{\gamma}$ and $I_{\nu}$ under varying $E_{\rm cut}$, $\alpha$, and $E_{th}$, and apply gamma-ray upper limits from H.E.S.S. and MAGIC to derive source-specific $L_{\mathrm{CR}}^{\mathrm{UL}}$, corrected for magnetic deflections via efficiency factors $\xi_{\mathrm{EGMF}}$ and $\xi_{\mathrm{GMF}}$. They find that proton-rich injections produce stronger secondary fluxes and that magnetic fields substantially modulate the inferred energetics, with Arp 220 and NGC 5128 exemplifying the broad range of source luminosities. The study also assesses NGC 1068 as a target for CTAO, showing potential for tighter constraints on CR-induced gamma rays and neutrinos, thereby strengthening multimessenger connections and informing models of AGN/starburst acceleration. Overall, the results illustrate the vital role of magnetic-field modeling in translating gamma-ray and neutrino ULs into physically meaningful CR luminosities and demonstrate the value of next-generation facilities like CTAO for probing UHECR sources.

Abstract

The detection of high-energy astrophysical multimessengers establishes a connection between ultra-high-energy cosmic rays (UHECRs) and powerful cosmic accelerators. Interactions of UHECRs with radiation fields and interstellar matter generate very-high-energy (VHE) gamma rays and neutrinos, making them key components in the multimessenger framework. This study examines the cosmogenic gamma-ray and neutrino fluxes resulting from UHECR propagation in starburst galaxies with supernova remnants, with a particular focus on NGC 1068, a well-established high-energy neutrino source. Using extragalactic simulations, we calculate the upper limit on cosmic-ray luminosity, applying upper limits on gamma-ray fluxes derived from observations by H.E.S.S. and MAGIC observatories. Our analysis incorporates the effects of both extragalactic and galactic magnetic fields on particle propagation, constraining the maximum extragalactic magnetic field (EGMF) intensity to $10^{-14}~\mathrm{G}$ to ensure that at least 90\% of injected UHECRs successfully reach Earth. The results provide upper limits on gamma-ray and neutrino fluxes, estimates of UHECR luminosity for individual sources, and predictions for the detection capabilities of the Cherenkov Telescope Array Observatory regarding gamma-ray emission from NGC 1068. Combining gamma-ray, neutrino, and UHECR observations reinforces the importance of multimessenger approaches in understanding the nature of high-energy astrophysical sources and their role in cosmic-ray acceleration.

Figures (12)

• Figure 1: Cosmogenic multimessenger fluxes simulated using CRPropa3 Alves_Batista_2022. The green curve shows the cosmic-ray spectrum injected at the location of NGC 1068, at a comoving distance of 14 Mpc from Earth. The red curves depict the secondary photon fluxes produced during the propagation of UHECRs, whereas the blue curves represent the resulting cosmogenic neutrino flux. The solid lines correspond to a proton composition for the injected particles, and the dashed lines represent an iron composition scenario. Additionally, the plot includes the UL of the flux measured by the PAO, which serves as a reference for normalizing the simulated cosmic-ray spectrum PhysRevLett.125.121106. This normalization was also applied to the gamma-ray and neutrino fluxes to ensure consistency across multimessenger predictions. See text for details.
• Figure 2: Upper limits (ULs) on the integral gamma-ray flux, $I^{\mathrm{UHECR}}_{\gamma}(> E_{\mathrm{th}})$, as a function of the source distance, calculated using the UL on the flux observed by the Pierre Auger Observatory at the 95% confidence level (CL) for a given energy threshold $E_{\mathrm{th}}$. (a) Dependence on the cutoff energy $E_{\mathrm{cut}}$, with fixed parameters $\alpha = 2.3$ and $E_{\mathrm{th}} = 0.1 \ \mathrm{GeV}$. (b) Dependence on the spectral index $\alpha$, for fixed parameters $E_{\mathrm{cut}} = Z \times 10^{21} \ \mathrm{eV}$ and $E_{\mathrm{th}} = 330 \ \mathrm{GeV}$. (c) Dependence on the energy threshold $E_{\mathrm{th}}$, for fixed parameters $E_{\mathrm{cut}} = Z \times 10^{21} \ \mathrm{eV}$ and $\alpha = 2.3$.
• Figure 3: UL on the integral neutrino flux ($I\rm_{\nu}^{\mathrm{UL}}$) as a function of the spectral index at the distance of NGC 1068. The maximum energy of the injected particles is set to $E_{\mathrm{cut}} = Z \times 10^{21} \ \mathrm{eV}$, while the energy threshold used in the integral calculation is $E\rm_{\mathrm{th}} = 200 \ \mathrm{GeV}$, as defined by MAGIC 2019ApJ...883..135A.
• Figure 4: Upper limits (ULs) on the neutrino flux, $I^{\mathrm{UHECR}}_{\nu}(> E_{\mathrm{th}})$, as a function of the source distance, calculated using the UL on the flux observed by the Pierre Auger Observatory at the 95% confidence level (CL) for a given energy threshold $E_{\mathrm{th}}$. (a) Dependence on the cutoff energy $E_{\mathrm{cut}}$, with fixed parameters $\alpha = 2.3$ and $E_{\mathrm{th}} = 0.1 \ \mathrm{PeV}$. (b) Dependence on the spectral index $\alpha$, for fixed parameters $E_{\mathrm{cut}} = Z \times 10^{21} \ \mathrm{eV}$ and $E_{\mathrm{th}} = 0.1 \ \mathrm{PeV}$. (c) Dependence on the energy threshold $E_{\mathrm{th}}$, for fixed parameters $E_{\mathrm{cut}} = Z \times 10^{21} \ \mathrm{eV}$ and $\alpha = 2.3$.
• Figure 5: Fraction of injected protons $\xi_{\mathrm{EGMF}}$, as a function of distance $D$, with a cutoff energy of $E_{\mathrm{cut}} = Z \times 10^{21} \ \mathrm{eV}$ that successfully reach the observer, shown as a function of source distance for different values of the spectral index $\alpha$.