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Study of Flat Spectrum Radio Quasars and BL Lacertae Objects as Sources of Diffusive Ultra High-Energy Cosmic Rays

Swaraj Pratim Sarmah, Umananda Dev Goswami

TL;DR

This work tests whether FSRQs and BL Lac objects can explain the diffuse UHECR flux by leveraging luminosity-dependent density evolution (LDDE) grounded in observed gamma-ray LFs to model source evolution. UHECR propagation is treated with a Syrovatskii-diffusion framework in turbulent extragalactic magnetic fields, including adiabatic and CMB energy losses, and the emissivity combines LDDE with a mixed nuclear composition across redshift. The authors compute all-sky flux maps using HEALPix, compare predicted spectra and X_max with Auger/TA data, and identify hotspots that correlate with nearby galaxies or AGN; they report chi-squared values indicating a reasonable match and emphasize the potential significant contribution of LDDE AGNs to the diffuse UHECR flux. Overall, the study provides a physically grounded, observation-driven assessment of AGN populations as UHECR sources and highlights anisotropy signatures and candidate counterparts that motivate further multi-messenger investigations.

Abstract

We examine whether Flat Spectrum Radio Quasars (FSRQs) and BL Lacertae objects (BL Lacs) can act as plausible astrophysical sources of diffuse ultra-high-energy cosmic rays (UHECRs). Using realistic luminosity-dependent density evolution (LDDE) functions derived from observed gamma-ray luminosity functions for FSRQs and BL Lacs, we calculate the redshift evolution of the cosmic ray source population through integrated luminosity functions. The diffuse UHECRs flux from these sources is modelled by propagating nuclei through extragalactic space, including energy losses from interactions with cosmic photon backgrounds. The resulting UHECRs spectra are compared with observational data from the Pierre Auger Observatory and the Telescope Array, with fluxes normalised at reference energies. In addition to spectral comparisons, we generate HEALPix-based sky maps and identify potential hotspots. Near these hotspots, several galaxies and extragalactic sources are found, suggesting possible associations with the enhanced flux regions. Our results indicate that LDDE-modelled AGNs could contribute significantly to the observed diffuse UHECRs flux and provide constraints on their role as dominant sources.

Study of Flat Spectrum Radio Quasars and BL Lacertae Objects as Sources of Diffusive Ultra High-Energy Cosmic Rays

TL;DR

This work tests whether FSRQs and BL Lac objects can explain the diffuse UHECR flux by leveraging luminosity-dependent density evolution (LDDE) grounded in observed gamma-ray LFs to model source evolution. UHECR propagation is treated with a Syrovatskii-diffusion framework in turbulent extragalactic magnetic fields, including adiabatic and CMB energy losses, and the emissivity combines LDDE with a mixed nuclear composition across redshift. The authors compute all-sky flux maps using HEALPix, compare predicted spectra and X_max with Auger/TA data, and identify hotspots that correlate with nearby galaxies or AGN; they report chi-squared values indicating a reasonable match and emphasize the potential significant contribution of LDDE AGNs to the diffuse UHECR flux. Overall, the study provides a physically grounded, observation-driven assessment of AGN populations as UHECR sources and highlights anisotropy signatures and candidate counterparts that motivate further multi-messenger investigations.

Abstract

We examine whether Flat Spectrum Radio Quasars (FSRQs) and BL Lacertae objects (BL Lacs) can act as plausible astrophysical sources of diffuse ultra-high-energy cosmic rays (UHECRs). Using realistic luminosity-dependent density evolution (LDDE) functions derived from observed gamma-ray luminosity functions for FSRQs and BL Lacs, we calculate the redshift evolution of the cosmic ray source population through integrated luminosity functions. The diffuse UHECRs flux from these sources is modelled by propagating nuclei through extragalactic space, including energy losses from interactions with cosmic photon backgrounds. The resulting UHECRs spectra are compared with observational data from the Pierre Auger Observatory and the Telescope Array, with fluxes normalised at reference energies. In addition to spectral comparisons, we generate HEALPix-based sky maps and identify potential hotspots. Near these hotspots, several galaxies and extragalactic sources are found, suggesting possible associations with the enhanced flux regions. Our results indicate that LDDE-modelled AGNs could contribute significantly to the observed diffuse UHECRs flux and provide constraints on their role as dominant sources.

Paper Structure

This paper contains 7 sections, 29 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Evolution of AGN Sources
  3. Flat Spectrum Radio Quasars (FSRQs)
  4. BL Lacertae (BL Lac) Objects
  5. Diffusion of Cosmic Rays in Turbulent Magnetic Fields
  6. Flux of UHECRs
  7. Summary and Conclusion

Figures (2)

  • Figure 1: Fluxes of UHECRs and $X_\text{max}$ values for a mixed composition scenario from FSRQs (top panel) and BL Lac objects (bottom panel), obtained by using different source separation distances (see text) and varying relative abundances of nuclear species. The fluxes and $X_\text{max}$ values are compared with Auger and TA measurements.
  • Figure 2: UHECR flux skymaps from FSRQs (top panel) and BL Lac objects (bottom panel) for $10$ EeV and $50$ EeV energies.