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

This study evaluates Flat Spectrum Radio Quasars and BL Lacertae objects as potential sources of ultra-high-energy cosmic rays and concludes that while both can reproduce the observed flux, only BL Lacertae objects remain consistent with observational constraints on anisotropy and source density, whereas Flat Spectrum Radio Quasars are disfavoured.

Original authors: Swaraj Pratim Sarmah, Umananda Dev Goswami

Published 2026-05-20

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CC BY 4.0

Original authors: Swaraj Pratim Sarmah, Umananda Dev Goswami

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, dark ocean. Floating in this ocean are tiny, super-fast particles called Ultra-High-Energy Cosmic Rays (UHECRs). These particles are the "bullets" of the cosmos, carrying more energy than anything we can create in a lab on Earth. For a long time, scientists have been trying to figure out: Who is shooting these bullets?

This paper is like a detective story where two suspects are brought in for questioning: Flat Spectrum Radio Quasars (FSRQs) and BL Lacertae objects (BL Lacs). Both are types of active galaxies with massive black holes at their centers, shooting out powerful jets of energy. The authors of this paper wanted to see which of these two galaxy types is the most likely source of our cosmic bullets.

Here is the breakdown of their investigation, explained simply:

1. The Problem: The Cosmic "Whodunit"

Unlike light (photons) or neutrinos, which travel in straight lines, these cosmic bullets are charged particles. As they fly through space, invisible magnetic fields act like a giant, chaotic maze, bending their paths. By the time they reach Earth, they have been deflected so much that we can't easily trace them back to their origin. It's like trying to find out who threw a ball in a hurricane; the wind (magnetic fields) has scrambled the direction.

2. The Suspects: The Two Galaxy Types

The researchers looked at two specific types of "active" galaxies:

FSRQs (The Loud, Distant Giants): These are like massive, booming speakers that were very loud in the distant past of the universe but are quieter now. They are very bright and energetic.
BL Lacs (The Local, Steady Shooters): These are also powerful, but they are more common in our "neighborhood" (closer to us in cosmic time) and have a different kind of energy signature.

3. The Investigation: Simulating the Journey

The scientists built a massive computer simulation to act as a "cosmic weather forecast." They asked: If these galaxies were shooting cosmic bullets, what would the sky look like when those bullets arrived at Earth?

They had to account for three main things:

The Energy Loss: As the bullets fly through space, they crash into the "fog" of the universe (background light and radiation), losing energy along the way.
The Magnetic Maze: They simulated how the magnetic fields would scatter the bullets, making them arrive from different directions.
The Composition: They tested if the bullets were made of light particles (like protons) or heavy ones (like iron nuclei), similar to how different types of balls react to wind differently.

4. The Verdict: Who is the Culprit?

When the researchers compared their simulation results with real data collected by giant observatories on Earth (the Pierre Auger Observatory and the Telescope Array), the results were clear:

The FSRQ Suspect (The Distant Giants):
- The Alibi: If FSRQs were the main shooters, the simulation predicted that the cosmic bullets would arrive with a very strong "directional bias" (a dipole anisotropy). In simple terms, the bullets would seem to be coming from one specific direction much more than they actually do.
- The Density Issue: To make the numbers work, the simulation required FSRQs to be packed incredibly close together (every 8 million light-years). This is like saying there is a gas station on every single street corner, which we know isn't true. The real universe doesn't have that many FSRQs.
- Result: Disqualified. The FSRQ scenario doesn't fit the evidence.
The BL Lac Suspect (The Local Shooters):
- The Alibi: When the researchers used BL Lacs as the source, the simulation matched the real data perfectly. The amount of cosmic rays, their energy, and the direction they came from all lined up with what the telescopes see.
- The Density: The required number of BL Lacs matched what we actually observe in the sky. They are spread out at a realistic distance (about 160 million light-years apart).
- Result: The Prime Suspect. BL Lac objects are the most plausible explanation for where these high-energy particles are coming from.

5. The Conclusion

The paper concludes that while both types of galaxies are powerful, BL Lac objects are the likely source of the diffuse ultra-high-energy cosmic rays we detect.

The FSRQs are like a suspect who claims to be the shooter but leaves behind a trail of evidence (too many of them, and the wrong direction of fire) that proves they couldn't have done it alone. BL Lacs, however, fit the profile perfectly: they are numerous enough, close enough, and their "firing pattern" matches the cosmic rays we see hitting Earth.

In short: The universe's most energetic bullets are likely being fired by the "local" active galaxies (BL Lacs), not the "distant giants" (FSRQs).

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

Problem Statement
The origin of ultra-high-energy cosmic rays (UHECRs, $E \gtrsim 10^{17}$ eV) remains a significant unresolved issue in modern astrophysics. While the extragalactic origin is suggested by spectral features, the precise sources are difficult to identify due to deflections by galactic and extragalactic magnetic fields. Recent high-precision data from the Pierre Auger Observatory and the Telescope Array (TA) reveal specific spectral features (hardening at the "ankle," steepening, and GZK suppression) and composition trends (transition from light to heavier nuclei with increasing energy). While nearby radio galaxies are strong candidates, the potential contribution of Active Galactic Nuclei (AGN), specifically Flat Spectrum Radio Quasars (FSRQs) and BL Lacertae (BL Lac) objects, requires rigorous testing against observational constraints regarding flux, composition, and anisotropy.

Methodology
The authors investigate FSRQs and BL Lacs as plausible sources of diffuse UHECRs using a comprehensive propagation model within the standard $\Lambda$ CDM cosmology.

Source Evolution Models:
- The study utilizes realistic Luminosity-Dependent Density Evolution (LDDE) functions derived from observed gamma-ray luminosity functions (LF) from Fermi-LAT data.
- FSRQs: Modeled using an LDDE function where the redshift peak of the source density depends on luminosity ( $z_c \propto L^\alpha$ ).
- BL Lacs: Modeled using an intrinsic distribution of photon indices (Gaussian) correlated with luminosity, combined with the same LDDE formalism.
- These models replace simple phenomenological evolution forms (e.g., power laws in $1+z$ ) with physically motivated evolutions based on observed gamma-ray data.
Propagation Physics:
- UHECRs are propagated through extragalactic space considering energy losses from interactions with the Cosmic Microwave Background (CMB) and Extragalactic Background Light (EBL).
- Processes included: Bethe-Heitler pair production, photopion production (for protons), and photodisintegration (for nuclei). The study employs the Continuous Energy Loss (CEL) approximation for photodisintegration, tracking the survival probability of primary nuclei (p, He, N, Si, Fe) without explicitly solving for secondary cascades.
- Magnetic Diffusion: Propagation occurs in a uniform, turbulent intergalactic magnetic field (IGMF) with RMS strength $B_{rms} = 1$ nG and coherence length $l_c = 0.5$ Mpc. The energy-dependent diffusion coefficient $D(E)$ is calculated based on Kolmogorov turbulence, separating resonant and non-resonant diffusion regimes.
Flux Calculation and Fitting:
- The diffuse flux is calculated by integrating the source emissivity over redshift and luminosity, applying a propagation theorem to sum contributions from a uniform distribution of synthetic sources.
- The model includes a mixed nuclear composition (p, He, N, Si, Fe) with fractions treated as free parameters.
- The source emissivity normalization is linked to the gamma-ray luminosity via a baryon loading factor $\kappa = L_{CR}/L_\gamma$ .
- Parameters (source separation distance $d_s$ , acceleration efficiency $\eta$ , and nuclear fractions $\epsilon_Z$ ) are fitted to observational data from Auger and TA (flux and mean shower depth $\langle X_{max} \rangle$ ).
- Statistical model comparison is performed using reduced $\chi^2$ , Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC).
- Full-sky maps of integral flux ($10-100$ EeV) and dipole anisotropy are generated using the HEALPix framework.

Key Results

Flux and Composition:
- Both FSRQ and BL Lac scenarios can reproduce the observed UHECR energy spectrum and $\langle X_{max} \rangle$ data with mixed compositions.
- The best-fit acceleration efficiency is $\eta \approx 0.1$ , consistent with numerical simulations of relativistic jet acceleration.
- The required baryon loading factor is $\kappa \approx 5.65$ , indicating the CR power is energetically viable (only a few times the gamma-ray luminosity).
- FSRQ Scenario: Requires a source separation distance $d_s \approx 8 \pm 1$ Mpc to fit the flux. This implies a source density significantly higher than observational estimates from Fermi-LAT luminosity functions.
- BL Lac Scenario: Requires $d_s \approx 160 \pm 21$ Mpc, which is consistent with observational estimates of BL Lac density.
Statistical Comparison:
- The reduced $\chi^2$ values for the combined Auger and TA data are 2.37 (FSRQ) and 2.55 (BL Lac).
- Model selection criteria (AIC and BIC) favor the BL Lac model ( $\Delta$ AIC = 4.17, $\Delta$ BIC = 4.83), providing moderate evidence that BL Lacs offer a better description of the data than FSRQs.
Anisotropy Constraints:
- BL Lacs: The predicted dipole anisotropy using the flux-fitted parameters ( $z_{max}=0.5$ ) agrees well with Auger observations.
- FSRQs: The predicted dipole amplitude is significantly higher than observed when using the same parameters. To match the observed anisotropy, the redshift range must be artificially restricted to $z_{max} \approx 0.01$ , which contradicts the flux-fitting requirements and the known strong cosmological evolution of FSRQs.
Photodisintegration:
- Calculations of optical depth and absorbed fractions show that heavy nuclei (e.g., Fe) undergo significant photodisintegration at lower energies compared to lighter nuclei (e.g., He), leading to a progressive suppression of heavy components at the highest energies.

Significance and Conclusions
The paper concludes that while both FSRQs and BL Lacs are capable of reproducing the observed UHECR flux, the BL Lac scenario is strongly favored when considering the full set of observational constraints.

FSRQs are disfavored as dominant sources of diffuse UHECRs because the scenario requires an unrealistically high source density (small $d_s$ ) to fit the flux and predicts a dipole anisotropy that exceeds observational limits unless the source population is artificially truncated at low redshifts.
BL Lacs remain consistent with observations, providing a self-consistent description of the flux, composition, and dipole anisotropy with a source density and redshift evolution that align with Fermi-LAT data.

The authors suggest that while FSRQs may still contribute to multi-messenger channels (neutrinos and gamma rays), they are likely subdominant contributors to the diffuse UHECR flux compared to BL Lac objects. The study highlights the importance of using realistic, luminosity-dependent source evolution models rather than simplified phenomenological forms when constraining UHECR origins.

1. The Problem: The Cosmic "Whodunit"

2. The Suspects: The Two Galaxy Types

3. The Investigation: Simulating the Journey

4. The Verdict: Who is the Culprit?

5. The Conclusion

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