Constraining the Photon Intensity of Extragalactic Background Light with the HAWC Observatory for the Blazar Mrk 421

Technical Summary: Constraining the Photon Intensity of Extragalactic Background Light with the HAWC Observatory for the Blazar Mrk 421

Problem Statement
The blazar Mrk 421 serves as a standard candle for studying Active Galactic Nuclei (AGN) and the mechanisms of particle acceleration and radiation. A critical challenge in gamma-ray astronomy is distinguishing between intrinsic spectral features of the source and attenuation effects caused by the Extragalactic Background Light (EBL). High-energy gamma rays traveling from distant sources interact with EBL photons via electron-positron pair production, creating an observable cutoff in the spectrum. However, the exact intensity of the EBL ($\nu I_\nu$) remains uncertain due to difficulties in direct measurement caused by galactic foregrounds. Furthermore, previous long-term average spectra of Mrk 421 have shown a cutoff, but it is unclear if this is intrinsic to the source or an EBL artifact. To accurately constrain the EBL intensity, precise knowledge of the intrinsic spectrum during high-emission states (HES) is required, as low-emission states (LES) often lack the statistical power to resolve these features.

Methodology
The authors utilized data from the High Altitude Water Cherenkov (HAWC) Observatory, comprising 2,460 transits of Mrk 421. The analysis employed the following steps:

1. State Selection via ARU: The "All-sky Root around in an Unbiased way" (ARU) algorithm was applied to identify periods of increased activity. This method compares observed counts in short time windows against a scaled long-term emission model without assuming specific spectral shapes or diffuse emission models.
   • High Emission States (HES): 15 weekly periods were selected where the significance of deviation ($\sigma_{ARU}$) exceeded 6.
   • Low Emission States (LES): 9 monthly periods were selected where $\sigma_{ARU} < 0$.
2. Spectral Modeling: Using the gammapy framework, the authors fitted the observed spectra with three models: Simple Power Law (SPL), Log-Parabola (LP), and Exponential Cutoff Power Law (ECPL).
3. EBL Attenuation: The observed flux was modeled as the intrinsic spectrum attenuated by the EBL opacity ($\tau_{\gamma\gamma}$). Four different EBL models (Dominguez, Franceschini, Finke, and Saldana-Lopez) were tested to evaluate systematic uncertainties.
4. Parameter Estimation: The study focused on determining the best-fit intrinsic spectrum for the joint HES and LES datasets. The cutoff energy ($E_c$) and spectral index ($\alpha$) were derived. The parameter $\alpha_{norm}$ was introduced to scale the EBL opacity, allowing for the derivation of upper limits on the specific EBL intensity ($\nu I_\nu$).

Key Contributions and Results

• Spectral Hardening: A moderate linear correlation ($r \approx 0.63-0.69$) was observed between the photon flux ($\Phi$) and the spectral index ($\alpha$). This confirms the "hardening" of the spectrum during high-emission states, consistent with leptonic models and previous observations by MAGIC and VERITAS.
• Detection of Intrinsic Cutoffs:
  • The Exponential Cutoff Power Law (ECPL) model was preferred over the Simple Power Law (SPL) at a significance of 3.8$\sigma$ for the joint HES dataset.
  • The cutoff energy for the HES joint spectrum was found to be 13 $\pm$ 3 TeV.
  • For the LES joint spectrum, a cutoff was also detected at 4.9 $\pm$ 0.8 TeV (3.3$\sigma$ significance).
• Intrinsic vs. EBL Origin: The observed cutoff energies (13 TeV for HES and 4.9 TeV for LES) differ significantly from the cutoff energies expected solely from EBL interactions (which are predicted to be around 6.6–7.2 TeV depending on the EBL model). This discrepancy leads to the conclusion that the cutoff is intrinsic to the source, likely caused by an energy budget limit of the accelerator or interaction with an external infrared radiation field near the central engine, rather than EBL attenuation.
• EBL Constraints: Using the derived intrinsic spectrum for the HES periods, the authors placed upper limits on the specific intensity of EBL photons ($\nu I_\nu$) in the wavelength range of 0.52 to 29.40 $\mu$m. These limits are consistent with those reported by the H.E.S.S. collaboration for M 87 during flaring periods.

Significance and Claims
The paper claims that by isolating high-emission states using the unbiased ARU methodology, it is possible to derive a more accurate intrinsic spectrum than is possible with long-term averages. The primary significance of this work lies in:

1. Confirming Intrinsic Cutoffs: Providing strong evidence that the spectral cutoff in Mrk 421 is an intrinsic property of the source, distinct from EBL attenuation effects.
2. EBL Constraints: Establishing competitive upper limits on the EBL specific intensity ($\nu I_\nu$) by leveraging the high-statistics data from HAWC during high-activity periods.
3. Methodological Validation: Demonstrating the utility of the ARU algorithm for selecting transient high-activity periods in wide-field observatories without spectral bias, which improves constraints on physical processes and attenuation effects.

The authors note that while the spectral hardening is observed, the data sample size (24 periods) is insufficient to conclusively confirm a "flattening" or saturation of the hardening at very high fluxes, a phenomenon reported in larger datasets from other observatories. The study concludes that long-term monitoring by wide-field observatories is essential for understanding the temporal evolution of extragalactic sources and their spectral properties.