Distinct High Energy Cutoff Variation Patterns in Seyfert Galaxies

1. Introduction

Active Galactic Nuclei (AGNs) represent some of the most energetic phenomena in the universe, with their hard X-ray emission primarily produced in hot, compact regions known as coronae. In the standard disc-corona paradigm, this emission results from inverse Compton scattering of seed photons from the accretion disk, producing a characteristic power-law continuum with a high-energy cutoff. The Nuclear Spectroscopic Telescope Array (NuSTAR), launched in 2012, has revolutionized our ability to study these high-energy processes with unprecedented sensitivity in the hard X-ray band (3-79 keV).

The high-energy cutoff (E_cut) parameter provides crucial constraints on coronal physics, as it relates directly to the coronal temperature. Previous studies have detected E_cut variations in several AGNs, including 3C 382, NGC 5548, Mrk 335, and 4C 74.26. Zhang et al. (2018) identified a potential "hotter-when-brighter" behavior in these sources, where the corona becomes hotter as the source brightens and softens. However, the limited sample size and potential counter-examples like Ark 564 highlight the need for further investigation into the universality of this pattern.

This study presents new detections of E_cut variations in two Seyfert galaxies—NGC 3227 and SWIFT J2127.4+5654—revealing distinct patterns that challenge simple unified models of coronal behavior.

2. Observations and Data Reduction

2.1 NGC 3227

NGC 3227 is a radio-quiet Seyfert 1.5 galaxy located at redshift z = 0.00391. The source exhibits highly variable X-ray emission and complex absorption features. Seven archival NuSTAR observations were analyzed, with particular attention to a rapid occultation event identified between observations 60202002010 and 60202002012 by Turner et al. (2018). This event revealed multiple absorber zones, making NGC 3227 an ideal laboratory for studying both absorption effects and intrinsic coronal properties.

2.2 SWIFT J2127.4+5654

SWIFT J2127.4+5654 is another Seyfert galaxy studied through multiple NuSTAR exposures. The source shows significant spectral variability across observations, providing an excellent opportunity to examine the relationship between spectral parameters and flux variations.

2.3 Data Processing

All NuSTAR data were reduced using standard procedures with the NuSTAR Data Analysis Software (NuSTARDAS) version 2.0.0. Cleaned event files were generated using the nupipeline task with standard filtering criteria. Source spectra were extracted from circular regions centered on the source, while background spectra were extracted from source-free regions on the same detector. All spectra were grouped to ensure a minimum of 20 counts per bin to facilitate χ² statistics.

3. Spectral Analysis Methodology

The spectral analysis employed physically motivated models to characterize the hard X-ray emission. The primary model components included:

• Continuum Modeling: A cutoff power-law model was used to represent the primary coronal emission, with parameters for the photon index (Γ) and high-energy cutoff (E_cut).
• Reflection Components: A relativistic reflection component was included using the relxill model to account for reprocessed emission from the accretion disk.
• Absorption Modeling: Complex absorption was modeled with appropriate absorption components, particularly important for NGC 3227 given its known variable absorption.
• Cross-calibration: Constant factors were included to account for minor cross-calibration uncertainties between NuSTAR's FPMA and FPMB detectors.

Model parameters were constrained through simultaneous fitting of all observations for each source, with key parameters (Γ and E_cut) allowed to vary between epochs while maintaining consistency in reflection and absorption components where physically justified.

4. Results and Findings

4.1 NGC 3227: Monotonic Relationship

In NGC 3227, we detected a clear monotonic relationship between E_cut and Γ, with E_cut increasing systematically as the spectrum softens (increasing Γ). This pattern aligns with the "hotter-when-softer" behavior previously reported in other AGNs. The correlation remains significant across different flux states, suggesting a fundamental connection between coronal heating and spectral softening.

4.2 SWIFT J2127.4+5654: Λ-shaped Pattern

SWIFT J2127.4+5654 exhibits a more complex behavior, with the E_cut–Γ relation following a distinct Λ shape. Below Γ ≈ 2.05, E_cut increases with increasing Γ, similar to the pattern seen in NGC 3227. However, above this break point, the relationship reverses, with E_cut decreasing as Γ continues to increase. This represents the first detection of such a complete Λ pattern in a single AGN, with the source's Γ variations crossing the critical break point.

4.3 Soften-when-Brighter Behavior

Both sources exhibit the conventional "softer-when-brighter" behavior common in Seyfert galaxies, where the spectrum softens (increasing Γ) as the X-ray flux increases. This pattern is well-established in AGN studies and is thought to relate to changes in the Comptonizing corona's optical depth or geometry.

4.4 Unified View of AGN Sample

When plotting all seven AGNs with confirmed E_cut variations in the E_cut–Γ diagram, we find they can be unified under the Λ pattern framework. While most sources only show partial segments of this pattern due to limited Γ ranges in individual objects, SWIFT J2127.4+5654 provides the complete picture by spanning both sides of the break point.

5. Discussion and Implications

5.1 Physical Mechanisms for E_cut Variations

The detected patterns suggest multiple underlying physical mechanisms operating in AGN coronae:

• Geometrical Changes: Variations in corona size or geometry could simultaneously affect both Γ and E_cut. A more compact corona might produce both harder spectra and higher cutoff energies.
• Pair Production: Electron-positron pair production could regulate the coronal temperature, creating a natural maximum temperature that manifests as the turning point in the Λ pattern.
• Heating-Cooling Balance: Changes in the heating rate or cooling efficiency could drive correlated variations in spectral parameters.

5.2 The Λ Pattern Break Point

The break point at Γ ≈ 2.05 in SWIFT J2127.4+5654 may represent a critical transition in coronal properties. Below this point, increased heating dominates, producing both softer spectra and higher cutoff energies. Above this point, additional cooling mechanisms or pair production may limit further temperature increases despite continued spectral softening.

5.3 Comparison with Previous Studies

Our results both support and extend previous findings. The initial "hotter-when-softer" pattern reported by Zhang et al. (2018) appears valid for the ascending part of the Λ pattern. However, the discovery of the descending branch reveals a more complex relationship that requires modification of simple unified models.

5.4 Implications for Coronal Physics

The Λ pattern suggests that AGN coronae may operate in different regimes depending on their fundamental parameters. The break point might correspond to specific physical conditions, such as the optical depth where Comptonization efficiency changes or where pair production becomes significant.

6. Conclusion

This study presents significant advances in understanding E_cut variations in AGNs through detailed analysis of NGC 3227 and SWIFT J2127.4+5654. The detection of distinct patterns—monotonic in NGC 3227 and Λ-shaped in SWIFT J2127.4+5654—reveals that multiple physical mechanisms likely operate in AGN coronae. The proposed unified Λ pattern framework accommodates all currently known AGNs with E_cut variations, though the small sample size necessitates caution.

Key insights from this research include:

• E_cut variations are more complex than previously recognized, with both increasing and decreasing branches possible
• The Λ pattern provides a potential unifying framework for diverse AGN behaviors
• Multiple physical mechanisms, including geometrical changes and pair production, likely contribute to the observed patterns
• SWIFT J2127.4+5654 represents a crucial source as the only AGN showing the complete Λ pattern within a single object

Future studies with larger samples and longer monitoring campaigns will be essential to verify the universality of the Λ pattern and refine our understanding of the underlying coronal physics. The continued operation of NuSTAR and upcoming X-ray missions will provide exciting opportunities to explore these phenomena further.