Powerful extragalactic jets dissipate their kinetic energy far from the central black hole

The study of extragalactic jets, powerful outflows emanating from supermassive black holes at the centers of active galactic nuclei (AGN), is crucial for understanding AGN physics and galaxy evolution. These jets, composed of relativistic plasma, are a primary mechanism for transporting energy from the black hole to intergalactic scales. A significant fraction of the jet's kinetic energy is dissipated, largely manifesting as gamma-ray radiation. Pinpointing the location of this energy dissipation is vital because it directly impacts our understanding of several key processes: particle acceleration mechanisms, the formation and collimation of the jets, and the overall energy budget of AGN. Previous research has attempted to locate the dissipation region, proposing possibilities ranging from the sub-parsec scale broad-line region (BLR) to the parsec-scale molecular torus and beyond. However, these efforts have yielded conflicting results, often limited by the use of small sample sizes or focusing on specific, potentially atypical, emission states. This study aims to overcome these limitations by employing a new diagnostic independent of rapid variability, allowing for analysis of a large, statistically robust sample.

Several methods have been previously used to localize gamma-ray emission in powerful jets, leading to contradictory findings. Short variability timescales of gamma-ray emission have suggested a sub-parsec scale origin within the BLR. However, TeV detections of powerful jets, and the absence of absorption features in average gamma-ray spectra, challenge this interpretation. Simultaneous gamma-ray/optical flares showing similar polarization behavior to very-long baseline interferometry (VLBI) radio emission have implicated the VLBI core, a region beyond the molecular torus. Furthermore, studies of energy-dependent and energy-independent cooling times in gamma-ray flares of individual sources have shown evidence for emission from both the molecular torus and VLBI core, depending on the flare. The inconsistencies across previous studies underscore the need for a robust, population-level analysis that accounts for the various spectral states and emission characteristics of powerful jets.

This research introduces a novel diagnostic, the "seed factor (SF)", to determine the location of gamma-ray emission. The SF is derived from observable quantities in the broadband spectral energy distribution (SED): the peak frequency and luminosity of both the synchrotron and inverse Compton emission components. The SF is uniquely sensitive to the seed photon population responsible for inverse Compton scattering (the primary mechanism for gamma-ray production in these jets). The authors calculate the expected SF values for both the BLR and molecular torus based on established models and observations of radio-quiet AGN. These models utilize information from reverberation mapping, near-infrared interferometry, and studies of covering factors for both regions. The analysis utilizes 62 quasi-simultaneous SEDs of flat spectrum radio quasars (FSRQs), obtained from several public catalogs and literature searches. The SEDs were carefully selected to ensure good spectral coverage, quasi-simultaneity (minimizing biases from temporal variability), and steady-state emission. Maximum likelihood regression, implemented via a simulated annealing optimization algorithm, was used to fit the SEDs, yielding estimates of peak frequencies and luminosities along with their uncertainties. Statistical analysis, including kernel density estimation, bootstrapping, and a Kolmogorov-Smirnov test, were employed to analyze the distribution of calculated seed factors and compare it to the expected values for BLR and molecular torus emission. The normality of the seed factor distribution was assessed, and a comparison was made with the distribution from weak extragalactic jets to verify consistency with the external Compton scattering process.

The analysis revealed that the distribution of observed seed factors peaks within the 1σ confidence interval of the expected seed factor for the molecular torus (SF_MT = 3.92 ± 0.11). The median observed seed factor (SF_median = 4.01 ± 0.10) shows a highly significant difference from the expected BLR seed factor (6.10σ), strongly rejecting the hypothesis of dominant BLR emission. In contrast, the difference between the median observed seed factor and the expected molecular torus seed factor is not significant (0.71σ). The seed factor distribution also passes a normality test, and its distinct shape differs significantly from that observed in weak extragalactic jets, suggesting its origin in external Compton scattering in powerful jets. These findings suggest a consistent, dominant location of energy dissipation in powerful jets at the molecular torus scale (~1 parsec).

The results strongly suggest that the molecular torus is the primary site of steady-state gamma-ray emission in powerful extragalactic jets. This has important implications for jet models. It implies that substantial jet energy dissipation does not occur at scales significantly smaller than ~1 pc. The jet must collimate to a few degrees and accelerate to Lorentz factors of 10-50 within this distance, as suggested by VLBI studies. The finding that energy dissipation occurs primarily in the molecular torus highlights the importance of considering this region in theoretical models of jet evolution and energy transport. The use of quasi-simultaneous SEDs helps mitigate biases associated with spectral variability, providing a clearer picture of the average emission characteristics of powerful jets. The observation of the peak in the seed factor distribution near the expected value for the molecular torus strongly suggests that this region is the primary location for the energy dissipation.

This research provides compelling evidence that the molecular torus is the dominant location of energy dissipation in powerful extragalactic jets. The robust statistical analysis of a large sample of quasi-simultaneous SEDs, utilizing the novel seed factor diagnostic, strengthens the conclusion. This finding provides strong constraints for jet models, highlighting the significance of the parsec-scale environment in jet evolution and energy dissipation. Future research could focus on refining the seed factor diagnostic with improved models of the BLR and molecular torus, as well as exploring potential variations in energy dissipation location across different AGN subtypes and evolutionary stages.

The study primarily focuses on steady-state emission; the seed factor may not be reliable for analyzing highly variable states. The analysis relies on existing SED models for the BLR and molecular torus; uncertainties in these models could potentially affect the conclusions. Furthermore, the study assumes that the primary mechanism for gamma-ray emission is external Compton scattering; alternative mechanisms might need to be considered for a truly comprehensive understanding.