Jet Power Estimates of FSRQs PKS 1441+25 and Ton 599 from Broadband SED Modeling

The gist: Jet power estimates derived from broadband SED modeling of FSRQs PKS 1441+25 and Ton 599 are relatively insensitive to the assumed particle energy distribution, reflecting the dominance of external Compton processes and weaker dependence on spectral curvature.

Data and Modeling Approach

The study performed broadband spectral energy distribution (SED) modeling of two Flat Spectrum Radio Quasars (FSRQs), PKS 1441+25 and Ton 599, using observations from SwiftXRT/UVOT, NuSTAR, Fermi-LAT, and VERITAS during 2015 and 2021 The analysis adopted the ΛCDM cosmological model with H0 = 71 km s−1 Mpc−1, ΩΛ = 0.73, and ΩM = 0.27. The broadband SED model assumed a leptonic distribution with a single emitting region characterized by several physical parameters, along with an isotropic electron distribution n(γ).

Particle Distribution Models Tested

The researchers considered four particle distribution models for the analysis:

1. A broken power law.

2. A log-parabola.

3. Two energy-dependent models in which either the diffusion or acceleration timescale depends on energy.

The specific mathematical forms for these distributions were detailed, including the log-parabola model where the particle density is given by n(γ) = K (γ/γr)−α − βlog(γ/γr) and the broken power law model defined piecewise with a break energy. Additionally, they employed models incorporating energy-dependent escape or acceleration timescales, such as the Energy Dependent Diffusion Model (EDD) and the Energy Dependent Acceleration (EDA) model.

Jet Power Estimates and Comparison

The results showed that jet power estimates derived from models with intrinsic curvature, such as the log-parabola and energy-dependent models, are of the same order as those obtained with a broken power-law distribution. This contrasts with High Synchrotron Peaked Blazars (HBLs), where the power estimates can differ by nearly two orders of magnitude between models. The paper attributes this difference to the lower electron break energies typically observed in FSRQs. Consequently, our findings suggest that, unlike in HBLs, the estimated jet powers in FSRQs are relatively insensitive to the assumed particle energy distribution, reflecting the dominance of external Compton processes and weaker dependence on spectral curvature.

Source-Specific Findings

For PKS 1441+25, intrinsic curvature models for a Lorentz factor Γ = 20 and a γmin ∼ 10 show powers higher than ∼ 1046 erg s−1. For the Broken Power Law distribution, the jet power was high as 1047 for a γmin ∼ 10, which reduced to ∼ 1045 (varies by an order of ∼ 2) for a γmin ∼ 100 for an acceptable equipartition value. In contrast, this behavior was not observed in the FSRQ source Ton 599, where the jet powers of all models for a Γ = 20, and a γmin ∼ 10 show power in the range ∼ 1045.5 − 1046.5 erg s−1.

Conclusion on Particle Distribution Sensitivity

The calculated proton power component which are reported in Table 3 and 4 are less than that of HBL like Mkn 501. This can shed light on the fact that, in the case of the FSRQs, the proton power didn’t seem to dominate, which might cause the jet power to be not sensitive to γmin variation. As noted by Bora et al. (2024), for FSRQs, the γ 2N(γ) values are nearly the same across the particle distributions considered, suggesting little to no notable difference in jet power in this study. This indicates that intrinsic curvature models for FSRQs produce systematically higher jet powers which is nearly same as BPL model, reflecting the effect of intrinsic curvature in the particle spectrum.

Physical Constraints

To ensure physically acceptable solutions, the researchers analyzed the variation of χ squared with γmin. Although the X-ray spectra could be fit with either SSC or EC components, EC fits yielded unphysical γmin and equipartition values, so they retained only SSC fits for the X-ray band. The analysis did not show a strong dependence on γmin.

Final Summary

The study successfully modeled the broadband SEDs of two FSRQs using a single-zone leptonic framework incorporating synchrotron, SSC, and EC processes. The analysis provided estimates for jet powers across four different particle energy distributions, demonstrating that for FSRQs, the inferred jet powers are relatively stable regardless of the specific curvature model chosen. This suggests that external Compton processes and weaker dependence on spectral curvature dominate the estimation of jet power in these sources. The calculated proton power component was found to be less than that of HBL like Mkn 501. The overall conclusion is that the jet power in FSRQs does not seem to be sensitive to γmin variation.

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DRAFT VERSION APRIL 7, 2026

Typeset using LATEX twocolumn style in AASTeX631

Jet Power Estimates of FSRQs PKS 1441+25 and Ton 599 from Broadband SED Modeling

HRITWIK BORA,

1 RANJEEV MISRA,

2 RUKAIYA KHATOON,

3 AND RUPJYOTI GOGOI 1

1Department of Physics, Tezpur University, Tezpur-784028, India

2

Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune, Maharashtra - 411007

3Centre for Space Research, North-West University, South Africa

(Received October 28, 2025; Revised February 26, 2026; Accepted March 20, 2026)

ABSTRACT

Flat-Spectrum Radio Quasars (FSRQs) are among the most energetic and powerful active galactic nuclei, often exhibiting jet powers comparable to or exceeding the Eddington luminosity In this work, we performed broadband spectral energy distribution (SED) modeling of two FSRQs PKS 1441+25 and Ton 599, using SwiftXRT/UVOT, NuSTAR, Fermi-LAT and VERITAS observations during 2015 and 2021, respectively. We considered four particle distribution models: a broken power law, a log-parabola, and two energy-dependent models in which either the diffusion or acceleration timescale depends on energy. Our results show that the jet power estimates derived from models with intrinsic curvature, such as the log-parabola and energy-dependent models, are of the same order as those obtained with a broken power-law distribution. This contrasts with the case of High Synchrotron Peaked Blazars (HBLs), where the power estimates can differ by nearly two orders of magnitude between models. We attribute this difference to the lower electron break energies typically observed in FSRQs. Consequently, our findings suggest that, unlike in HBLs, the estimated jet powers in FSRQs are relatively insensitive to the assumed particle energy distribution, reflecting the dominance of external Compton processes and weaker dependence on spectral curvature.

Keywords: acceleration of particles – diffusion – radiation mechanisms: non-thermal – galaxies: active – FSRQ: individual: PKS 1441+25, Ton 599 – gamma-rays: galaxies.

1. Ability to predict jet power sensitivity based on particle distribution models: The improved AI system can estimate jet power estimates for FSRQs by comparing results across different electron energy distributions, such as broken power law, log-parabola, energy dependent diffusion timescale (EDD), and energy dependent acceleration timescale (EDA).

2. Differentiation of spectral curvature effects: The system can distinguish between the effects of intrinsic curvature and other physical parameters on jet power estimates. This is achieved by noting that the jet power estimates derived from models with intrinsic curvature, such as the log-parabola and energy-dependent models, are of the same order as those obtained with a broken power-law distribution.

3. Identification of source class dependence: The AI can determine if jet power estimates are sensitive to the assumed particle energy distribution based on the source type. Specifically, it can identify that unlike in HBLs, the estimated jet powers in FSRQs are relatively insensitive to the assumed particle energy distribution, reflecting the dominance of external Compton processes.

4. Constraint checking based on physical plausibility: The system can flag physically implausible model fits during spectral analysis. For example, it will recognize that EC fits yielded unphysical gamma min and equipartition values for X-ray bands in FSRQs like Ton 599, leading to the retention of only SSC fits for the X-ray band.

5. Parameter correlation mapping: The system can map correlations between spectral parameters across various models to guide model selection. It can analyze the physical significance of observed correlations between best-fit spectral parameters across various models to help choose the most physically motivated distribution, such as identifying that LP, EDA, and EDD models produced systematically higher jet powers which is nearly same as BPL model.

Flat-Spectrum Radio Quasars (FSRQs) are among the most energetic and powerful active galactic nuclei, often exhibiting jet powers comparable to or exceeding the Eddington luminosity. In this work, we performed broadband spectral energy distribution (SED) modeling of two FSRQs PKS 1441+25 and Ton 599, using Swift-XRT/UVOT, NuSTAR, Fermi-LAT and VERITAS observations during 2015 and 2021, respectively. We considered four particle distribution models: a broken power law, a log-parabola, and two energy-dependent models in which either the diffusion or acceleration timescale depends on energy. Our results show that the jet power estimates derived from models with intrinsic curvature, such as the log-parabola and energy-dependent models, are of the same order as those obtained with a broken power-law distribution. This contrasts with the case of High Synchrotron Peaked Blazars (HBLs), where the power estimates can differ by nearly two orders of magnitude between models. We attribute this difference to the lower electron break energies typically observed in FSRQs. Consequently, our findings suggest that, unlike in HBLs, the estimated jet powers in FSRQs are relatively insensitive to the assumed particle energy distribution, reflecting the dominance of external Compton processes and weaker dependence on spectral curvature.