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Impact of Spectral Coverage on Parameter recovery in Blazar Modeling

N. Sahakyan, D. Bégué, P. Giommi, H. Dereli-Bégué, Asaf Pe'er

TL;DR

This work investigates how spectral coverage shapes the reliability of parameter recovery in one-zone SSC blazar modeling by generating 63,000 synthetic SED fits for three representative blazars spanning LSP, ISP, and HSP classes. Using a CNN surrogate within a Bayesian framework, the authors quantify parameter recovery via coverage probabilities across 21 observational configurations, identifying minimal-band sets that yield robust inferences for each class ($p$, $ ext{log}_{10}( ext{gamma}_{ m min})$, $ ext{log}_{10}( ext{gamma}_{ m cut})$, $B$, $R$, $oldsymbol{\\delta}$, $ ext{log}_{10}(L_e)$). They find LSPs require modest optical/UV–X-ray–GeV coverage, ISPs benefit from broader X-ray–VHE or optical/UV–X-ray–HE coverage, and HSPs demand optical/UV–X-ray–VHE data, with VHE data most impactful for HSPs and sometimes nuanced for ISPs. The study offers practical guidance for multi-wavelength campaigns and highlights CTAO’s potential to improve parameter inferences, especially for ISP sources, while validating the value of extended VHE coverage for HSPs.

Abstract

Understanding the impact of spectral coverage on parameter recovery is critical for accurate interpretation of blazar spectra. In this study, we examine how the data coverage influences the reliability of parameter estimation within the one-zone synchrotron self-Compton (SSC) framework. Using OJ 287, TXS 0506+056, and Mrk 421 as representative of the low-, intermediate- and high synchrotron peak classes (LSP, ISP and HSP), respectively, we generate synthetic SEDs based on their best-fit models and perform 1,000 fits for each of the 21 observational configurations per source type. Our analysis quantifies the coverage probability for all model parameters, such has the magnetic field strength and the electron luminosity, and reveals that different blazar subclasses exhibit distinct sensitivities to spectral gaps. For LSPs, a minimal dataset comprising optical/UV, X-ray, and GeV $γ$-ray bands is sufficient for robust parameter inference. In contrast, ISPs and HSPs require broader spectral coverage to constrain the physical parameters. For ISP, we find that reliable parameter recovery can be achieved with two different minimal band combinations: \textit{(i)} X-ray, high energy $γ$-ray, and very high energy $γ$-ray data, or \textit{(ii)} optical/UV, X-ray, and high energy $γ$-ray data. For HSPs, the minimal configuration enabling reliable parameter recovery includes the optical/UV, X-ray, and very high energy $γ$-ray bands. We discuss the role of very high energy $γ$-ray observations, showing that they significantly enhance parameter recovery for HSPs. Our results provide practical guidelines for designing optimized multi-wavelength observation campaigns and for assessing the robustness of SSC model inferences under incomplete spectral coverage.

Impact of Spectral Coverage on Parameter recovery in Blazar Modeling

TL;DR

This work investigates how spectral coverage shapes the reliability of parameter recovery in one-zone SSC blazar modeling by generating 63,000 synthetic SED fits for three representative blazars spanning LSP, ISP, and HSP classes. Using a CNN surrogate within a Bayesian framework, the authors quantify parameter recovery via coverage probabilities across 21 observational configurations, identifying minimal-band sets that yield robust inferences for each class (, , , , , , ). They find LSPs require modest optical/UV–X-ray–GeV coverage, ISPs benefit from broader X-ray–VHE or optical/UV–X-ray–HE coverage, and HSPs demand optical/UV–X-ray–VHE data, with VHE data most impactful for HSPs and sometimes nuanced for ISPs. The study offers practical guidance for multi-wavelength campaigns and highlights CTAO’s potential to improve parameter inferences, especially for ISP sources, while validating the value of extended VHE coverage for HSPs.

Abstract

Understanding the impact of spectral coverage on parameter recovery is critical for accurate interpretation of blazar spectra. In this study, we examine how the data coverage influences the reliability of parameter estimation within the one-zone synchrotron self-Compton (SSC) framework. Using OJ 287, TXS 0506+056, and Mrk 421 as representative of the low-, intermediate- and high synchrotron peak classes (LSP, ISP and HSP), respectively, we generate synthetic SEDs based on their best-fit models and perform 1,000 fits for each of the 21 observational configurations per source type. Our analysis quantifies the coverage probability for all model parameters, such has the magnetic field strength and the electron luminosity, and reveals that different blazar subclasses exhibit distinct sensitivities to spectral gaps. For LSPs, a minimal dataset comprising optical/UV, X-ray, and GeV -ray bands is sufficient for robust parameter inference. In contrast, ISPs and HSPs require broader spectral coverage to constrain the physical parameters. For ISP, we find that reliable parameter recovery can be achieved with two different minimal band combinations: \textit{(i)} X-ray, high energy -ray, and very high energy -ray data, or \textit{(ii)} optical/UV, X-ray, and high energy -ray data. For HSPs, the minimal configuration enabling reliable parameter recovery includes the optical/UV, X-ray, and very high energy -ray bands. We discuss the role of very high energy -ray observations, showing that they significantly enhance parameter recovery for HSPs. Our results provide practical guidelines for designing optimized multi-wavelength observation campaigns and for assessing the robustness of SSC model inferences under incomplete spectral coverage.

Paper Structure

This paper contains 15 sections, 3 equations, 5 figures, 2 tables.

Figures (5)

  • Figure 1: Observed SEDs of the three selected sources. Top left: the LSP blazar OJ 287. Top right: the ISP blazar TXS 0506+056. Bottom left: the HSP blazar Mrk 421. The data used for fitting are shown in blue, and the best-fit model is represented by the red line. Archival data retrieved from MMDC and Firmamento are shown in gray. Bottom right: best-fit models for all three blazars, displayed together with the instrumental bands used in this analysis. We note that the redshifts of these blazars differ, and therefore their observed fluxes also strongly differ. Studying the systematics induced by the different flux levels is beyond the scope of this work.
  • Figure 2: The density plots for selected LSP (top two rows), ISP (three middles rows), and HSP (three bottom rows) cases. The cases were chosen to show for each blazar type an acceptable recovery (HSP - case 3, ISP - case 12, LSP - case 11), a mediocre one (HSP - case 2, ISP - case 6) and an intermediate one (HSP - case 13, ISP - case 14, LSP - case 10) see the text for the details. The true parameter value, determined from the fits (see Table \ref{['tab:param']}), is shown as the red dashed line. If the distribution is narrowly peaked around the red dashed line at its center, the corresponding parameter is likely adequately recovered. Note that this is in fact quantified by the coverage probability.
  • Figure 3: Density matrix for the LSP OJ 287 showing the coverage probability for each parameter (line) in each case (column). The number in each cell corresponds to the coverage probability, which is also encoded in the colormap. Yellow cells correspond to high coverage probability while green cells represent lower coverage probability. A high coverage probability means that the fit retrieve the true parameter within its uncertainty. For LSPs, only cases without MAGIC data are presented.
  • Figure 4: Same as Figure \ref{['fig:LSP_coverage']} but for the ISP TXS 0506+056.
  • Figure 5: Same as for Figures \ref{['fig:LSP_coverage']} and \ref{['fig:ISP_coverage']}, but for HSP.