Preamble

Vol. 66 No. 5
Sept., 2025

Acta Astronomica Sinica

doi: 10.15940/j.cnki.0001-5245.2025.05.008

Multiband Radiation Correlations of Fermi Blazars

LIU Xin-tao ZHANG Hao-jing†
(School of Physics and Electronic Information, Yunnan Normal University, Kunming 650500)

Abstract

We collected multi-band radiation flux density data for blazar samples from the Fermi Large Area Telescope Fourth Source Catalog Data Release 3 (4FGL-DR3). The collected data cover radio (1.4 and 143 GHz), near-infrared (J, H, and K), optical (u, g, r, i, and z), ultraviolet (far ultraviolet and near ultraviolet), X-ray, and γ-ray bands across six energy segments (0.1–0.3, 0.3–1, 1–3, 3–10, 10–30, and 30–100 GeV) in the 0.1–100 GeV range. We analyzed correlations among different γ-ray energy bands and between γ-ray bands and multi-band radiation from radio to X-ray for the total blazar sample and its subclasses. Linear regression fitting results show that: among γ-ray energy bands, 70% of the results have correlation coefficients greater than 0.7, and 95% have confidence levels above 95%; between γ-ray and synchrotron radiation, 42% have correlation coefficients greater than 0.4 and 94.4% have confidence levels above 95%, indicating moderate correlation; the correlation between high-energy γ-ray and synchrotron radiation in blazars of unknown type (BCU) is very weak, with all correlation coefficients below 0.4. The analysis indicates that the fitting slopes for the BCU sample fall between those of the BL Lac object (BLL) and flat-spectrum radio quasar (FSRQ) samples, suggesting that the BCU sample is likely a mixture of BLL and FSRQ. The correlation between synchrotron radiation and γ-ray emission suggests that high-energy γ-ray in BLL is dominated by the synchrotron self-Compton (SSC) mechanism, while X-ray may be a mixture of synchrotron radiation and inverse Compton (IC) radiation.

Keywords galaxies: nuclei, gamma rays: galaxies, methods: data analysis, radiation mechanisms: non-thermal

1 Introduction

Blazars are a special subclass of radio-loud active galactic nuclei, characterized observationally by violent multi-band variability and high polarization in optical and radio bands. Based on the presence of prominent emission lines in their spectra, blazars are classified into flat-spectrum radio quasars (FSRQ) and BL Lac objects (BLL), with equivalent width (EW) > 5 Å for the former and EW < 5 Å for the latter. FSRQ have higher luminosity and lower synchrotron peak frequency than BLL, while BLL show extremely high radiation intensity from hard X-ray to TeV energy bands. Blazars that cannot be definitively classified as either FSRQ or BLL are called blazars of unknown type (BCU). The observed variability of blazars is believed to be caused by relativistic jets oriented toward the observer, whose radiation is greatly enhanced by relativistic beaming and dominates the overall emission. The low-energy radiation component (radio to soft X-ray) is widely believed to be produced by synchrotron radiation, while the high-energy component (hard X-ray, γ-ray) originates from inverse Compton (IC) scattering. However, the origin of γ-ray emission in blazars requires further investigation, with major controversies concerning the seed photons and high-energy charged particles involved in the IC process. The external Compton (EC) mechanism proposes that seed photons mainly come from dust torus, broad-line region, or accretion disk, while the synchrotron self-Compton (SSC) mechanism suggests that seed photons are dominated by synchrotron radiation produced by high-energy charged particles. Previous studies have discussed the relationship between synchrotron radiation and γ-ray emission in blazars. Abdo et al. analyzed strong correlations between optical and γ-ray bands in the blazar PKS 1510–089. Rajput et al. found different flux variation relationships between optical and GeV bands in four FSRQ. Tuo et al. analyzed relationships between multi-band γ-ray and radio emission in Fermi blazars. Yang et al. and Fossati et al. discussed relationships between synchrotron peak frequency and γ-ray emission. Zhang et al. found differences in the relationship between optical and γ-ray bands among blazars. This paper analyzes correlations between γ-ray and synchrotron radiation fluxes across various bands for blazars in the Fermi 4th source catalog, discussing the dominant mechanisms of γ-ray radiation and differences between blazar types (BLL and FSRQ).

2.1 Sample Selection

This study uses blazars from the 4FGL-DR3 catalog as the analysis sample. The Fermi survey telescope, launched in 2008, is dedicated to detecting high-energy γ-rays in the universe, with its Large Area Telescope providing a wide field of view. Blazars constitute a significant fraction of γ-ray sources detected by Fermi, collectively known as Fermi blazars. We collected high-energy γ-ray (0.1–100 GeV) flux data from Abdollahi et al., who calculated 12-year average fluxes for blazars in the 4FGL-DR3 catalog across eight energy bands (bands 1–8 corresponding to 0.05–0.1, 0.1–0.3, 0.3–1, 1–3, 3–10, 10–30, 30–100, and 100–1000 GeV) and provided test statistic (TS) values. Considering data reliability, we used data with TS > 4 (corresponding to standard deviation σ > 2). We excluded bands 1 and 8 due to their generally low TS values (mean values of 2.3 and 2.7, respectively, with some TS = 0). Additionally, Abdollahi et al. cross-matched their sources with the 4FGL catalog; we selected blazars with 4FGL associations, yielding 3437 sources after filtering. We converted fluxes in each band to flux density at the band's central frequency, with units of W·m⁻²·Hz⁻¹. The data are presented in Table 1 [TABLE:1] (due to the large volume, only partial sources are listed; complete data are available in Appendix B1).

2.2 Radio, Optical, and X-ray Band Data

Abdollahi et al. used Bayesian probability to estimate the most likely counterparts for their blazar sample. We retrieved average flux density data for these counterparts from the NASA/IPAC Extragalactic Database (NED) at radio (1.4 GHz), near-infrared (NIR) J, H, and K bands, optical u, g, r, i, and z bands, ultraviolet (UV) far UV (FUV) and near UV (NUV) bands. Optical data come from the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), which since DR2 no longer performs extinction correction, requiring manual compensation. NED calculated extinction magnitudes in each direction based on Schlafly et al., which we used to correct the optical data. Radio 143 GHz data are from Massaro et al. X-ray (0.1–2.4 keV) data are from Ackermann et al. Flux density data from radio to X-ray are presented in Table 2 [TABLE:2] (due to the large volume, only partial data are shown as reference; complete data are available in Appendix B2).

3.1 Relationships Among γ-ray Multi-band Flux Densities

Some studies analyzing relationships among γ-ray bands typically calculate total γ-ray flux in the 0.1–100 GeV range, which may mask detailed characteristics of γ-ray radiation. To minimize this effect, we directly use multi-band data from Fermi/LAT observations to discuss their relationships. We calculated flux densities at central energies for each band based on fluxes provided by Abdollahi et al., with results shown in Table 1. For convenience, we follow Abdollahi et al.'s convention and designate the six bands from low to high energy as numbers 2–7: "2" represents the 0.1–0.3 GeV band, using flux density at 0.2 GeV for correlation analysis; "3" represents the 0.3–1 GeV band, using flux density at 0.65 GeV, and so on. Linear regression fitting results for flux densities between γ-ray bands 2–7 for the total blazar sample and its subclasses are shown in Table 3 [TABLE:3].

3.2 Relationships Between γ-ray Multi-band and Radio-to-UV Flux Densities

Blazar observed radiation is dominated by non-thermal emission, though thermal radiation may become apparent during low states. Since thermal radiation does not cause significant effects, Yang et al. and Mingaliev et al. obtained blazar synchrotron peak frequency distributions through polynomial fitting. Therefore, we treat data from 1.4 GHz to UV bands obtained from NED and literature as synchrotron radiation data, analyzing correlations with γ-ray fluxes and discussing SSC mechanism applicability. In our correlation analysis, linear regression fitting results between NIR band J, H, and K flux densities and γ-ray band flux densities show minimal differences, and historical literature indicates these three frequency light curves vary synchronously with near-zero time delay. Thus, we use the sum of flux densities at these three frequencies as NIR fitting data. The optical band shows the same pattern, with minimal differences in linear regression results. However, UV band NUV and FUV flux densities show significant differences in correlation with γ-ray band flux densities, so we discuss them separately. Additionally, since radio band frequencies differ substantially, we discuss them separately. Correlation analysis results between synchrotron radiation and γ-ray flux densities show significant differences among blazar subclasses. Overall, BLL samples show the most significant correlation between γ-ray and synchrotron radiation, followed by FSRQ, with BCU showing the weakest. Balancing data quantity and representativeness, we present fitting results for γ-ray band 3 (0.3–1 GeV) and band 6 (10–30 GeV) in Table 4 [TABLE:4]; complete results are available in Appendix A.

3.3 Relationships Between X-ray and Radio, Optical, and γ-ray Multi-band Flux Densities

In blazars' double-peaked spectra, X-ray appears at the junction between synchrotron radiation and IC radiation. Therefore, analyzing correlations between different X-ray energy bands (typically divided into very soft, soft, hard, and very hard X-ray) and various bands helps comprehensively understand interactions between high-energy charged particles and synchrotron radiation, though such data are rarely reported. We collected 0.1–2.4 keV X-ray data to explore related radiation mechanisms through flux density correlation analysis. Different blazar subclasses show significant differences in correlation results between X-ray flux density and synchrotron radiation bands as well as γ-ray energy bands. Overall, FSRQ samples show the strongest correlation between X-ray and synchrotron/γ-ray bands (though weaker than BLL in UV bands), followed by BLL. BCU samples have insufficient data, but show extremely weak correlation between X-ray and γ-ray. Linear regression fitting results are shown in Table 5 [TABLE:5].

4.1 Relationships Among γ-ray Multi-band Flux Densities

We conventionally refer to the direction near 0.1 GeV in the 0.1–100 GeV γ-ray range as the "low-energy end" and near 100 GeV as the "high-energy end." Correlation analysis results show clear differences between high-energy and low-energy ends in 4FGL blazars, with different samples displaying different variation patterns. Using adjacent bands with the low-energy end as fit X and high-energy end as fit Y, we examine differences among samples through correlation strength and linear regression slope variations in bands 2–3, 3–4, 4–5, 5–6, and 6–7 (Table 3). All these band pairs show strong correlation (r > 0.7), allowing reliable discussion of slope differences. BLL sample regression slopes are 0.341, 0.324, 0.312, 0.331, and 0.311 sequentially; FSRQ sample slopes are 0.251, 0.216, 0.166, 0.128, and 0.080; BCU sample slopes (with few data points) are 0.328, 0.233, 0.181, 0.177, and 0.200; total sample slopes are 0.328, 0.233, 0.181, 0.177, and 0.200. Figure 1 [FIGURE:1] shows slope differences among blazar samples. In Figure 1, ■ represents BLL, ● represents FSRQ, ▲ represents BCU, and ▼ represents the total sample. The slope variation curve changes according to the proportion of different blazar subclasses in the sample. The BCU sample's slope curve transitions from near the FSRQ curve to near the BLL curve, corresponding roughly to the BLL/FSRQ number ratio changes in the total sample (Table 3): 161/372, 667/595, 1006/506, 1004/273, and 637/78. This demonstrates that the BCU sample is a mixture of BLL and FSRQ.

4.2 Relationships Between γ-ray and Radio/Optical Band Flux Densities

Significant disagreements exist between SSC and EC models for blazars. Case studies show: PKS 0537–441 (classified as BLL) was fitted with a single-zone SSC model by Pian et al., while Ammando et al. argued that SSC is insufficient and used an EC model; for FSRQ 3C273, Sokolov et al. used the SSC model to explain time delays. Additionally, Arsioli et al. studied low-synchrotron-peaked blazars (with 104 sources, comparable numbers of BLL and FSRQ), finding that EC mechanisms dominated by infrared radiation fields better explain their sample spectra; in Ghisellini et al.'s unified blazar theory study (also with mixed BLL and FSRQ samples), they found it difficult to distinguish between SSC and EC models in basic spectral fitting. This study investigates blazar γ-ray production mechanisms based on correlations among observed flux densities in various bands. Using band 3 as the low-energy representative and band 6 as the high-energy representative, we show correlation variations between γ-ray and synchrotron radiation in Figures 2 [FIGURE:2] to 4 [FIGURE:4]. Figure 2 shows correlations between γ-ray band 3 and synchrotron radiation bands; Figure 3 [FIGURE:3] shows correlations between γ-ray band 6 and synchrotron radiation bands; Figure 4 shows correlation variations between γ-ray and synchrotron radiation bands for the BLL sample. Hollow data points indicate linear regression P-values < 0.05; dashed lines cross bands lacking data. Generally, correlation coefficients > 0.7 or < -0.7 indicate strong correlation, 0.4 to 0.7 or -0.4 to -0.7 indicate moderate correlation, and 0.2 to 0.4 or -0.2 to -0.4 indicate weak correlation. These ranges are marked with dot-dashed lines in Figures 2–5. Complete correlation analysis results are in Tables 1–6 of Appendix A. Overall: BLL shows moderate correlation between synchrotron radiation and γ-ray; FSRQ shows weak correlation; BCU shows almost no correlation. These results support the view that SSC dominates in BLL. The different trends of the two curves in Figure 4 indicate that high-energy γ-ray in BLL is more influenced by high-energy synchrotron radiation (optical and UV bands), while low-energy γ-ray is more influenced by low-energy synchrotron radiation (radio bands). In Figure 2, FSRQ shows moderate correlation between radio bands and low-energy γ-ray, suggesting SSC is important for its low-energy γ-ray. The significant negative correlation between NIR and low-energy γ-ray in FSRQ (Figure 2) may be due to dust torus effects on NIR, though data are too limited for further speculation.

4.3 Relationships Between X-ray and Radio, Optical, and γ-ray Multi-band Flux Densities

To investigate X-ray radiation mechanisms, we analyzed correlation variations between X-ray flux density and radio, optical, and γ-ray multi-band flux densities. In the BLL sample, X-ray shows the strongest correlation with FUV (correlation coefficient 0.495, Table 5), and the rising curve trend in Figure 5 [FIGURE:5] suggests stronger correlation at higher frequencies. The FSRQ sample shows the strongest correlation between X-ray and optical bands (correlation coefficient 0.700, Table 5). Observing synchrotron radiation region curve variations in Figure 5, they resemble those in Figures 2 and 3 (for BLL, similar curve inflection points; for FSRQ, similar curve shapes if ignoring data-deficient NIR bands). Combined with correlation results, we conclude that SSC contributes significantly to X-ray in both FSRQ and BLL, and is more important for FSRQ. Fan et al. proposed that X-ray originates from synchrotron radiation or a mixture of synchrotron and IC mechanisms, which we believe better explains the complex relationship between X-ray and γ-ray shown in Figure 5. The two curves on the right side of Figure 5 rise from band 5 onward, possibly because high-energy charged particles producing high-energy γ-ray also produce part of the X-ray through synchrotron radiation. Tavecchio calculated that electrons radiating X-ray (1–10 keV) via synchrotron in low magnetic fields (≤ 0.1 G) have Lorentz factors of order 10⁴–10⁵. According to Rybicki & Lightman, these electrons would produce γ-ray at observed frequencies of 10²²–10²⁴ Hz via inverse Compton scattering of NIR photons (10¹⁴–10¹⁵ Hz), precisely the range from band 5 onward. In the FSRQ sample's γ-ray region, the curve declines from band 2 to band 5 (BLL shows no reliable correlation here, only a trend from band 2 to band 3), possibly because although seed photons for low-energy γ-ray and part of X-ray in the IC process come from the same radiation field, and combined with Section 4.2 discussion this IC process should be dominated by SSC, the high-energy charged particles producing the two types of radiation are far apart in their distribution spectrum. If we speculate that blazar X-ray is a mixture of synchrotron radiation from particles producing high-energy γ-ray and SSC radiation from particles producing low-energy γ-ray, the contributions of the two particle populations to the two X-ray components vary inversely as their distance in the distribution spectrum increases. The boundary point between the two populations in the distribution spectrum corresponds to the turning point in the γ-ray region curves in Figure 5: the boundary is at bands 3–4 for BLL and band 5 for FSRQ.

5 Conclusions

This study investigates relationships among flux densities of γ-ray energy bands and between γ-ray bands and radio, optical, and X-ray bands for the 4FGL-DR3 blazar sample. Main conclusions are: (1) BCU sample regression fitting slopes fall between BLL and FSRQ samples, and the slope variation curve matches the BLL/FSRQ number ratio changes, indicating BCU is a mixture of BLL and FSRQ. (2) Correlation between synchrotron radiation and γ-ray suggests BLL γ-ray radiation is dominated by SSC, while FSRQ low-energy γ-ray has significant SSC components and high-energy γ-ray is dominated by EC. (3) Both BLL and FSRQ samples show significant correlation between X-ray and synchrotron radiation, similar to their γ-ray vs. synchrotron correlation results, suggesting SSC's importance in the X-ray band. Combined with analysis of the complex relationship between X-ray and γ-ray, X-ray in both blazar types is mainly a mixture of synchrotron radiation and IC radiation dominated by SSC.

Acknowledgments

We thank Professor Yi Tingfeng from Yunnan Normal University for suggestions on data searching and collection.

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Appendix A: Correlation Tables

Table 1 Correlation between 1.4 GHz flux density and γ-ray energy band flux densities

Blazar Sample γ-ray Band Count Slope Slope Error P-value Total 0.1–0.3 GeV 598 1.81×10⁻³⁰ 1.19×10⁻³⁰ <0.001 Total 0.3–1 GeV 598 8.94×10⁻³² 8.94×10⁻³² <0.001 Total 1–3 GeV 598 5.43×10⁻³² 1.46×10⁻³⁰ <0.001 Total 3–10 GeV 598 1.06×10⁻³⁰ 4.57×10⁻³² <0.001 Total 10–30 GeV 598 2.15×10⁻³⁰ 2.48×10⁻³⁰ <0.001 Total 30–100 GeV 598 2.70×10⁻³⁰ 8.28×10⁻³² <0.001

Note: γ-ray Band represents the band set as Y in fitting.

Table 2 Correlation between 143 GHz flux density and γ-ray energy band flux densities

Blazar Sample γ-ray Band Count Slope Slope Error P-value Total 0.1–0.3 GeV 358 1.19×10⁻³¹ 1.27×10⁻³⁰ <0.001 Total 0.3–1 GeV 358 8.88×10⁻³¹ 1.02×10⁻³¹ <0.001 Total 1–3 GeV 358 1.56×10⁻³⁰ 1.78×10⁻³⁰ <0.001 Total 3–10 GeV 358 2.05×10⁻³⁰ 5.83×10⁻³³ <0.001 Total 10–30 GeV 358 7.46×10⁻³⁰ 8.55×10⁻³⁰ <0.001 Total 30–100 GeV 358 9.57×10⁻³⁰ 4.57×10⁻³⁰ <0.001

Table 3 Correlation between NIR flux density and γ-ray energy band flux densities

Blazar Sample γ-ray Band Count Slope Slope Error P-value Total 0.1–0.3 GeV 289 -0.644 -0.718 <0.001 Total 0.3–1 GeV 289 -0.615 -0.603 <0.001 Total 1–3 GeV 289 -0.467 -0.495 <0.001 Total 3–10 GeV 289 -0.519 -0.380 <0.001 Total 10–30 GeV 289 -0.243 -0.089 <0.001 Total 30–100 GeV 289 -0.075 -0.033 <0.001

Table 4 Correlation between optical flux density and γ-ray energy band flux densities

Blazar Sample γ-ray Band Count Slope Slope Error P-value Total 0.1–0.3 GeV 750 2.54×10⁻¹¹ 1.65×10⁻⁴ <0.001 Total 0.3–1 GeV 750 5.51×10⁻²⁸ 8.72×10⁻⁵⁹ <0.001 Total 1–3 GeV 750 9.08×10⁻³³ 3.52×10⁻⁵¹ <0.001 Total 3–10 GeV 750 1.07×10⁻³¹ 1.48×10⁻⁵⁸ <0.001 Total 10–30 GeV 750 1.26×10⁻³⁴ 4.01×10⁻²⁷ <0.001 Total 30–100 GeV 750 2.20×10⁻³⁰ 1.32×10⁻²⁸ <0.001

Table 5 Correlation between NUV flux density and γ-ray energy band flux densities

Blazar Sample γ-ray Band Count Slope Slope Error P-value Total 0.1–0.3 GeV 1132 1.95×10⁻¹¹ 1.81×10⁻³³ <0.001 Total 0.3–1 GeV 1132 3.50×10⁻²¹ 1.15×10⁻³⁶ <0.001 Total 1–3 GeV 1132 6.52×10⁻³⁵ 5.99×10⁻⁴² <0.001 Total 3–10 GeV 1132 2.31×10⁻³⁵ 3.25×10⁻³⁵ <0.001 Total 10–30 GeV 1132 4.09×10⁻³³ 1.06×10⁻³³ <0.001 Total 30–100 GeV 1132 3.31×10⁻³¹ 1.12×10⁻³¹ <0.001

Table 6 Correlation between FUV flux density and γ-ray energy band flux densities

Blazar Sample γ-ray Band Count Slope Slope Error P-value Total 0.1–0.3 GeV 713 1.66×10⁻¹¹ 1.47×10⁻³¹ <0.001 Total 0.3–1 GeV 713 1.98×10⁻²⁶ 6.59×10⁻⁴¹ <0.001 Total 1–3 GeV 713 1.32×10⁻³¹ 1.76×10⁻⁴¹ <0.001 Total 3–10 GeV 713 1.28×10⁻³¹ 2.57×10⁻³⁸ <0.001 Total 10–30 GeV 713 2.83×10⁻³¹ 9.30×10⁻⁴⁷ <0.001 Total 30–100 GeV 713 2.00×10⁻³¹ 1.95×10⁻³² <0.001

Appendix B: Data Availability

Due to the large data volume, Appendix B data are publicly available on figshare for readers to access.

Appendix B1 link: https://figshare.com/s/a93999a6c299acda9b72
Appendix B2 link: https://figshare.com/s/a93999a6c299acda9b72