# The Classification of Blazar Candidates of Uncertain Types

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## Abstract

**:**

## 1. Introduction

## 2. Sample and Classifications

#### 2.1. Samples

#### 2.2. Average Values

**$\gamma $-Ray Photon Flux-$\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$**: Based on the photon flux intensity from the 4FGL catalogue [1,3], we obtained the logarithm of the $\gamma $-ray photon flux ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$) and show their distributions for FSRQs and BL Lacs in the upper-left panel of Figure 1, and their cumulative distributions are in the upper-right panel of Figure 1. Their averaged values are $\langle \mathrm{log}\phantom{\rule{0.166667em}{0ex}}F\rangle \phantom{\rule{0.166667em}{0ex}}=-9.294\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.520$ for FSRQs and $\langle \mathrm{log}\phantom{\rule{0.166667em}{0ex}}F\rangle \phantom{\rule{0.166667em}{0ex}}=-9.434\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.482$ for BL Lacs. When a K-S test is performed to the distributions, a probability $p=6.708\times {10}^{-7}$ for the two distributions to be from the same parent distribution is obtained.

**Photon Spectral Index-${\alpha}_{\mathrm{ph}}$**: We show the distributions of ${\alpha}_{\mathrm{ph}}$ for FSRQs and BL Lacs in the middle-left panel in Figure 1, and their cumulative distributions are shown in the middle-right panel of Figure 1. The average photon spectral indexes are $\langle {\alpha}_{\mathrm{ph}}\rangle \phantom{\rule{0.166667em}{0ex}}=2.470\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.201$ for 795 FSRQs and $\langle {\alpha}_{\mathrm{ph}}\rangle \phantom{\rule{0.166667em}{0ex}}=2.032\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.212$ for 1432 BL Lacs. The K-S test gives $p=7.77\times {10}^{-16}$.

**Variability Index-VI**: For the variability index, we calculated the corresponding logarithm and show their distributions for FSRQs and BL Lacs in the lower-left panel of Figure 1, and their cumulative distributions are in the lower-right panel of Figure 1. For the averaged values, we have $\langle \mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I\rangle \phantom{\rule{0.166667em}{0ex}}=2.025\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.777$ for FSRQs and $\langle \mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I\rangle \phantom{\rule{0.166667em}{0ex}}=1.393\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.481$ for BL Lacs. The probability for the two distributions to be from the same parent distribution is $p=7.77\times {10}^{-16}$.

#### 2.3. Correlations

**Photon Flux versus Photon Spectral Index$(F-{\alpha}_{\mathrm{ph}})$**: From the given $\gamma $-ray photon flux and the photon spectral index from the 4FGL catalogue, we investigated their mutual correlation and obtained

**Photon Spectral Index versus Variability Index$({\alpha}_{\mathrm{ph}}-V\phantom{\rule{-0.166667em}{0ex}}I)$**: The photon spectral index and variability index give the following linear mutual correlation

**Flux versus Variability Index$(F-V\phantom{\rule{-0.166667em}{0ex}}I)$**: From the $\gamma $-ray photon flux and the variability index, we obtained their mutual correlation

#### 2.4. Classifications

## 3. Discussions

#### 3.1. The Average Values

#### 3.2. The Correlations for FSRQs and BL Lacs

#### 3.3. The Classification for BCUs

## 4. Conclusions

- The $\gamma $-ray photon flux, spectral index and variability index of FSRQs were higher than those of BL Lacs for the known blazar sample. There is a sequence from FSRQs to LBLs to HBLs that is similar to that in Fossati et al. [39].
- A positive correlation was found between the $\gamma $-ray flux and the photon spectral index for the whole sample; however, an anti-correlation was found for FSRQs and a positive correlation for BL Lacs. In addition, a positive correlation was found between the variability index ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I$) and the $\gamma $-ray photon spectrum index (${\alpha}_{\mathrm{ph}}$) for the whole sample but an anti-correlation for FSRQs and a positive correlation for BL Lacs. We found that those two positive correlations for the whole sample were apparent.
- We adopted the SVM machine-learning method to classify BL Lacs and FSRQs in the ${\alpha}_{\mathrm{ph}}\mathrm{vs}.\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$, and ${\alpha}_{\mathrm{ph}}\mathrm{vs}.V\phantom{\rule{-0.166667em}{0ex}}I$ plots and $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F\mathrm{vs}.V\phantom{\rule{-0.166667em}{0ex}}I$. We obtained 932 BL Lac candidates and possible BL Lac candidates as well as 585 FSRQ candidates and possible FSRQ candidates.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Histograms (

**left panel**) for FSRQs and BL Lacs and their corresponding cumulative probability distribution (CPD,

**right panel**) for three parameters. In this plot, the dashed red line for the BL Lacs and the solid black line for the FSRQs.

**Upper panel**: for logarithm of the $\gamma $-ray photons, $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$ in units of ph/cm

^{2}/s, middle panel: for the $\gamma $-ray photon spectral index, ${\alpha}_{\mathrm{ph}}$,

**bottom panel**: for logarithm of the $\gamma $-ray variability index, $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I$.

**Figure 2.**Plot of mutual correlations. The symbol ‘plus’ is for FSRQs, and the ‘open circle’ is for BL Lacs. The straight blue line stands for the best fitting result for blazars (BL Lacs and FSRQs), the ‘broken black line’ for FSRQs and the ‘broken red line’ for BL Lacs. The

**upper panel**is for the plot of photon spectral index (${\alpha}_{\mathrm{ph}}$) versus $\gamma $-ray photon flux ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$ (photon/cm

^{2}/s));

**middle panel**for photon spectral index (${\alpha}_{\mathrm{ph}}$) against variability index ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I$) and

**lower panel**for variability index ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I$) against $\gamma $-ray photon flux ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$ (photon/cm

^{2}/s)).

**Figure 3.**Plot of photon spectral index (${\alpha}_{\mathrm{ph}}$) against $\gamma $-ray photon flux ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$). Open circles stand for BL Lacs, plus for FSRQs and triangle points for BCUs. The solid line (${\alpha}_{\mathrm{ph}}=-0.223\phantom{\rule{0.166667em}{0ex}}\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F+1.170$) is obtained from the SVM method; it separates FSRQs and BL Lacs.

**Figure 4.**Plot of variability index ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I$) against gamma-ray photon flux ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F$). Open circles stand for BL Lacs, plus for FSRQs and triangle points for BCUs. The solid line (${\alpha}_{\mathrm{ph}}=-0.161\phantom{\rule{0.166667em}{0ex}}\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I+2.594$) is obtained from the SVM method; it separates FSRQs and BL Lacs.

**Figure 5.**Plot of variability index ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I$) against gamma-ray photon flux (log F). Open circles stand for BL Lacs, plus for FSRQs and triangle points for BCUs. The solid line ($\mathrm{log}\phantom{\rule{0.166667em}{0ex}}V\phantom{\rule{-0.166667em}{0ex}}I=0.792\mathrm{log}\phantom{\rule{0.166667em}{0ex}}F+9.203$) is obtained from the SVM method; it separates FSRQs and BL Lacs.

Type | Lower | Intermediate | Higher | Ref. | N |
---|---|---|---|---|---|

BL Lacs | $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<14.5$ | $14.5<\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<16.5$ | $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)>16.5$ | Nieppola et al. [20] | 308 |

$\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<14.0$ | $14.0<\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<15.0$ | $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)>15.0$ | Abdo et al. [21] | 48 | |

Blazars | $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<14.0$ | $14.0<\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<15.3$ | $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)>15.3$ | Fan et al. [22] | 1392 |

$\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<13.7$ | $13.7<\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)<14.9$ | $\mathrm{log}\phantom{\rule{0.166667em}{0ex}}{\nu}_{\mathrm{p}}\phantom{\rule{0.166667em}{0ex}}\left(\mathrm{Hz}\right)>14.9$ | Yang et al. [9] | 2709 |

4FGL Name | $\mathbf{log}\phantom{\rule{0.166667em}{0ex}}\mathit{F}$ | $\mathbf{log}\phantom{\rule{0.166667em}{0ex}}\mathit{V}\phantom{\rule{-0.166667em}{0ex}}\mathit{I}$ | ${\mathit{\alpha}}_{\mathbf{ph}}$ | Class${}^{{\mathit{\alpha}}_{\mathbf{ph}}-\mathit{F}}$ | Class${}^{{\mathit{\alpha}}_{\mathbf{ph}}-\mathit{V}\phantom{\rule{-0.166667em}{0ex}}\mathit{I}}$ | Class${}^{\mathit{F}-\mathit{V}\phantom{\rule{-0.166667em}{0ex}}\mathit{I}}$ | Class-TW | Class(K19) |
---|---|---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) |

4FGL J0001.2+4741 | −9.900 | 1.403 | 2.272 | BL Lac | BL Lac | FSRQ | P-B | BL Lac |

4FGL J0001.6-4156 | −9.549 | 1.421 | 1.775 | BL Lac | BL Lac | BL Lac | BL Lac | BL Lac |

4FGL J0001.8-2153 | −10.043 | 1.390 | 1.877 | BL Lac | BL Lac | FSRQ | P-B | NN |

4FGL J0002.1-6728 | −9.587 | 1.098 | 1.848 | BL Lac | BL Lac | BL Lac | BL Lac | BL Lac |

4FGL J0002.3-0815 | −9.924 | 1.114 | 2.092 | BL Lac | BL Lac | BL Lac | BL Lac | NN |

4FGL J0002.4-5156 | −10.108 | 1.248 | 1.914 | BL Lac | BL Lac | FSRQ | P-B | NN |

4FGL J0003.1-5248 | −9.463 | 0.903 | 1.916 | BL Lac | BL Lac | BL Lac | BL Lac | BL Lac |

4FGL J0003.3-1928 | −9.372 | 1.698 | 2.282 | BL Lac | BL Lac | BL Lac | BL Lac | P-F |

4FGL J0003.3-5905 | −9.916 | 1.006 | 2.274 | BL Lac | BL Lac | BL Lac | BL Lac | P-B |

4FGL J0003.5+0717 | −9.814 | 1.039 | 2.217 | BL Lac | BL Lac | BL Lac | BL Lac | NN |

4FGL J0007.7+4008 | −9.351 | 1.552 | 2.140 | BL Lac | BL Lac | BL Lac | BL Lac | BL Lac |

4FGL J0008.0-3937 | −9.920 | 1.220 | 2.626 | FSRQ | FSRQ | BL Lac | P-F | FSRQ |

4FGL J0008.4+1455 | −9.286 | 1.715 | 2.079 | BL Lac | BL Lac | BL Lac | BL Lac | BL Lac |

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## Share and Cite

**MDPI and ACS Style**

Fan, J.-H.; Chen, K.-Y.; Xiao, H.-B.; Yang, W.-X.; Liang, J.-C.; Chen, G.-H.; Yang, J.-H.; Yuan, Y.-H.; Wu, D.-X.
The Classification of Blazar Candidates of Uncertain Types. *Universe* **2022**, *8*, 436.
https://doi.org/10.3390/universe8080436

**AMA Style**

Fan J-H, Chen K-Y, Xiao H-B, Yang W-X, Liang J-C, Chen G-H, Yang J-H, Yuan Y-H, Wu D-X.
The Classification of Blazar Candidates of Uncertain Types. *Universe*. 2022; 8(8):436.
https://doi.org/10.3390/universe8080436

**Chicago/Turabian Style**

Fan, Jun-Hui, Ke-Yin Chen, Hu-Bing Xiao, Wen-Xin Yang, Jing-Chao Liang, Guo-Hai Chen, Jiang-He Yang, Yu-Hai Yuan, and De-Xiang Wu.
2022. "The Classification of Blazar Candidates of Uncertain Types" *Universe* 8, no. 8: 436.
https://doi.org/10.3390/universe8080436