The luminosity correlation analysis for Fermi blazars

Abstract

In this paper, multiwavelength chromatic luminosity at radio ($\log L _{\mathrm{R}}$), optical ($\log L_{\mathrm{O}}$), X-ray ($\log L _{\mathrm{X}}$), and $\gamma$-rays ($\log L_{\gamma }$) for a sample of 442 Fermi blazars with known redshifts are collected from Fan et al. (2016), to study the correlations between the $\gamma$-rays and the low-energy bands using a multiple linear regression analysis. In this way, we can see which band is more important for the $\gamma$-ray emissions. Mutual correlation analysis is also used to discuss the correlations between the $\gamma$-ray and the low energy bands for the whole sample and subclasses. We come to following conclusions:

• 1. The multiple linear correlation indicates that the $\gamma$-rays are correlated with the radio, optical and the X-ray emissions for the whole sample and the subclasses of flat spectrum radio quasars (FSRQs) and BL Lac objects (BL Lacs), the correlation between the $\gamma$-rays and the radio emissions is the strongest one.

• 2. For BL Lacs, the optical emissions are more important than the X-rays for the $\gamma$-rays, while the X-ray emissions are more important than optical ones in FSRQs.

• 3. The $\gamma$-ray emissions in HBL are from an synchrotron self-Compton, while those in FSRQs may be from external Compton and synchrotron self-Compton as well.