Multi-band luminosity correlation analysis for Fermi blazars

Abstract Multi-band and $\gamma$-ray radiation are important properties of blazars. In this paper, the luminosity correlations between the $\gamma$-ray and lower-energy (radio, optical, and X-ray) bands for both the observed and intrinsic data are investigated using the multiple linear regression analysis for a sample of 642 blazars (227 flat spectrum radio quasars and 415 BL Lacertae objects). In addition, we employ a partial correlation analysis to exclude the redshift effect in the mutual correlation analysis. We also investigate the intrinsic luminosity correlations using the second-order partial correlation analysis to exclude the effects of redshift and Doppler factor, which has allowed us to obtain the intrinsic correlation without the influence of relativistic beaming effect or redshift. We find that both the observed and intrinsic $\gamma$-ray emissions are correlated with the radio, optical, and the X-ray bands, with the radio and optical bands being important for the $\gamma$-ray emissions, indicating that the $\gamma$-ray emissions originate from the lepton model, including self-synchrotron Compton and external Compton processes.