The relativistic jet and its central engine of $Fermi$ blazars

Jet origination is one of the most important questions of AGN, yet it stays obscure. In this work, we made use of information of emission lines, spectral energy distributions (SEDs), \textit{Fermi}-LAT $\gamma$-ray emission, construct a blazar sample that contains 667 sources. We notice that jet power originations are different for BL Lacs and for FSRQs. The correlation between jet power $P_{\rm jet}$ and the normalized disk luminosity $L_{\rm Disk}/L_{\rm Edd}$ shows a slope of -1.77 for BL Lacs and a slope of 1.16 for FSRQs. The results seem to suggest that BL Lac jets are powered by extracting blackhole rotation energy, while FSRQ jets are mostly powered by accretion disks. Meanwhile, we find the accretion ratio $\dot{M} / \dot{M}_{\rm Edd}$ increase with the normalized $\gamma$-ray luminosity. Base on this, we propose a dividing line, ${\rm log} (L_{\rm BLR}/L_{\rm Edd}) = 0.25 \ {\rm log} (L_{\rm \gamma}/L_{\rm Edd}) - 2.23$, to separate FSRQs and BL Lacs in the diagram of $L_{\rm BLR}/L_{\rm Edd}$ against $L_{\rm \gamma}/L_{\rm Edd}$ through using the machine learning method, the method gives an accuracy of 84.5\%. In addition, we propose an empirical formula, $M_{\rm BH}/M_{\rm \odot} \simeq L_{\rm \gamma}^{0.65}/21.46$, to estimate blackhole mass based on a strong correlation between $\gamma$-ray luminosity and blackhole mass. Strong $\gamma$-ray emission is typical in blazars, and the emission is always boosted by a Doppler beaming effect. In this work, we generate a new method to estimate a lower-limit of Doppler factor $\delta$ and give $\delta_{\rm BL Lac} = 7.94$ and $\delta_{\rm FSRQ} = 11.55$.