The Intrinsic $gamma$-ray Emissions of $Fermi$ Blazars

Beaming effect is important for the observational properties of blazars. In this work, we collect 91 $Fermi$ blazars with available radio Doppler factors. $gamma$-ray Doppler factors are estimated and compared with radio Doppler factors for some sources. The intrinsic (de-beamed) $gamma$-ray flux density ($f^{rm in}_{gamma}$), intrinsic $gamma$-ray luminosity ($L^{rm in}_{gamma}$), and intrinsic synchrotron peak frequency ($ u_{rm p}^{rm in}$) are calculated. Then we study the correlations between $f^{rm in}_{gamma}$ and redshift and find that they follow the theoretical relation: $log f = -2.0 log z + {rm const}$. When the subclasses are considered, we find that stationary jets are perhaps dominant in low synchrotron peaked blazars. 63 $Fermi$ blazars with both available short variability time scales ($Delta T$) and Doppler factors are also collected. We find that the intrinsic relationship between $L ^{rm in}_{gamma}$ and $Delta T^{rm in}$ obeys the Elliot & Shapiro and the Abramowicz & Nobili relations. Strong positive correlation between $f_{gamma}^{rm in}$ and $ u_{rm p}^{rm in}$ is found, suggesting that synchrotron emissions are highly correlated with $gamma$-ray emissions.