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 ($\nu_{\rm p}^{\rm in}$) 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 $\nu_{\rm p}^{\rm in}$ is found, suggesting that synchrotron emissions are highly correlated with $\gamma$-ray emissions.