On estimators of the jet bolometric luminosity of Fermi 2LAC blazars

Bolometric luminosity is a basic physical parameter that is widely used in the study of blazars. Due to the lack of simultaneous full wavelength data, several estimators of the bolometric luminosity are being used in practice. In this paper, we study and evaluate the reliability and significance of six estimators, the $5GHz$ luminosity, the 1keV luminosity, the $\gamma$-ray luminosity, the $5GHz$ luminosity+the 1keV luminosity, the $5GHz$ luminosity+the $\gamma$-ray luminosity and the 1keV luminosity+the $\gamma$-ray luminosity, by analyzing the linear correlations between the integrated bolometric luminosity and them. Our main results are as follows. (i) All the six estimators are reliable in the sense that they are all significant correlated with the bolometric luminosity. (ii) Ranking from the higher significance of the reliability to lower one the six estimators are the the $5GHz$ luminosity+the $\gamma$-ray luminosity, the 1keV luminosity+the $\gamma$-ray luminosity, $\gamma$-ray luminosity, the $5GHz$ luminosity+the 1keV luminosity, the $5GHz$ luminosity and the 1keV luminosity. (iii) We suggest that the bolometric luminosity can be well estimated by the $\gamma$-ray luminosity using the best linear equation that given in this paper for Fermi FSRQs. (iv) According to the linear regressions obtained in the analysis, we provide calibration for each estimator.