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Blazars show extreme observational properties that are due to the beaming effect with the jet being close to the line of sight. It was found that the observed luminosity is anticorrelated with the synchrotron peak frequency but the debeamed luminosity and the frequency is positively correlated. In this work, we revisit this correlation for a large sample of 255 blazars from the fourth Fermi catalog with available Doppler factors. Our analysis comes to the following conclusions. (1) The observed radio, X-ray, Îł -ray, and synchrotron peak luminosity are all anticorrelated with the peak frequency, but the debeamed luminosity is positively correlated with the debeamed peak frequency. The anticorrelation is due to a selection effect or a beaming effect. (2) The Compton dominance parameter is correlated with both the bolometric luminosity and Doppler factor, implying that the more highly Compton-dominated sources are more luminous. (3) The bolometric luminosity can be represented by the Îł -ray luminosity for Fermi blazars. [ABSTRACT FROM AUTHOR]

In this paper, a sample of 451 blazars (193 flat spectrum radio quasars (FSRQs), 258 BL Lacertae objects) with corresponding X-ray and Fermi γ-ray data is compiled to investigate the correlation both between the X-ray spectral index and the γ-ray spectral index and between the spectral index and the luminosity, and to compare the spectral indexes αX, αγ, αXγ, and αγXγ for different subclasses. We also investigated the correlation between the X-ray and the γ-ray luminosity. The following results have been obtained. (1) Our analysis indicates that an anti-correlation exists between the X-ray and the γ-ray spectral indexes for the whole sample. However, when we considered the subclasses of blazars (FSRQs, the low-peaked BL Lacertae objects (LBLs) and the high-peaked BL Lacertae objects (HBLs)) separately, there is not a clear relationship for each subclass. For the average values, , we have ; and (2) For the correlations between the X-ray and the γ-ray luminosities, we have log νLγ = (1.033 ± 0.002)log νLX + (0.213 ± 0.094) for the whole sample, log νLγ = (0.741 ± 0.004)log νLX + (12.378 ± 0.162) for HBLs, and log νLγ = (1.032 ± 0.003)log νLX + (0.643 ± 0.138) for the LBLs and FSRQs; the correlation slope for HBLs is different from that for FSRQs and LBLs. For the average values, , we have , , and for the X-ray luminosity; and , , and for the γ-ray luminosity. (3) There is an anti-correlation between the effective spectral index, αXγ, and log νLγ for the whole sample, and the subclasses (FSRQs, LBLs, and HBLs). The effective spectral index shows that (4) For the spectral index difference, αγXγ(=αXγ – αγ) of the effective spectral index, αXγ, and the γ-ray spectral index, αγ, we obtain (5) Based on the Fermi-detected sources, we can say that the HBLs are different from FSRQs, while the LBLs are similar to FSRQs. [ABSTRACT FROM AUTHOR]