Ratio of the Core to the Extended Emissions in the Comoving Frame for Blazars

Abstract

In a two-component jet model, the emissions are the sum of the core and extended emissions: $S^{\mathrm{ob}}=S_{\mathrm{core}}^{\mathrm{ob}}+S_{\mathrm{ext}}^{\mathrm{ob}}$, with the core emissions, $S_{\mathrm{core}}^{\mathrm{ob}}= f S_{\mathrm{ext}}^{\mathrm{ob}}\delta ^{q}$ being a function of the Doppler factor $\delta$, the extended emission $S_{\mathrm{ext}}^{\mathrm{ob}}$, the jet type dependent factor q, and the ratio of the core to the extended emissions in the comoving frame, f. The f is an unobservable but important parameter. Following our previous work, we collect 65 blazars with available Doppler factor $\delta$, superluminal velocity $\beta _{\mathrm{app}}$, and core-dominance parameter, R, and calculated the ratio, f, and performed statistical analyses. We found that the ratio, f, in BL Lacs is on average larger than that in FSRQs. We suggest that the difference of the ratio f between FSRQs and BL Lacs is one of the possible reasons that cause the difference of other observed properties between them. We also find some significant correlations between $\log f$ and other parameters, including intrinsic (de-beamed) peak frequency, $\log \nu _{\mathrm{p}}^{\mathrm{in}}$, intrinsic polarization, $\log P^{\mathrm{in}}$, and core-dominance parameter, $\log R$, for the whole sample. In addition, we show that the ratio, f, can be estimated by R.