Detection of the cosmological evolution of the Doppler factor for blazars jets

The Doppler factor ($\delta$) is a fundamental quality for the relativistic jets from active galactic nuclei (AGNs). It is also fundamental to assessing the number of the entire population of the jetted AGN at high redshift ($z$), and therefore is important for tracing the growth of supermassive black holes (SMBHs) across cosmic time. Here we present the identification of the positive cosmic evolution of the Doppler factor in {\it Fermi}-detected bright $\gamma -$ray blazars. The redshift dependence of the Doppler factor, $\delta \propto (1+z{)}^{0.8}$, is measured from the observed characteristic energies in the gamma-ray spectra of 141 blazars. Moreover, the analysis of the characteristic timescales derived from modeling the long-term optical light curves of 89 blazars with Gaussian process regression gives $\delta \propto (1+z{)}^{1.1}$, but with a larger scatter. $\mathbf{\text{Note}}\mathbf{\text{that}}\mathbf{\text{each}}\mathbf{\text{index}}\mathbf{\text{is}}\mathbf{\text{derived}}\mathbf{\text{from}}\mathbf{\text{the}}\mathbf{\text{entire}}\mathbf{\text{sample,}}\mathbf{\text{representing}}\mathbf{\text{an}}\mathbf{\text{average}}\mathbf{\text{evolution.}}\mathbf{\text{Interestingly,}}\mathbf{\text{the}}\mathbf{\text{index}}\mathbf{\text{itself}}\mathbf{\text{also}}\mathbf{\text{appears}}\mathbf{\text{to}}\mathbf{\text{evolve,}}\mathbf{\text{with}}\mathbf{\text{low-luminosity}}\mathbf{\text{sources}}\mathbf{\text{showing}}\mathbf{\text{stronger}}\mathbf{\text{evolution,}}\mathbf{\text{as}}\mathbf{\text{indicated}}\mathbf{\text{by}}\mathbf{\text{a}}\mathbf{\text{larger}}\mathbf{\text{index.}}$ This detection straightly suggests that relativistic jets from AGNs are much more common at high redshifts than what is previously estimated.