Radio-Gamma-Ray Properties and High-Energy Implications for Fermi Blazars

Radio and $\gamma$-ray emissions in blazars, a subclass of active galactic nuclei (AGNs), provide important insight into their high-energy radiation processes. We studied the relation between radio and $\gamma$-ray emissions using a large sample of 1687 \textit{Fermi} blazars, based on the Radio Fundamental Catalogue and the latest Third Data Release of the Fourth \textit{Fermi} AGN Catalogue. A clear correlation between radio and $\gamma$-ray fluxes for both BL Lacertae objects (BL Lacs) and flat-spectrum radio quasars (FSRQs) suggests a synchrotron self-Compton (SSC) contribution to both subclasses. The ratio of $\gamma$-ray and radio emissions, $\gamma$-ray loudness ($G_{\rm r}$), is further examined with the $\gamma$-ray photon index ($\Gamma_\gamma$) and the synchrotron peak frequency ($\nu_{\rm{peak}}$). An anti-correlation between $G_{\rm r}$ and $\Gamma_\gamma$ is explained by the shift of the spectral energy distribution rather than the Compton cooling effect. We found that $G_{\rm r}$ shows a positive dependence on $\nu_{\rm{peak}}$ for low-synchrotron-peaked BL Lacs (LBLs) and FSRQs, in line with the SSC-contributed scenario, although additional external Compton contributions may account for the substantial scatter observed in LBLs and FSRQs. In contrast, high-synchrotron-peaked BL Lacs (HBLs) reach the plateau of $G_{\rm r}$ between $\log (\nu_{\rm peak}/{\rm Hz}) \simeq15.5-16$, possibly indicating the transition from the Thomson to the Klein--Nishina (KN) regime. Interpreting this feature within a one-zone SSC framework could constrain the magnetic field strength of $-4.14 < \log (B/{\rm G}) < -1.69$ for those HBLs affected by the KN suppression.