Radio Core Size of Low-luminosity Active Galactic Nuclei under the MAD-jet model

After decades of efforts, there are now fruitful high-resolution radio observations of low-luminosity active galactic nuclei (LLAGNs), and the observed frequency has extended from $\sim$10 GHz up to $\sim$200 GHz. In this work, based on a model that combines a magnetically arrested disk (MAD) and a Blandford-Znajek-like jet, we carried out detailed analysis on size and location of the radio core of LLAGNs. The radio core size of nearby LLAGN M104 is re-visited based on this new model. We successfully reproduce a $size\propto\nu^{-1}$ scaling between 1 GHz and tens of GHz, if more than $50\%$ of electrons in jet follow a power-law (PL) distribution. We further confirm that, at high radio frequencies emission from MAD exceeds that from jet, and a flatter size-frequency slope is observed. The impact of PL electrons in MAD is also investigated. For those $L_{\rm bol}/L_{\rm Edd} \gtrsim (3-8)\times 10^{-6}$ LLAGNs and black hole binaries in their hard state, PL electrons are expected to be highly suppressed due to strong radiative cooling (so-called `synchrotron boiler' effect).