Extreme Variability Reveals How the Eddington Ratio Regulates Coronal Power in Active Galactic Nuclei

The bolometric luminosity ($L_{\mathrm{b}\mathrm{o}\mathrm{l}}$) of active galactic nuclei (AGNs) is a key tracer of accretion physics, but its direct determination is often hindered by limited spectral coverage and contamination of the host galaxy. Bolometric corrections (${\kappa }_{\lambda }=L_{\mathrm{b}\mathrm{o}\mathrm{l}}\mathrm{/}{L}_{\lambda }$) offer a practical means of estimating $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$, with the X-ray bolometric correction (${\kappa }_{2-10}$) being crucial for exploring the coupling between the accretion disk and the X-ray corona. Here we present multi-epoch, multi-wavelength observations of five highly variable, changing-state AGNs that span more than three orders of magnitude in Eddington ratio ($-3.6\lesssim \log {\lambda }_{\mathrm{E}\mathrm{d}\mathrm{d}}\lesssim -0.5$). This unique data set reveals a remarkably tight relation between ${\kappa }_{2-10}$ and ${\lambda }_{\mathrm{E}\mathrm{d}\mathrm{d}}$, with an intrinsic scatter of only $\sim 0.05$ dex. We find that while the sources show bolometric corrections following different tracks in luminosity space that depend on black hole mass, they all display the same ${\kappa }_{2-10}-{\lambda }_{\mathrm{E}\mathrm{d}\mathrm{d}}$ trend. This shows unambiguously that ${\lambda }_{\mathrm{E}\mathrm{d}\mathrm{d}}$ is the primary driver of X-ray bolometric corrections, and points to a tight underlying trend that can be used to obtain reliable estimates of bolometric output from X-ray luminosities. Our results highlight how time-domain, multi-wavelength observations of variable AGN offer unique insights into the accretion flow structure and its radiative output.