Changing-look Active Galactic Nuclei from the Dark Energy Spectroscopic Instrument. VII. Testing Disk–Corona Diagnostics with eROSITA

Changing-look active galactic nuclei (CL-AGN) have been proposed to follow an X-ray-binary-like, V-shaped relation between the optical/ultraviolet-to-X-ray spectral slope, αOX, and the Eddington ratio, λEdd ≡ Lbol/LEdd. We test this interpretation using CL-AGN selected from the Dark Energy Spectroscopic Instrument (DESI) and control samples matched to the eROSITA all-sky survey (eRASS). We find that the apparent positive correlation between αOX and the optical-continuum-based Eddington ratio, λEdd, opt, is not unique to CL-AGN, but also appears in matched non-changing-look samples. In broad-Hα AGN, our main statistical sample, this structure is largely driven by the known dependence of αOX on ultraviolet luminosity and by the covariance between the rest-frame 2500 Å luminosity, L2500, the black-hole mass, MBH, and λEdd, opt. When an X-ray-based Eddington ratio is used instead, the relation reverses sign because the X-ray luminosity, LX, enters the two axes with opposite signs. An apparent αOX–Eddington-ratio V-shape can therefore be induced by the luminosity estimator and is not a standalone accretion-state diagnostic. As a complementary test, we examine the eRASS effective photon index, Γeff, inferred from catalogue band fluxes. In broad-line AGN, it shows a weak positive association with the X-ray-independent optical Eddington ratio. However, the weaker hard-band trend depends on the null model and does not isolate coronal softening. These results motivate further X-ray spectroscopy, combined with independently estimated Eddington ratios, to test for intrinsic changes in the disk–corona system.