Recent intense X-ray and UV monitoring campaigns with Swift have detected clear UV lags behind X-ray in several local active galactic nuclei (AGNs). The UV to X-ray lags are often larger (by a factor up to ~ 20) than expected if the UV variation is simply due to the X-ray reprocessing. We previously developed a model in which the UV/optical variations are attributed to disk turbulences, and the effect of large-scale turbulence is considered. Our model, which overcomes many severe challenges to the reprocessing scheme, can well explain the observed variations in NGC 5548, particularly the correlations and lags among the UV/optical bands. In this work, assuming the corona heating is associated with turbulences in the inner accretion disk, we extend our study to model the correlations and lags between the X-ray and UV/optical bands. We find that our model, without the need of light echoing, can well reproduce the observed UV to X-ray lags and the optical to UV lags simultaneously in four local Seyfert galaxies, including NGC 4151, NGC 4395, NGC 4593, and NGC 5548. In our scenario, relatively larger UV to X-ray lag is expected for AGN with smaller innermost disk radius and thus more compact corona. Interestingly, for these Seyfert galaxies studied in this work, sources with relatively larger UV to X-ray lags do have broader Fe Ka lines, indicative of relativistic broadening due to more compact corona and smaller innermost disk radius. If confirmed with more X-ray and UV monitoring campaigns, this interesting discovery would provide a new probe to the inner disk/corona.
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