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The variation in the high energy cut-off E_c in active galactic nuclei uniquely probes the corona physics. In this work we show that the ratio of two NuSTAR spectra (in analogy to difference imaging technique widely used in astronomy) is uniquely useful in studying E_c variations. The spectra ratio could directly illustrate potential E_c variation between two spectra. By comparing with the ratio of two spectral fitting models, it also examines the reliability of the spectral-fitting measured E_c variation. Assisted with this technique, we revisit the 5 AGNs in literature (MCG -5-23-16, 3C 382, NGC 4593, NGC 5548 and Mrk 335) for which E_c (kT_e) variations have been claimed with NuSTAR observations. We show the claimed E_c variations appear inconsistent with the spectra ratios in three of them, thus need to be revised, demonstrating the striking usefulness of spectra ratio. We present thereby improved spectral fitting results and E_c variations. We also report a new source with E_c variations based on NuSTAR observations (radio galaxy 4C +74.26). We find the corona tends to be hotter when it brightens (hotter-when-brighter) in 3C 382, NGC 5548, Mrk 335 and 4C +74.27, but MCG -5-23-16 and NGC 4593 show no evidence of significant E_c variations. Meanwhile all 6 sources in this small sample appear softer-when-brighter. Changes in corona geometry are required to explain the observed hotter-when-brighter trends., Comment: 14 pages, 13 figures, ApJ in press

The reprocessing scenario is widely adopted in literature to explain the observed tight inter-band correlation and short lags in the UV/optical variations of active galactic nuclei (AGNs). In this work we look into the color variability of the famous Seyfert galaxy NGC 5548 with high quality Swift multi-band UV/optical light curves. We find the color variation of NGC 5548 is clearly timescale-dependent, in a way that it is more prominent at shorter timescales. This is similar to that previously detected in quasar samples, but for the first time in an individual AGN. We show that while a reprocessing model with strict assumptions on the driving source and the disk size can apparently match the observed light curves and inter-band lags, it fails to reproduce the observed timescale dependency in the color variation. Such discrepancy raises a severe challenge to, and can hardly be reconciled under the widely accepted reprocessing diagram. It also demonstrates that the timescale dependency of the color variation is uniquely powerful in probing the physics behind AGN UV/optical variations., Comment: 13 pages, 5 figures; ApJ accepted