On Measuring the Variation of High-energy Cutoff in Active Galactic Nuclei

The variation in the high-energy cutoff, E _c , in active galactic nuclei (AGNs) uniquely probes the corona physics. In this work, we show that the ratio of two NuSTAR spectra (analogous to the 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 five AGNs in the 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 that the claimed E _c variations appear inconsistent with the spectra ratios in three of them, thus they 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 six sources in this small sample appear softer when brighter. Changes in corona geometry are required to explain the observed hotter-when-brighter trends.