Correlated variability of the reflection fraction with the X-ray flux and spectral index for Mrk 478

The X-ray spectrum of Mrk 478 is known to be dominated by a strong soft excess that can be described using relativistic blurred reflection. Using observations from XMM-Newton, AstroSat, and Swift, we show that for the long-term (~years) and intermediate-term (days to months) variability, the reflection fraction is anticorrelated with the flux and spectral index, which implies that the variability is due to the hard X-ray producing corona moving closer to and further from the black hole. Using flux-resolved spectroscopy of the XMM-Newton data, we show that the reflection fraction has the same behaviour with flux and index on short time-scales of hours. The results indicate that both the long- and short-term variability of the source is determined by the same physical mechanism of strong gravitational light bending causing enhanced reflection and low flux as the corona moves closer to the black hole.