Constraining Energy-dependent emissivity profiles of AGN inflows

The emissivity of the accretion flow is a key parameter affecting the shape of both the energy and variability power spectrum of AGN. We explore the energy-dependence of the power spectrum for five AGN, across the XMM-Newton bandpass, and across the 0.01-1 mHz frequency range, finding a ubiquitous flattening of the power spectrum towards higher energies. We develop a framework to explore this behaviour and thereby extract the energy dependence of the emissivity assuming a simple disc-like geometry for the inflow. We find that the emissivity ranges from R^-2 at energies around the soft excess and increases to R^-4 or steeper above ~4-6 keV. We describe the changing emissivity index with a linear function in energy, finding the best-fitting slopes to vary between AGN. We attempt to correlate the slope of the linear function against key AGN parameters but, as yet, the sample size is too small to confirm hints of a correlation with Eddington ratio.