Modelling X-ray RMS spectra II: the ultra-fast outflow of PDS 456

We present an improved model for excess variance spectra describing ultra-fast outflows and successfully apply it to the luminous (L ~ 10^47 erg/s) low-redshift (z = 0.184) quasar PDS 456. The model is able to account well for the broadening of the spike-like features of these outflows in the excess variance spectrum of PDS 456, by considering two effects: a correlation between the outflow velocity and the logarithmic X-ray flux and intrinsic Doppler broadening with v_int = 10^4 km/s. The models were generated by calculating the fractional excess variance of count spectra from a Monte Carlo simulation. We find evidence that the outflow in PDS 456 is structured, i.e., that there exist two or more layers with outflow velocities 0.27-0.30 c, 0.41-0.49 c, and 0.15-0.20 c for a possible third layer, which agrees well with the literature. We discuss the prospects of generally applicable models for excess variance spectra for detecting ultra-fast outflows and investigating their structure. We provide an estimate for the strength of the correlation between the outflow velocity and the logarithmic X-ray flux and investigate its validity.