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

We present an improved model for excess variance spectra describing ultrafast outflows and successfully apply it to the luminous ($L_{\rm bol}\sim 10^{47}\mathrm{erg}\, \mathrm{s}^{-1}$) low-redshift (z = 0.184) quasar Pico del Dias Survey (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 $v_\mathrm{int} = 10^4\, \mathrm{km}\, \mathrm{s}^{-1}$. 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. 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 ultrafast 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.