A physical model for the X-ray time lags of narrow-line Seyfert type 1 active galactic nuclei

We study the origin of the soft X-ray excess seen in the `simple' narrow-line Seyfert 1 galaxy PG1244+026 using all available spectral-timing information. This object shows the now ubiquitous switch between soft leading the hard band on long time-scales, to the opposite behaviour on short time-scales. This is interpreted as a combination of intrinsic fluctuations propagating down through the accretion flow giving the soft lead, together with reflection of the hard X-rays giving the soft lag. We build a full model of the spectral and time variability including both propagation and reflection, and compare our model with the observed power spectra, coherence, covariance, lag-frequency and lag-energy spectra. We compare models based on a separate soft excess component with those based on reflection-dominated soft emission. Reflection-dominated spectra have difficulty reproducing the soft lead at low frequency since reflection will always lag. They also suffer from high coherence and nearly identical hard- and soft-band power spectra in disagreement with the observations. This is a direct result of the power-law and reflection components both contributing to the hard and soft energy bands, and the small radii over which the relativistically smeared reflection is produced allowing too much high-frequency power to be transmitted into the soft band. Conversely, we find the separate soft excess models (where the inner disc radius is >6R_g) have difficulty reproducing the soft lag at high frequency, as reflected flux does not contribute enough signal to overwhelm the soft lead. However, reflection should also be accompanied by reprocessing and this should add to the soft excess at low energies. This model can quantitatively reproduce the switch from soft lead to soft lag seen in the data and reproduces well the observed power spectra and other timing features which reflection-dominated models cannot.