Mapping the X-ray corona evolution of IRAS 13224-3809 with the power spectral density

We develop the power spectral density (PSD) model to explain the nature of the X-ray variability in IRAS 13224-3809, including the full effects of the X-ray reverberation due to the lamp-post source. We utilize 16 XMM-Newton observations individually as well as group them into three different luminosity bins: low, medium and high. The soft (0.3-1 keV) and hard (1.2-5 keV) PSD spectra are extracted and simultaneously fitted with the model. We find that the corona height changes from h ~ 3 $r_{\mathrm{g}}$ during the lowest luminosity state to ~ $25r_{\mathrm{g}}$ during the highest luminosity state. This provides further evidence that the source height from the reverberation data is significantly larger than what constrained by the spectral analysis. Furthermore, as the corona height increases, the energy spectrum tends to be softer while the observed fractional excess variance, $F_{\mathrm{v}\mathrm{a}\mathrm{r}}$, reduces. We find that the PSD normalization is strongly correlated with $F_{\mathrm{v}\mathrm{a}\mathrm{r}}$, and moderately correlated with the PSD bending index. Therefore, the normalization is dependent on accretion rate that controls the intrinsic shape of the PSD. While the intrinsic variability of the disk is manifested by the reverberation signals, the disk and corona may evolve independently. Our results suggest that, during the source height increases, the disk itself generates less overall variability power but more high-frequency variability resulting in the PSD spectrum that flattens out (i.e. the inner disk becomes more active). Using the luminosity-bin data, the hint of Lorentzian component is seen, with the peak appearing at lower frequencies with increasing luminosity.