XMM-Newton observations of the narrow-line Seyfert 1 galaxy IRAS 13224-3809: X-ray spectral analysis II

Previously, we modelled the X-ray spectra of the narrow-line Seyfert 1 galaxy IRAS 13224-3809 using a disc reflection model with a fixed electron density of 10¹⁵ cm^-3. An additional blackbody component was required to fit the soft X-ray excess below 2 keV. In this work, we analyse simultaneously five flux-resolved XMM-Newton spectra of this source comprising data collected over 2 Ms. A disc reflection model with an electron density of n_e ≈ 10²⁰ cm^-3 and an iron abundance of $Z_{\rm Fe}=3.2\pm 0.5\, \mathrm{Z}_{\odot }$ is used to fit the broad-band spectra of this source. No additional component is required to fit the soft excess. Our best-fitting model provides consistent measurements of black hole spin and disc inclination angle as previous models where a low disc density was assumed. In the end, we calculate the average illumination distance between the corona and the reflection region in the disc of IRAS 13224-3809 based on best-fitting density and ionization parameters, which changes from 0.43$\sqrt{f_{\rm AD}/f_{\rm INF}}$ r_g in the lowest flux state to 1.71$\sqrt{f_{\rm AD}/f_{\rm INF}}$ r_g in the highest flux state assuming a black hole mass of $2\times 10^{6}\, \mathrm{M}_{\odot }$. f_AD/f_INF is the ratio between the flux of the coronal emission that reaches the accretion disc and infinity. This ratio depends on the geometry of the coronal region in IRAS 13224-3809. So we only discuss its value based on the simple 'lamppost' model, although detailed modelling of the disc emissivity profile of IRAS 13224-3809 is required in future to reveal the exact geometry of the corona.