Understanding coronal geometry in NGC 4593 using Fourier frequency-resolved covariance and time-lag spectral analysis

TL;DR

The study targets the origin and geometry of the X-ray corona in NGC 4593 by exploiting two long XMM-Newton observations and applying frequency-resolved covariance and energy-dependent time-lag spectral analyses. By separating high- and low-flux states, the authors demonstrate a flux-dependent swap from a direct power-law–dominated variability regime to a reflection-dominated one, and they infer substantial changes in coronal size, from $<3.3\,R_g$ to $>7.2\,R_g$, accompanied by a rise in disc ionization and a reverberation delay of about $483\pm135$ s in the high-flux state. The joint timing and spectral modelling indicates that the soft excess in high flux is best described by blurred disc reflection, while low flux shows a more subdued reflection component and a more compact corona. These results highlight a dynamically evolving disc–corona geometry in response to flux changes and showcase the power of Fourier-frequency resolved covariance and lag analyses for probing AGN inner regions. Overall, the work provides quantitative constraints on coronal height and disc ionization tied to flux states, improving our understanding of reverberation variability in Seyfert galaxies.

Abstract

Understanding disc-corona geometry through X-ray reverberation variability studies in Seyfert galaxies is crucial, yet our knowledge mostly relies on flux-averaged mean spectral analysis. In this study, we investigate the origin of the large X-ray variability of the Seyfert 1 galaxy NGC 4593 using two \xmm{} observations, which are at least 65 ksec long and have a 0.3-10 keV X-ray flux difference by a factor of $\sim$2.5. We extracted mean spectra, Fourier-frequency resolved covariance, and time-lag spectra and performed modelling of all spectra in a self-consistent manner. From the best-fit covariance spectra, we have shown that energy-dependent covariance during low flux shows dominances of direct powerlaw continuum over reflection continuum at all Fourier frequencies (2.1 $-$ 390 $\times$ 10$^{-5}$ Hz). However, during high flux, the variabilities are dominated by the reflection components most of the time. Our results are further supported by the Fourier frequency-dependent time-lag (between soft: 0.3-1 keV and hard: 1-5 keV bands) spectral modeling during high and low fluxes. A significant change is observed in the X-ray reverberation delay timescale from 483 $\pm$ 135 sec (during high flux) to $<$96 sec (during low flux), indicating a change in coronal size at least by a factor of $\sim$2 (from $<$3.3 R$_g$ to $>$7.2 R$_g$) during low to high flux transitions.

Figures (12)

• Figure 1: Both panel shows XMM-Newton/EPIC-pn 0.3-10.0 keV light curve of NGC 4395 during 2002 (left panel) and 2016 (right panel) observations with 128s bin size. Red circles in both panels show 65 ksec segment selections of lightcurves, which have well-separated count rates during high and low flux observations and were used for further analysis in this work.
• Figure 2: Top left panel shows the average energy spectra of NGC 4593 fitted only with a powerlaw, along with its residual. A soft excess component, an absorption and a Fe line complex can be seen in the residual. To elaborate on the nature of the Iron line complex, we have zoomed the fitting residual in 4-8 keV (top right panel) when low and high flux spectra are fitted only with a power-law. The bottom left panel shows best-fit spectra during high flux, along with model components and residuals, while the bottom right panel shows the same during the low flux observations.
• Figure 3: Photon-energy dependent rms (triangle) and covariance (circle) spectra extracted during the low and high fluxes observation for the S4B3 segment (see Table \ref{['tab-freq']}) are shown in the top and bottom panels, respectively. During both flux states, unbounded errors are observed in rms spectral bins mostly above 2 keV; however, covariance errors are constrained at all energies.
• Figure 4: Comparison of covariance spectra at different Fourier frequencies when fitted with a powerlaw: Top panel shows data to powerlaw fitted model ratio for 0.3-9 keV covariance spectra extracted in the frequency range 1.1-48 (grey dots; seg S1B4), 6.7-97 (red triangles; seg S4B3) and 9.9-390 (black stars; seg S6B1) $\times$ 10$^{-5}$ Hz during low flux. A significant departure from the ratio=1 line at different energies and differences in ratio values can be observed at different Fourier frequencies. The bottom panel shows the same during the high flux.
• Figure 5: Modelling of covariance spectra: best-fit covariance energy spectra fitted with a combination of powerlaw and reflection continuum are shown along with model components and residuals in the Fourier frequency (in the unit of 10$^{-5}$ Hz) range of 6.7-390 (top left) and 6.7-195 (top right) during the low flux while the same during the high flux are shown in the bottom left and bottom right panels respectively.