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

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–Newton observations, which are at least 65 ks long and have a 0.3–10 keV X-ray flux difference by a factor of ~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-fitting covariance spectra, we have shown that energy-dependent covariance during low flux shows dominances of direct power-law continuum over reflection continuum at all Fourier frequencies (2.1–390 × 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 modelling during high and low fluxes. A significant change is observed in the X-ray reverberation delay time-scale from 483 ± 135 s (during high flux) to <96 s (during low flux), indicating a change in coronal size at least by a factor of ~2 (from <3.3 to >7.2 Rg) during low to high flux transitions.