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

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.