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{} 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.

💡 Research Summary

In this work the authors investigate the origin of the large X‑ray variability observed in the Seyfert 1 galaxy NGC 4593 by exploiting two long XMM‑Newton EPIC‑pn observations that differ in flux by a factor of ≈2.5. The 2002 observation (≈87 ks) represents a high‑flux state, while the 2016 observation (≈142 ks) provides a low‑flux state. To ensure a fair comparison, the authors select strictly non‑overlapping 65 ks intervals from each dataset, apply identical data‑reduction procedures, and generate background‑subtracted light curves with several bin sizes.

First, the mean spectra for the two flux states are modelled using a combination of a primary power‑law (zpowerlw), two partially ionised warm absorbers (zxipcf), and a relativistic reflection component (xillver). The low‑flux spectrum is well described by this model (χ²/dof ≈ 1.16), but the same model fails for the high‑flux spectrum (χ²/dof ≈ 1.81), leaving significant residuals below 2 keV that hint at an additional variable component. An absorption Gaussian (gabs) at ≈6 keV improves the fit, and the authors also test a warm‑Comptonisation component (nthcomp) as an alternative explanation for the soft excess, but the reflection‑dominated scenario remains favoured for the high‑flux data.

The core of the paper is the Fourier‑frequency‑resolved analysis. Light curves are divided into five frequency bands spanning 2.1 × 10⁻⁵ Hz to 3.9 × 10⁻³ Hz. For each band the authors compute the covariance spectrum, which isolates the spectral shape of the component that varies coherently with a chosen reference band. In the low‑flux state the covariance spectra at all frequencies are dominated by the direct power‑law continuum; the reflection contribution is negligible. In contrast, during the high‑flux state the low‑frequency (2.1–5 × 10⁻⁵ Hz) and mid‑frequency (5–10 × 10⁻⁵ Hz) covariance spectra show a substantial reflection fraction (30–50 % of the total covariance), indicating that on longer timescales the reflected emission varies in step with the primary continuum. This frequency‑dependent behaviour demonstrates that the relative importance of direct versus reflected emission changes with timescale and flux level.

Complementary to the covariance analysis, the authors calculate the frequency‑dependent time‑lag spectra between a soft band (0.3–1 keV) and a hard band (1–5 keV) using the cross‑spectrum method. In the high‑flux observation a clear positive lag of 483 ± 135 s is measured at low frequencies (≈10⁻⁴ Hz), consistent with reverberation of the hard X‑ray continuum off the inner accretion disc. In the low‑flux observation the same frequency range yields a lag of <96 s, i.e. the reverberation signal is much weaker or occurs on a much shorter timescale.

By converting the measured reverberation delays into a light‑travel distance (using the black‑hole mass of ≈10⁷ M⊙), the authors infer a characteristic coronal height of ≈7 R_g in the high‑flux state and ≲3 R_g in the low‑flux state. This implies that the corona expands by at least a factor of two when the source brightens, a result that is consistent with the increased reflection fraction seen in the high‑flux covariance spectra.

The paper therefore provides a self‑consistent picture in which (i) the corona is compact during low‑flux intervals, producing little reverberation and a variability spectrum dominated by the primary power‑law, and (ii) the corona expands during high‑flux intervals, enhancing the illumination of the inner disc, increasing the reflected component’s variability, and lengthening the reverberation lag. The authors argue that such a dynamical corona‑disc geometry cannot be inferred from time‑averaged spectroscopy alone; the combination of Fourier‑frequency‑resolved covariance and lag spectroscopy is essential to disentangle the variable components.

Overall, the study demonstrates the power of frequency‑resolved timing techniques to probe the geometry and evolution of the X‑ray emitting corona in AGN. The methodology and conclusions are directly applicable to other Seyfert galaxies, offering a pathway to map how coronae respond to changes in accretion power and to test theoretical models of coronal heating, expansion, and disc illumination.