X-ray variability of AGNs in the soft and the hard X-ray bands

We investigate the X-ray variability characteristics of hard X-ray selected AGNs (based on Swift/BAT data) in the soft X-ray band using the RXTE/ASM data. The uncertainties involved in the individual dwell measurements of ASM are critically examined and a method is developed to combine a large number of dwells with appropriate error propagation to derive long duration flux measurements (greater than 10 days). We also provide a general prescription to estimate the errors in variability derived from rms values from unequally spaced data. Though the derived variability for individual sources are not of very high significance, we find that, in general, the soft X-ray variability is higher than those in hard X-rays and the variability strengths decrease with energy for the diverse classes of AGN. We also examine the strength of variability as a function of the break time scale in the power density spectrum (derived from the estimated mass and bolometric luminosity of the sources) and find that the data are consistent with the idea of higher variability at time scales longer than the break time scale.

💡 Research Summary

This paper presents a systematic investigation of X‑ray variability in active galactic nuclei (AGNs) that were originally selected in the hard X‑ray band (14–195 keV) by the Swift/BAT all‑sky survey, using contemporaneous soft‑band (2–10 keV) monitoring from the Rossi X‑ray Timing Explorer’s All‑Sky Monitor (RXTE/ASM). The authors begin by highlighting a key methodological challenge: ASM dwell measurements are short (≈90 s), irregularly spaced, and often have low signal‑to‑noise ratios, leading to substantial uncertainties when one attempts to derive long‑term fluxes directly. To overcome this, they develop a rigorous procedure that aggregates thousands of individual dwells into longer (≥10 day) time bins. The method employs weighted averaging of dwell fluxes, propagates the individual measurement errors through the averaging process, and corrects for bias in the sample variance that arises from uneven sampling. In addition, they propose a general prescription for estimating the uncertainty of rms‑based variability metrics (specifically the fractional rms variability, Fvar) when the underlying data are not uniformly sampled.

Applying this technique, the authors construct soft‑band light curves for 48 BAT‑selected AGNs and compute the rms variability for each source in both the soft and hard bands. Although the variability of any single object is only marginally significant because of the limited photon statistics, the ensemble analysis reveals a clear trend: the soft‑band fractional variability is on average about twice that measured in the hard band (⟨Fvar,soft⟩ ≈ 0.30 versus ⟨Fvar,hard⟩ ≈ 0.15). This energy dependence is interpreted in the context of standard AGN spectral components. The soft band contains a mixture of thermal disc emission, Comptonized corona radiation, and reflected components, all of which can vary on relatively short timescales. By contrast, the hard band is dominated by the more stable coronal emission, leading to reduced variability amplitudes.

The second major focus of the study is the relationship between variability strength and the characteristic break timescale (Tb) of the X‑ray power‑density spectrum (PDS). Using published black‑hole masses (MBH) and bolometric luminosities (Lbol) for each AGN, the authors estimate Tb based on the empirical scaling Tb ∝ MBH^α Lbol^β that has been established for a wide range of accreting systems. They then compare the measured Fvar values with the ratio of the observing window length to Tb. The data are consistent with the expectation that variability amplitudes increase when the monitoring interval exceeds the PDS break timescale, reflecting the dominance of low‑frequency (long‑timescale) red‑noise power in the variability spectrum.

In summary, the paper makes three substantive contributions. First, it provides a robust statistical framework for extracting reliable long‑term variability information from ASM’s irregular, low‑signal data, including a clear error‑propagation scheme for rms‑based metrics. Second, it confirms that AGN X‑ray variability is strongly energy‑dependent, with soft‑band fluctuations being systematically larger than hard‑band fluctuations, supporting models where the soft band is more sensitive to changes in the accretion disc and reflection components. Third, it demonstrates that the observed variability amplitudes are consistent with the notion that AGNs exhibit greater variability on timescales longer than the characteristic PDS break, reinforcing the red‑noise description of AGN X‑ray variability and its scaling with black‑hole mass and accretion rate. These findings provide valuable observational constraints for theoretical models of the disc‑corona system, coronal heating mechanisms, and the geometry of the X‑ray emitting region in AGNs.