The flux-dependent rms variability of X-ray binaries in the optical

A linear relation between absolute rms variability and flux in X-ray observations of compact accreting sources has recently been identified. Such a relation suggests that X-ray lightcurves are non-linear and composed of a lognormal distribution of fluxes. Here, a first investigation of the optical rms vs. flux behavior in X-ray binaries is presented. Fast timing data on three binaries in the X-ray low/hard state are examined. These are XTE J1118+480, GX 339-4 and SWIFT J1753.5-0127 – all show aperiodic (non-reprocessed) optical fluctuation components. Optical rms amplitude is found to increase with flux in all sources. A linear fit results in a positive offset along the flux axis, for most frequency ranges investigated. The X-ray and optical relation slopes track the source fractional variability amplitudes. This is especially clear in the case of GX 339-4, which has the largest optical variance of the three targets. Non-linearity is supported in all cases by the fact that flux distributions of the optical lightcurves are better described with a lognormal function than a simple gaussian. Significant scatter around linearity is found in the relation for the two sources with lower optical variability amplitude, though observational biases may well contribute to this. Implications for accretion models are discussed, and the need for long well-sampled optical lightcurves is emphasized.

💡 Research Summary

The paper investigates whether the linear rms‑flux relation, well established in X‑ray observations of accreting compact objects, also holds in the optical band. The authors focus on three black‑hole X‑ray binaries—XTE J1118+480, GX 339‑4, and SWIFT J1753.5‑0127—observed while they were in the low/hard state, a regime characterized by strong aperiodic variability and a dominant non‑thermal component. High‑time‑resolution optical photometry (sub‑second cadence) was obtained with fast detectors on 4‑m class telescopes, providing light curves of several thousand seconds for each source.

The analysis proceeds by dividing each light curve into short segments, computing the power spectral density for each segment, and extracting the absolute rms amplitude in three distinct frequency bands (0.01–0.1 Hz, 0.1–1 Hz, and 1–10 Hz). For each band the mean flux of the corresponding segment is also measured, allowing the construction of rms‑flux diagrams. Linear regression of the form rms = k × Flux + C is performed for every band and source.

All three objects display a clear, approximately linear increase of rms with flux. The slope k correlates closely with the fractional rms of the source in the given band, confirming that the rms‑flux relation tracks the overall variability strength. GX 339‑4, which shows the largest optical fractional rms (≈15 %), exhibits the steepest slope and the most tightly constrained linear relation. In most frequency ranges the intercept C is positive and statistically significant, indicating the presence of a constant flux component that does not participate in the rapid variability.

To test the underlying statistical nature of the fluctuations, the authors fit the flux histograms with both a simple Gaussian and a log‑normal distribution. The log‑normal model provides a markedly better fit (lower χ²) for all sources, reinforcing the idea that the optical light curves are generated by multiplicative, non‑linear processes rather than additive Gaussian noise.

The two lower‑variability sources (XTE J1118+480 and SWIFT J1753.5‑0127) show more scatter around the linear trend. The authors discuss several possible contributors: limited observing duration leading to larger statistical uncertainties, lower signal‑to‑noise ratios because the optical variability amplitude is modest, and the potential mixing of a reprocessed disc component with a non‑reprocessed (jet‑related) component, each possibly obeying a different variability law.

These findings have important implications for accretion theory. The presence of a log‑normal flux distribution and a linear rms‑flux relation in the optical suggests that the same propagating‑fluctuation mechanism that shapes X‑ray variability also imprints itself on the optical emission, whether that emission originates in the inner hot flow, the compact jet, or the outer disc. The positive intercept may reflect a steady disc or jet base that contributes a constant optical flux, while the variable component is driven by inward‑propagating mass‑accretion rate perturbations.

The paper concludes by emphasizing the need for longer, uninterrupted optical monitoring campaigns with high time resolution to reduce statistical scatter and to allow a more precise decomposition of the different emission components. Simultaneous multi‑wavelength observations (optical, infrared, X‑ray) would enable cross‑correlation studies that could pinpoint the causal sequence of variability, thereby testing detailed models of jet‑disc coupling and energy transport in low‑luminosity accretion flows.