A synchrotron self-Compton -- disk reprocessing model for optical/X-ray correlation in black hole X-ray binaries

Physical picture of the emission mechanisms operating in the X-ray binaries was put under question by the simultaneous optical/X-ray observations with high time resolution. The light curves of the two energy bands appeared to be connected and the cross-correlation functions observed in three black hole binaries exhibited a complicated shape. They show a dip of the optical emission a few seconds before the X-ray peak and the optical flare just after the X-ray peak. This behavior could not be explained in terms of standard optical emission candidates (e.g., emission from the cold accretion disk or a jet). We propose a novel model, which explains the broadband optical to the X-ray spectra and the variability properties. We suggest that the optical emission consists of two components: synchrotron radiation from the non-thermal electrons in the hot accretion flow and the emission produced by reprocessing of the X-rays in the outer part of the accretion disk. The first component is anti-correlated with the X-rays, while the second one is correlated, but delayed and smeared relative to the X-rays. The interplay of the components explains the complex shape of the cross-correlation function, the features in the optical power spectral density as well as the time lags.

💡 Research Summary

This paper addresses the puzzling optical–X‑ray correlation observed in several black‑hole X‑ray binaries (BHBs) when high‑time‑resolution simultaneous data are available. The cross‑correlation functions (CCFs) show a characteristic “precognition dip” – a decrease in the optical flux a few seconds before the X‑ray peak – followed by an optical flare that lags the X‑ray maximum. Standard models that attribute the optical emission solely to reprocessing of X‑rays in the outer accretion disc, or to jet synchrotron, cannot reproduce this combination of anti‑correlated and delayed components.

The authors propose a two‑component optical model. The first component is synchrotron radiation from non‑thermal electrons residing in the hot inner flow (the “corona” or radiatively inefficient accretion flow). These electrons also serve as seed photons for synchrotron‑self‑Compton (SSC) scattering, which produces the observed hard‑state X‑ray spectrum. Because the synchrotron self‑absorption frequency lies in the optical band, an increase in the mass accretion rate (ṁ) raises the magnetic field and electron density, thereby strengthening SSC X‑rays but simultaneously suppressing the observable synchrotron flux. Consequently, the synchrotron optical flux is anti‑correlated with the X‑rays.

The second component is the classic reprocessed emission from the outer, cold accretion disc. Hard X‑rays irradiate the disc, heating its surface and producing thermal optical/UV photons. This component is positively correlated with the X‑rays but delayed by the light‑travel time and smeared by the disc’s finite response.

Spectral model. The authors adopt a spherical homogeneous region of radius (R\approx30,R_{\rm S}) (≈9×10⁷ cm for a 10 M⊙ black hole), Thomson optical depth (\tau=1), magnetic field (B=3\times10^{5}) G, and total luminosity (L=10^{37}) erg s⁻¹. Electrons are injected with a power‑law distribution (dN_{\rm e}/d\gamma\propto\gamma^{-\Gamma_{\rm inj}}) (Γ_inj=3) between (\gamma_{\rm min}=1) and (\gamma_{\rm max}=10^{3}). Using the kinetic code of Vurm & Poutanen (2009) they solve for the steady‑state electron distribution and photon spectrum, including cyclo‑synchrotron emission/absorption, Compton scattering, and electron‑electron Coulomb collisions. The resulting synchrotron self‑absorption turnover falls in the 1–10 eV range, ensuring that modest changes in (\dot m) produce opposite trends in the optical synchrotron and X‑ray SSC fluxes.

Timing model. The light curves are expressed as mean plus fractional variations: (x(t)=\bar x