An Electron-scattering Time Delay in Black Hole Accretion Disks

Universal to black hole X-ray binaries, the high-frequency soft lag gets longer during the hard-to-intermediate state transition, evolving from ≲1 to ~10 ms. The soft lag production mechanism is thermal disk reprocessing of nonthermal coronal irradiation. X-ray reverberation models account for the light-travel time delay external to the disk, but assume instantaneous reprocessing of the irradiation inside the electron-scattering-dominated disk atmosphere. We model this neglected scattering time delay as a random walk within an α-disk atmosphere, with approximate opacities. To explain soft lag trends, we consider a limiting case of the scattering time delay that we dub the thermalization time delay, t _th; this is the time for irradiation to scatter its way down to the effective photosphere, where it gets thermalized, and then scatter its way back out. We demonstrate that t _th plausibly evolves from being inconsequential for low mass accretion rates $\dot{m}$ ṁ characteristic of the hard state, to rivaling or exceeding the light-travel time delay for $\dot{m}$ ṁ characteristic of the intermediate state. However, our crude model confines t _th to a narrow annulus near peak accretion power dissipation, so cannot yet explain in detail the anomalously long-duration soft lags associated with larger disk radii. We call for time-dependent models with accurate opacities to assess the potential relevance of a scattering delay.