An Electron-scattering Time Delay in Black Hole Accretion Disks

Abstract

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 m ̇ characteristic of the hard state, to rivaling or exceeding the light-travel time delay for m ̇ 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.

A variable corona during the transition from type-C to type-B quasi-periodic oscillations in the black hole X-ray binary MAXI J1820+070

“…According to Nathan et al (2022), other effects that could lead to these results are the possible shadowing of the illumination profile, or that the model ignores the light crossing delay in the disc illumination profile, which could affect the disc temperature profile. Recently, Salvesen (2022) modeled thermalization as a random walk of photons in an 𝛼-disc, and found that for most of the disc 𝑡 th <1 ms, much smaller than the values reported by Nathan et al (2022).…”

Tracking the X-Ray Polarization of the Black Hole Transient Swift J1727.8–1613 during a State Transition

“…Another potentially important effect is the time that reflected photons spend scattering in the disk atmosphere before escaping (Salvesen 2022). This additional time lag is negligible for iron-line photons (García et al 2013), but may be important for soft emergent photons, many of which have experienced many scatterings.…”

Simulating X-Ray Reverberation in the Ultraviolet-emitting Regions of Active Galactic Nuclei Accretion Disks with Three-dimensional Multifrequency Radiation Magnetohydrodynamic Simulations

“…Higher absorption opacities would result in a larger energy transfer from the X-ray irradiation to the gas and likely increase the correlation between the X-ray and UV light curves. Salvesen (2022) found there was a nonzero thermalization time for the reprocessing of X-ray irradiation. We tested whether there is a lag between the X-ray and UV light curves and found that the strongest correlation between the X-ray and UV light curves in Run A is still at <0.08 day.…”

“…There are many radiation MHD simulations of AGN disks, but most are one-frequency simulations, and none focus on the impact of X-ray irradiation on the UV-optical region of AGN disks and the light curves emitted by the disk. On the other hand, there are numerous sophisticated (semi)analytical calculations for disk reprocessing of X-ray irradiation (e.g., Sun et al 2020;Kammoun et al 2021;Panagiotou et al 2022b;Salvesen 2022). However, they all make assumptions about the vertical profiles of AGN disk parameters and do not evolve the gas turbulence in three dimensions nor the impact that radiation has on the gas and vice versa as a function of time.…”

“…While there has been considerable observational work done using reverberation mapping, theoretical work to model the underlying physics of the reprocessing of hard irradiation into the softer radiation emitted by the disk has lagged behind. Most of the previous work modeling this reprocessing is (semi) analytic and makes assumptions about the vertical profiles of various disk parameters, which often remain fixed over time or are not calculated self-consistently to include the interaction of radiation and gas (e.g., Sun et al 2020;Kammoun et al 2021;Panagiotou et al 2022b;Salvesen 2022). The recent development of accurate, high-speed, numerical methods to calculate radiative transfer coupled to magnetohydrodynamics (MHD) makes it possible for the first time to examine how both radiation and magnetic fields have an impact on AGN disk structure and turbulence (Jiang et al 2013;Jiang & Blaes 2020;Jiang 2021).…”