Non-Equilibrium Thermodynamics of Black-Hole Coronae: QPOs, Turbulence, and Jets

TL;DR

This paper presents a novel framework in which black-hole coronae are modeled as autonomous, non-equilibrium heat engines driven by thermal disequilibrium between heating and Compton cooling, with the pair thermostat mediating the feedback. Central to the approach is a Rayleigh-Eddington-type criterion, expressed as $T_d \sim \dot S$, which allows cyclic extraction of net work $W_{\rm net}>0$ and sustains self-oscillations that manifest as QPOs. The model further links these oscillations to turbulence and jet production, offering a mechanism for energy transfer from coronal heating to outflows. A key testable prediction is that QPO activity should correlate with a high-energy tail above the pair-production threshold near $1\ \mathrm{MeV}$, guiding future observational comparisons and model refinements.

Abstract

The variability of X-rays observed from accreting black hole systems, including quasi-periodic oscillations (QPOs), suggests a complex nonlinear dynamics in the corona. Here, we propose a new theoretical framework for this problem, based on non-equilibrium thermodynamics. In this model, coronal variability arises from feedback between a macroscopic oscillation of the plasma and the rate at which it is cooled by the inverse Compton scattering of soft photons from the disc. The "pair thermostat'' mechanism then allows the corona to act as a heat engine that extracts work cyclically from the underlying thermal disequilibrium between the low-entropy heating and the high-entropy cooling by the soft photons, in close analogy to the well-known $κ$-mechanism for pulsating stars. This coronal self-oscillation may explain QPOs without the need to invoke an external resonant driving. Moreover, we argue that this mechanism can provide the power to generate turbulence and jets in the corona.

Figures (3)

• Figure 1: Diagram of a heat engine as a self-oscillator, powered by a feedback between the position $x$ of the piston and the coupling of the working fluid to two external baths at different temperatures. Image adapted from 2017AnPhy.378...71A.
• Figure 2: Schematic representation of the "pair thermostat" as a plot of the temperature $T_c$ of the corona versus its optical depth $\tau$. The dotted line illustrates a possible transformation of the plasma as heat is injected. Within the allowed region, more heat increases both $T_c$ and $\tau$. When the plasma reaches the boundary of the forbidden region, further heating leads to an increase in the density of pairs (and therefore of $\tau$) while $T_c$ falls due to equipartition. This image is adapted from 1997ApJ...487..747D.
• Figure 3: Proposed thermodynamic cycle of the corona, which would manifest itself as a QPO of the X-ray luminosity. The work generated by this cycle may drive the generation of turbulence and jets in the corona.