[Paper Review] Accretion Discs Around Black Holes: Developement of Theory

Г. С. Бисноватый-Коган|arXiv (Cornell University)|Nov 11, 1999

Astrophysical Phenomena and Observations4 citations

TL;DR

This paper develops a theoretical framework for accretion discs around black holes, emphasizing turbulent viscous heating and radiative cooling via local energy balance. It identifies two solution branches—optically thick and thin—and demonstrates that low-luminosity, advection-dominated discs can carry most energy into the black hole, with magnetic fields limiting energy inflow and raising accretion efficiency beyond 25% of the standard model.

ABSTRACT

Standard accretion disk theory is formulated which is based on the local heat balance. The energy produced by a turbulent viscous heating is supposed to be emitted to the sides of the disc. Sources of turbulence in the accretion disc are connected with nonlinear hydrodynamic instability, convection, and magnetic field. In standard theory there are two branches of solution, optically thick, and optically thin. Advection in accretion disks is described by the differential equations what makes the theory nonlocal. Low-luminous optically thin accretion disc model with advection at some suggestions may become advectively dominated, carrying almost all the energy inside the black hole. The proper account of magnetic filed in the process of accretion limits the energy advected into a black hole, efficiency of accretion should exceed $\sim 1/4$ of the standard accretion disk model efficiency.

Motivation & Objective

• To formulate a comprehensive theory of accretion discs around black holes based on local energy balance.
• To investigate the role of turbulence from hydrodynamic instability, convection, and magnetic fields in driving viscous heating.
• To analyze the two distinct solution branches: optically thick and optically thin discs.
• To examine the conditions under which advection dominates over radiation in low-luminosity discs.
• To assess the impact of magnetic fields on energy advection and accretion efficiency, particularly in advectively dominated flows.

Proposed method

• Formulates a local energy balance model where viscous heating is balanced by radiative cooling through emission from the disc's upper and lower surfaces.
• Uses differential equations to describe energy advection in the disc, making the theory nonlocal and dependent on radial profiles.
• Applies assumptions of turbulent viscosity (α-prescription) to model angular momentum transport and energy generation.
• Considers magnetic fields as a regulator of energy inflow, limiting the fraction of energy advected into the black hole.
• Compares the efficiency of energy extraction in standard thin disc models with that in advectively dominated, low-luminosity configurations.
• Derives that accretion efficiency exceeds 1/4 of the standard model's efficiency when magnetic fields are properly accounted for.

Experimental results

Research questions

• RQ1 How does turbulent viscous heating in accretion discs lead to energy balance and radiative output?
• RQ2 What determines the existence of two distinct solution branches—optically thick and thin discs—in the standard accretion model?
• RQ3 Under what conditions can advection dominate over radiation in low-luminosity accretion discs?
• RQ4 How do magnetic fields influence the energy budget and efficiency of accretion into black holes?
• RQ5 To what extent can the accretion efficiency exceed that of the standard thin disc model when magnetic effects are included?

Key findings

• The standard accretion disc model exhibits two solution branches: optically thick and optically thin, depending on the disc's density and cooling efficiency.
• In low-luminosity, optically thin discs, advection can dominate over radiation, leading to advectively dominated flows that carry most energy into the black hole.
• The inclusion of magnetic fields in the accretion process limits the amount of energy advected into the black hole, preventing runaway energy inflow.
• Properly accounting for magnetic fields increases the accretion efficiency beyond 25% of the standard thin disc model's efficiency.
• The theory is nonlocal due to the differential equations governing advection, which depend on radial energy transport rather than local conditions.
• The model suggests that in certain regimes, especially in low-luminosity systems, the disc may become thermally unstable or transition to a different accretion mode due to advection dominance.