Questions: Accretion Disk Physics and Radiative Efficiency

Question 1

Classical molecular viscosity — like that which slows honey — is far too weak to explain the angular momentum transport observed in accretion disks. What mechanism is currently understood to provide the effective 'viscosity' that actually drives accretion?

• A. Gravitational scattering between clumps of infalling gas
• B. Magneto-rotational instability (MRI), which amplifies even a weak magnetic field into turbulence through differential rotation
• C. Radiation pressure from the luminous inner disk, which pushes outer material inward
• D. Frequent collisions between gas molecules at the extreme temperatures near the compact object

Answer: (B)

Even a tiny magnetic field threading the disk gets stretched by differential rotation (inner rings orbit faster than outer rings). This stretching amplifies the field and generates MHD turbulence — the magneto-rotational instability. The resulting turbulent stresses transport angular momentum outward millions of times more effectively than classical molecular viscosity ever could, allowing mass to spiral inward. Before MRI was understood, accretion disk theory had no satisfactory physical mechanism for the observed accretion rates.

Question 2

Accretion onto a maximally spinning black hole can convert approximately 42% of infalling rest-mass energy into radiation. How does this compare to energy production in stellar nuclear fusion?

• A. Nuclear fusion is more efficient, converting roughly 90% of rest mass to energy
• B. They are roughly equivalent — nuclear fusion also converts about 40% of rest mass
• C. Accretion is far more efficient; nuclear fusion in stars converts only about 0.7% of rest mass to energy
• D. Accretion is slightly less efficient; nuclear fusion converts about 50% of rest mass

Answer: (C)

Hydrogen fusion converts about 0.7% of rest-mass energy (via E=mc², the mass defect of helium relative to hydrogen). Accretion onto a non-rotating black hole is ~6% efficient; onto a maximally rotating black hole, ~42% efficient. This means accretion around spinning black holes is roughly 60 times more energy-efficient than the most powerful nuclear process powering stars. This extraordinary efficiency is why quasars powered by accreting supermassive black holes can outshine entire galaxies of a trillion stars.

Question 3

The reason matter forms an accretion disk rather than falling directly onto a compact object is that angular momentum must be conserved, and infalling gas retains its angular momentum during infall.

• T. True
• F. False

Answer: True

If gas falling toward a compact object could simply lose its angular momentum instantly, it would plunge straight in. But angular momentum is conserved in the absence of external torques. Gas with even a small initial angular momentum relative to the compact object will swing into orbit rather than fall directly. It then spreads into a rotating disk, and only by gradually transporting angular momentum outward (via MRI-driven turbulence) can mass slowly spiral inward. Angular momentum conservation is thus the fundamental reason accretion disks exist.

Question 4

At very high accretion rates above the Eddington limit, accretion becomes more radiatively efficient because the enormous mass flux generates proportionally more gravitational energy.

• T. True
• F. False

Answer: False

Above the Eddington limit, radiation pressure becomes so intense that it pushes material outward faster than it can accrete. The disk transitions to a geometrically thick, optically thick flow where much of the radiation is trapped and advected inward rather than radiated away, and strong outflows/jets carry away mass and energy. Radiative efficiency actually drops at super-Eddington rates — the system 'wastes' energy in winds and jets and the geometry changes fundamentally. The Eddington limit represents a ceiling, not a launching point for greater efficiency.

Question 5

Why is transporting angular momentum outward — rather than simply releasing gravitational energy — the central theoretical challenge of accretion disk physics?

Model answer: Energy release follows automatically once mass moves inward, but mass cannot move inward unless angular momentum is shed, and conservation laws prevent it from disappearing.

Gravitational potential energy converts to heat and radiation whenever mass moves toward the compact object — that part is straightforward. The difficulty is the 'why can mass move inward at all?' question. Angular momentum is conserved, so infalling gas keeps spinning. For mass to spiral inward, angular momentum must be transferred elsewhere — specifically, to the outer regions of the disk and ultimately away from the system. Classical molecular viscosity is far too weak to accomplish this at the observed rates. MRI solves this problem by generating turbulent magnetic stresses that efficiently transport angular momentum outward, making inward mass flow — and thus accretion — possible.