Question 1

What is an accretion disk?

Accepted Answer

An accretion disk is a rotating structure of gas and dust that forms when matter falls into a gravitational potential well � around a star, black hole, neutron star, or white dwarf � but has too much angular momentum to fall straight in. Viscosity (or turbulence driven by magneto-rotational instability, MRI) transports angular momentum outward, allowing matter to slowly spiral inward while releasing enormous amounts of gravitational potential energy as radiation. In protoplanetary disks, this energy heats the disk and the accreting star; around black holes, accretion efficiency can reach 40% of mc� (far exceeding nuclear fusion's ~0.7%).

Question 2

What is the Shakura-Sunyaev a-disk model?

Accepted Answer

Proposed by Shakura and Sunyaev in 1973, the a-disk (alpha disk) model parameterises the kinematic viscosity as ? = a�c_s�H, where c_s is the local sound speed, H is the disk scale height, and a is a dimensionless parameter (typically 0.01�0.3). This elegant parameterisation circumvents our ignorance of the exact microphysical viscosity mechanism. a effectively encodes the ratio of turbulent stress to thermal pressure. Modern understanding attributes a-disk-like angular momentum transport to turbulence driven by the magneto-rotational instability (MRI, Balbus-Hawley 1991) in sufficiently ionised disks.

Question 3

What is the ISCO and why does matter heat up near a black hole?

Accepted Answer

The Innermost Stable Circular Orbit (ISCO) is the smallest radius at which matter can stably orbit a black hole. For a Schwarzschild (non-spinning) black hole of mass M, ISCO = 6 GM/c�, or about 3 Schwarzschild radii. Inside the ISCO, there are no stable orbits � infalling matter plunges rapidly inward. Because orbital energy (? -GM/2r) increases as r decreases, matter must radiate away its binding energy as it spirals from the outer disk to the ISCO. The effective temperature at the ISCO scales as T ? M^(-1/4) (?)^(1/4) � for a stellar-mass black hole this is millions of Kelvin (X-ray emission), while for supermassive black holes it is ~tens of thousands of Kelvin (UV/optical emission).

Question 4

How do planets open gaps in protoplanetary disks?

Accepted Answer

A sufficiently massive planet (roughly Jupiter-mass or above) embedded in a protoplanetary disk excites Lindblad resonances � locations where the disk's orbital frequency is a simple fraction of the planet's. These resonances launch density waves that carry angular momentum away from the resonance location. If the angular momentum deposition rate exceeds the disk's ability to diffuse it away via viscosity, the disk material near the planet is repelled, opening an annular gap centred on the planet's orbit. The condition for gap opening is M_p/M_star > f(H/r, a), where H/r is the disk aspect ratio and a the viscosity parameter. After gap opening, spiral density waves (Lindblad spirals) propagate both inward and outward from the planet.

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