Neighbouring rings of gas orbit at different Keplerian speeds and rub against each other; that shear is dissipated as heat by viscosity (magnetic turbulence in a real disk). The steady-state Shakura–Sunyaev disk temperature profile is:
T(r) = T_in · (r/r_in)^(-3/4) · [1 - √(r_in/r)]^(1/4)
Hot gas radiates roughly as a blackbody, so the disk's color runs from dull infrared/red far out to blue-white and X-rays near the inner edge. The inner edge itself sits at the innermost stable circular orbit (ISCO), which general relativity pulls closer to the horizon as the black hole spins faster:
r_isco = 3 + Z₂ − √[(3−Z₁)(3+Z₁+2Z₂)] (units of Rg = GM/c²)
- Accretion rate scales how much gravitational energy is released per second, raising T_in and overall brightness.
- Spin a* drags the ISCO inward, letting the hottest gas orbit deeper in the gravitational well.
- View inclination tilts the disk plane, revealing the Doppler-boosted bright side where gas orbits toward you.
Peak emission wavelength follows Wien's law, λ_max = b / T, with b ≈ 2.898×10⁶ nm·K.