# What is the temperature of an accretion disc surrounding a supermassive black hole?

What is the temperature of an accretion disc surrounding a supermassive black hole? Is there plasma in the disc?

• This is a fantastic resource on accretion disks, and this section in particular may help with accretion rates. Jan 6, 2015 at 23:36

It depends on the distance from the central body. This gives the temperature $T$ at a given point as a function of the distance from that point to the center ($R$): $$T(R)=\left[\frac{3GM \dot{M}}{8 \pi \sigma R^3} \left(1-\sqrt{\frac{R_{\text{inner}}}{R}} \right) \right]^{\frac{1}{4}}$$ where $G$, $\pi$, and $\sigma$ are the familiar constants, $M$ is the mass of the central body (and $\dot{M}$ is the rate of accretion onto the body), and $R_{\text{inner}}$ is the inner radius of the disk - possibly (if the object is a black hole) the Schwarzschild radius $R_s$, in which case we can simplify this a little more. So the temperature in the accretion disk is far from constant.