### 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.

7 years ago

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.

Whether or not there is plasma depends on the exact nature of the disk, the central object and the region around it. For example, a supermassive black hole may have different matter in its disk than that of a stellar-mass black hole. I should think, though, that black holes in binary systems accreting mass from a companion should have plasma in their accretion disks, and supermassive black holes might also have plasma from nearby stars.

I imagine, it would be more interesting to see this equation in number form.

@AlexeyBobrick With specific numbers from an actual accretion disk?

Yes, like something you can on page 9 of your reference.

Content dated before 7/24/2021 11:53 AM

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