<p>It depends on the distance from the central body. <a href="http://jila.colorado.edu/~pja/astr3830/lecture26.pdf" rel="noreferrer">This</a> 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 <a href="https://en.wikipedia.org/wiki/Gravitational_constant" rel="noreferrer">$G$</a>, $\pi$, and <a href="https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant" rel="noreferrer">$\sigma$</a> 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.</p>

<p>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.</p>

CC BY-SA 3.0
2015-01-06T17:22:44.400Z
I imagine, it would be more interesting to see this equation in number form.
Alexey Bobrick
CC BY-SA 3.0
2015-01-06T23:04:04.143Z
@AlexeyBobrick With specific numbers from an actual accretion disk?
HDE 226868
CC BY-SA 3.0
2015-01-06T23:16:18.677Z
Yes, like something you can on page 9 of your reference.
Alexey Bobrick
CC BY-SA 3.0
2014-12-31T01:59:45.963Z
2014-12-31T14:59:44.707Z
2014-12-31T14:59:44.707Z
HDE 226868
<p>What is the temperature of an accretion disc surrounding a supermassive black hole? Is there plasma in the disc?</p>

CC BY-SA 3.0
2015-01-06T23:36:09.280Z
[This](http://www.scholarpedia.org/article/Accretion_discs#Extreme_mass_supply_:_.22sub.22_and_.22super.22_Eddington_accretion_rates) is a fantastic resource on accretion disks, and this section in particular may help with accretion rates.
HDE 226868
<supermassive-black-hole><temperature><accretion-discs>
What is the temperature of an accretion disc surrounding a supermassive black hole?
Declan Konroyd
# What is the temperature of an accretion disc surrounding a supermassive black hole?

(Asked by: username_0 on 2014-12-31)

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

**Tags:** supermassive-black-hole, temperature, accretion-discs

> **Comments:**
> **username_1**: [This](http://www.scholarpedia.org/article/Accretion_discs#Extreme_mass_supply_:_.22sub.22_and_.22super.22_Eddington_accretion_rates) is a fantastic resource on accretion disks, and this section in particular may help with accretion rates.  

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## 1 answers

### Answer by username_1 on 2014-12-31. Score: 7 | Accepted answer

It depends on the distance from the central body. [This](http://jila.colorado.edu/~pja/astr3830/lecture26.pdf) 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 [$G$](https://en.wikipedia.org/wiki/Gravitational_constant), $\pi$, and [$\sigma$](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant) 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.

> **Comments:**
> **username_2**: I imagine, it would be more interesting to see this equation in number form.  
> **username_1**: @AlexeyBobrick With specific numbers from an actual accretion disk?  
> **username_2**: Yes, like something you can on page 9 of your reference.  

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