# Habitability zone around a Supermassive Black Hole

I have just found perhaps the biggest thing in the universe: A black hole named SDSS J010013.02+280225.8. It itself is 12 billion times more massive than our sun, and its accretion disk is 439 trillion times brighter. This could mean the universe's biggest habitable zone, right?

Here is the scenario: A black hole identical in dimension to SDSS J010013.02+280225.8 is orbited by co-orbital of trinary star systems within its habitable zone. All the stars are white dwarves, each one only 20% more massive than our sun. Therefore, the "sunlight" comes only from the black hole's accretion disk.

In regards to the black hole's mass, its accretion disk's luminosity and the amount of X-rays being emitted, how far and how wide would the habitable zone be?

• The title is misleading. I think you mean "around a black hole", not in one, because you can't really survive getting inside. Though some people have argued that the universe is actually the inside of a black hole. However, for folks outside, there's no way of knowing what's going on inside, or indeed, if there even IS an inside :-) Sep 5, 2021 at 3:27
• Interestingly TON 618 is about 5x more massive but 0.25x as brigjt by those numbers. Sep 5, 2021 at 3:56
• @TheSquare-CubeLaw Could you expand on that comment? Sep 5, 2021 at 3:57
• You said you found the biggest thing, but the size of a black hole is proportional to its mass and TOM 618 is 66 billion solar masses massive (2 billion more solar masses than all Milky Way stars combined). youtube.com/watch?v=0FH9cgRhQ-k Sep 5, 2021 at 4:14
• A remark.. so this black hole's accretion disk, which is many light years away, provides for the heat to let life exist on the planet. As opposed to a near sun, it would show as a single spot, a permanent, extremely bright star. Wouldn't that have impact on the viability of evolution on this planet ? Will all life need to be blind ? I imagine looking into the black hole once would result in loss of eyesight.. Sep 5, 2021 at 11:41

Taking "439 trillion times brighter" to mean the "stellar" luminosity is 439 trillion times the sun, we can make some rough calculations.

The inner boundary of a stellar habitable zone is approximated by:

$$inner = \sqrt{L_s \over 1.1}$$

Where Ls is luminosity is solar units and the result is in AUs.

Plugging in the given value, we get:

$$inner = \sqrt{4.39 \times10^{14} \over 1.1} = 2.00 \times10^{7} AU$$

There are approximately 63,241 AUs in a light year so we can simplify that to 316 ly.

The outer boundary is approximated by:

$$outer = \sqrt{L_s \over 0.53}$$

Plugging in again:

$$outer = \sqrt{4.39 \times10^{14} \over 0.53} = 2.88 \times10^{7} AU$$

Which simplifies to 455 ly.

Making the width: 455-316 = 139 ly.

CAVEAT: these formulas were never meant to apply to this situation so I have no idea if they're right.

• Have you also taken the excessive amounts of x-rays from the black hole into consideration? Sep 5, 2021 at 3:48
• I did not. I meant to include a note about that but forgot. Basically, I couldn't find any good info on the x-ray component of the emissions of this little beastie. Given the nasty properties of quasars, I'd suspect your habitable zone would get routinely fried with high-energy radiation making the whole thing moot. Sep 5, 2021 at 4:13
• @JohnWDailey You're going to have to stop them with atmosphere. Sep 5, 2021 at 4:13
• At this distance you shouldn't be bound by the black hole's gravity. Sep 5, 2021 at 4:16
• @LorenPechtel What sort of atmosphere? I suspect that "identical in composition and thickness to Earth's" wouldn't be enough. Sep 5, 2021 at 4:32

legio1's answer is jaw-dropping but I see nothing in the math to disagree with. However, I am going to disagree anyway and say there is no habitable zone--the problem is the luminosity of the black hole won't hold steady enough for life. Planets might at times be of a suitable temperature but that state won't persist over long periods.

• "won't persist over long periods." Why? Also have seen claims that change in lyminosity of the sun, over time, was important for our life(and or evolution, do not remember exact statement) Sep 5, 2021 at 20:05
• The luminosity of a star slowly grows over billions of years. A black hole has no innate luminosity, it's entirely dependent on what falls in. That's not going to be remotely consistent, the habitable zone will fluctuate too much for life. Sep 6, 2021 at 1:07