Massive Black Holes and Size

Artist’s concept of a wind from a supermassive blackhole

Question from a friend:

Multiple News sources (Time Magazine, Wired, now Salon) are all claiming that this new “Monster” Black Hole which is 12+ billion light years away (thank god) is 12 Billion Times the size of our sun…

But, every time I read the article it says “12 billion times the MASS of our sun.”

http://www.salon.com/2015/02/25/scientists_discover_theory_defying_black_hole_12_billion_times_the_size_of_the_sun/?utm_source=facebook&utm_medium=socialflow

I understand the thing is EPICALLY HUGE, but I also understand Mass and Size are not always directly proportional. Also, black holes are SUPER dense right?

So, long story – short question:

How big is this thing really in size?

Okay, so this is actually a pretty subtle question. I’ll parse it two ways:

How big is the event horizon of the black hole?

By answering this question we get to neatly sidestep all of the issues about “what’s the black hole made of” and get down to brass tacks. Any object (including you and me) that has some mass (say, the mass of the earth) has an event horizon, which is the size where if you cram all of the objects mass into a ball of that size then it will bend space around it so that light can’t escape. This is also known as the Schwarschild Radius, named after the Germon mathematician/astronomer who first thought it up. It varies roughly proportionally to the mass of the object:

R = 2 G M / c^2

…where G is the Gravitational constant, M is the mass, and c is the speed of light.

In human terms, this is a pretty small space. If you took something the mass of the Earth, then it’s Schwarzchild Radius is about the size of a shooting marble (with a radius of about 1 cm). There’s a cool calculator that gives you the size vs mass if you want to play around with it.

For our Sun, the Schwarzchild radius is about 3 km in radius. So for the 12 billion solar mass blackhole, the Schwarzshild radius is about 36 billion km, which is about 240 times the distance from the Earth to the Sun or about 10 times the distance from the Sun to Pluto. So…big.

But not unimagineably big. The distance to the nearest star is about 275,000 times the distance from the Earth to the Sun, so a billion solar mass black hole wouldn’t even come close to filling up the space between two stars in our local neighborhood.

There are some caveats to this, of course (things that only people like me really know about like black hole spin, etc), but that gets you pretty close to understanding how big the thing is.

Okay, so that’s it’s “black hole radius”, what’s it’s actualy physical size?

This is the trickier one, and I’m going to punt on this. This is the crux behind Interstellar (spoilers?), but no one really knows what physics is like inside of a black hole. All kinds of funny things may happen (or not). But in this case asking the question of “What is a black hole’s physical size” is just not the same as asking the question “What is a basketball’s physical size?”. It’s a good question, it’s just one that we don’t really know the answer to.