Just Two Numbers Is All You Need

NARRATOR: Black holes sound wildly complicated. After all, there are all sorts of bizarre things going on: intense gravity, the warping of the fabric of space, the distortion of time itself. But when it comes to describing black holes, it comes down to just two numbers: the mass of the black hole and its spin. That’s right. Everything you physically need to describe a black hole is found in just these two numbers.
So, if it’s so simple, astronomers must know these two numbers for lots and lots of black holes, right? In fact, getting these two numbers turns out to be incredibly hard. Dr. Jeffrey McClintock of the Harvard-Smithsonian Center for Astrophysics has been trying to tackle this problem. Just recently, it turns out he and his colleagues did.

SCIENTIST: Getting the mass is the easy part. These small black holes we study are orbited by an ordinary star like the sun. Using an optical telescope, we measure the speed of this sun-like star and the time it takes to completely orbit the black hole. This is old hat. This is how astronomers have measured the masses of stars in ordinary binary systems and planetary systems for many years. But when I say that getting the mass is easy, I should be more careful. For example, we just spent two years getting the mass of one special black hole in the nearby galaxy M33. So it's really no piece of cake. Anyway, we found that the mass of this X-ray source, called M33 X-7, is about 16 times more massive than our sun, with a margin of error of one and a half times the mass of the sun. This is the most accurate mass that has been measured for any black hole.

NARRATOR: But this wasn’t the end of the story with M33 X-7. McClintock and his colleagues set out to find that other elusive number: the spin.

SCIENTIST: Measuring spin is really hard, because you have to understand what’s going on in the Alice-in-Wonderland world close to a black hole. Let's start the story out near the ordinary star. The black hole’s gravity strips gas from that star, and the gas falls toward the black hole, forming a swirling disk of orbiting matter. Very near the black hole, this gas gets heated to millions of degrees by the colossal force of the gravity, and it shines brightly in X-rays, which we easily observe using Chandra.
Of course, eventually, all this hot gas is destined to disappear forever once it falls through the event horizon, which is located 25 km from the dead center of the black hole. But far away from this dreaded event horizon, a point is reached where the force of gravity becomes so immense that the super-hot gas can’t any longer maintain itself in a stable orbit around the black hole. At this point, the disk abruptly ends and the gas in orbit there suddenly plunges inward, reaching the event horizon in less than one-thousandth of a second.

NARRATOR: But what happens next?

SCIENTIST: This leaves a large dark hole in the center of the disk that extends down to the event horizon. The radius of this dark hole depends only on the two numbers in question, namely, the black hole's mass and how fast it is spinning. For a black hole that is not spinning at all and that weighs 16 sun masses (like our M33 X-7), the radius of this dark region is 75 km, which is 3 times the radius of the event horizon. The faster the black hole spins, the smaller this radius becomes. For a black hole with the maximum spin allowed by relativity theory, the radius becomes equal to the radius of the event horizon.
By studying the spectrum of the X-rays from M33 X-7, we’ve been able to accurately measure the inner radius of the hot disk to be 45 km, and this tells us that the spin of M33 X-7 is about three quarters of its theoretical maximum value. Near the event horizon, the black hole's spin drags everything around with it, an apple, an astronaut, even space itself, at the dizzying rate of 750 revolutions per second.

NARRATOR: So what does this all mean? Jeff McClintock puts the result into perspective.

SCIENTIST: As you said at the beginning, only two numbers are needed to describe a black hole. A black hole’s as simple as an electron and far simpler to describe than, say a grain of sand. It is absolutely amazing to me that Chandra has allowed us to obtain a complete description of an object the size of an asteroid that is situated at a distance of about 3 million light years.

NARRATOR: So there you have it. Two numbers to describe one of the Universe’s most mysterious objects. Getting to know these values is not just for fun. When they are plugged into theoretical models, they can help astronomers better understand things like how black holes are born, how gravity behaves under extreme conditions, and how black holes make powerful relativistic jets, and more. Who would have guessed that just two numbers could do all of that?