Black Holes Don’t Just ‘Eat’…

While reading an article in Gizmodo the other day, I ended up taking umbrage with a particular comment. I’ve found in the past that it’s difficult to respond to the comments people make on these heavy traffic Gawker blogs in part because of how extraordinarily censored the comments section is and because of the pace at which people move on. In the past, I’ve come to the conclusion that the fastest response to a comment is not always the best considered and I would rather take time to think about what I want to say before I say it. So, by the time I’m ready to say anything about a particular piece, frequently the blog has already moved elsewhere, where no one will see what I have to say. A little frustrating since the comment response is usually not directed at the person who said it, who probably will never admit that they said anything wrong, but at the casual reader who will file it away in the back of their mind and not make the same mistake. The comment was this:

“This supermassive black hole, however, was found in a modestly-sized elliptical galaxy”

Sure, modestly-sized NOW. That’s like commenting on how few fish are in the aquarium exhibit with the great white shark.

Welcome to snark infested waters, the place where metaphors fly fast and furious and where a metaphor should sound like it came out of the mouth of one of Joss Wheden’s characters for it to float. Never mind if the person who said it stopped to think whether it made sense.

The article in question was about an unusual supermassive black hole found in a galaxy that is not considered big enough to support a black hole of that mass and how the discoverers were hypothesizing that the object they found is actually the product of a merging event where two black holes have combined to form a new one, not unlike the event the LIGO observed in order to confirm the existence of gravitational waves recently.

I can’t really say much about a majority of the commenters. You know how the comments sections in those blog articles go: the usual mix of arrogant, stupid, trolling, attention seeking and sometimes very astute and thoughtful. I fixated on the comment quoted above because it reflects a misconception that I’ve seen a few times recently, going back to the Ant-Man article that I wrote previously.

The popular image of a black hole is a huge vacuum cleaner out in space that busily sucks up everything that gets near it. That image is a distortion. The implication that a black hole is a shark which will ultimately eat up every star in the galaxy around it, as if it were eating smaller fish in an aquarium, is wrong. If I could cure this popular image, I would, but changing the world when people actively resist listening to what others are saying is difficult.

First of all, black holes do suck in matter. They do! Nothing of what I’m about to say contradicts that. The issue at hand actually comes down to the scale of what they do and eating matter is only a small part. Can you say that a black hole is going to devour all the stars around it? Actually, no. The conditions at which a black hole can eat something are limited by whether physics allows the object falling in to ever reach the ‘mouth’ –and if you know anything about orbital mechanics and conservation of energy, you’ll immediately realize that the story is not as simple as ‘falling in.’

As you approach a black hole, in order to ‘fall in,’ your ultimate trajectory must cross through the event horizon, the Schwarzchild radius where all in-falling trajectories can’t lead back out. That may not seem like much of a distinction, but you have to consider that the radius of the event horizon around the singularity at the heart of a black hole is actually quite small relative to the volume of space that a black hole effectively influences with its gravity. Pure gravitational potential energy looks like this:

u-graph01

In this image from Physicstutor, you can see the differences in potential energy between a position far away from the gravitating body and a position nearer to it –energy value is read off the vertical axis while position is read off the horizontal axis. In this curve, your potential energy does not change much when you are far away over large radii. This means that if you are far away, as you get much closer, you do not gain much kinetic energy for the change in potential energy that accompanies your change in position. On the other hand, if you are relatively close, when you become closer, your potential energy can change by much more, approaching some asymptote relative to the origin where the potential energy goes to negative infinity. In this particular curve, the difference in energy between sitting far away and sitting infinitesimally close is basically infinite energy and by moving from one position to the other, you convert that potential energy into kinetic energy. This is a small part of why it takes the moon a month to go around the earth, but the International Space Station only takes about 90 minutes.

With most planets and stars, the surface of that body prevents you from ever approaching a position infinitesimally close to the center of mass, meaning that you crash against the surface before you ever acquire ‘infinite’ kinetic energy. In addition, if your trajectory does not take you straight through that mass, you experience an increase in your kinetic energy which effectively changes your orbital speed with respect to the center of mass, which causes you to climb back up away from the body toward higher orbit. Taking this effect into account, the falling mass actually tends to experience a potential energy curve that looks more like this:

graphpotential_434_271

In this image taken from this website, you can see the potential energy curve that a satellite tends to experience. You get down to a particular altitude and you’re suddenly going ‘up-hill’ on the energy landscape and the kinetic energy you’ve gained tends to cause you to slide back out to a wider radius. Even if the pure gravitational potential energy curve offers a seductively huge amount of potential energy change, the effect of ‘going there’ will tend to push you back out for many trajectories. Orbits work because an object can get stuck in the bottom of that effective well: if you have an energy no greater than ‘a’ in the image above, you bob back and forth between ‘A’ and ‘A’ on that graph.

The same situation is true with a black hole. If you’re in a particular orbit, as you move closer to the black hole, your own kinetic energy will tend to rescue you and keep you from getting spaghettified and then squished. In fact, most galaxies live in this situation around their central black hole: the stars bob back and forth on some effective potential energy curve, never coming closer to the black hole than a particular radius. You can live happily next to a black hole like that without ever having to worry about ‘getting eaten.’ Some shark, huh, never quite being able to reach that morsel of food!

Fact is that since most trajectories within a black hole’s region of influence are like this and black holes are usually very small, only a remarkably few paths through the object’s influence ever actually cross the event horizon. As such, black holes are usually not denuding the galaxies they inhabit of surrounding stars.

In one case in our own solar system, we sent a probe to the planet Mercury. In our solar system, if the Earth is at the bottom of that effective potential well with respect to the sun, Mercury is way over to the left close to the origin on a completely different potential. For most of the kinetic energies that our rockets can actually impart, the planet Mercury cannot be directly reached. Launching a space probe to reach Mercury required us to figure out a way to dump enough kinetic energy during the trip that the probe could ever reach the planet Mercury with enough fuel to be able to establish an orbit. This was done by an orbital maneuver called a slingshot, which is performed by flying in close to a planetary mass and allowing that planet to redirect your flight path in such a way that your velocity vector, essentially your speed relative to the sun, is significantly altered. You basically use gravity to trade angular momentum with whatever planet you approach and the planet’s mass is so much bigger than the spacecraft that the planet is essentially unaltered by the interaction while the spacecraft gains or loses energy. The mission to Mercury required multiple slingshot assists with Venus and Mercury both (it was five or six IIRC) before the probe had bled off enough energy to be able to go into orbit at Mercury. This anecdote may seem a non sequitur, but it actually plays a deep role in the functioning of a black hole.

The one great trick that a black hole plays which changes this whole story is that they have no surface. There is essentially no ground to crash into as you get close! The potential energy changes that are available therefore become colossal. For the size of the object, it also possesses monumental mass, meaning that if it’s moving, it’s momentum is stupendous. It does have the momentum of at least a star, even if it doesn’t have the physical size. A gravity slingshot off a black hole can impart can so much kinetic energy that the flung object might be traveling at relativistic velocities.

18lr5ep9z65o1jpg

This image, pulled from Kinja, shows the effects of a black hole. Gases encountering the black hole are flung away by gravity slingshot with velocities approaching the speed of light. If a black hole of many stellar masses were to pass through our solar system, it could fling all the planets in every direction and rip the sun in half by tidal force alone and fling it in several directions all at once, eating very little in the process.

Once you encounter a black hole, there is a good chance this will be the outcome. In order to be eaten, if your path doesn’t just take you straight into the singularity, which it probably won’t, some other stuff usually has to happen first. Usually you have to dump kinetic energy somehow. In a situation with gas and dust and moving bodies, physical interactions between grains of dust or molecules of gas can allow energy to move between materials, slowing some, speeding others and generally scrambling up everybody’s flight paths. Those slowed can fall inward while those accelerated will tend to not want to. As charged particles fly about, constantly changing direction, they tend to emit light, also bleeding off energy… which means that everything around a black hole is glowing bright and that the accretion disk is emitting radiation up into the X-rays, all so that particles trapped there ever have a chance of falling in. Deeper in, the changes of gravitational potential may be appreciable across the length of something as small as a human being, meaning that the gravity force at your feet is greater than that at your head by something more than the tensile strength of the materials in between, tearing you apart. Most black holes act something like a cosmic blender and the reasons can be understood somewhat classically without even adding in the craziness of applied general relativity, or mistakenly reducing it to ‘sucking stuff in.’

Believe it or not, the picture I just painted is applicable depending on the mass of the black hole. The more mass a black hole has, the less it tends to pathologically torture the spacetime outside of its event horizon. If the black hole is massive enough, like maybe the supermassive black hole in the gizmodo article, a person can live to travel down to the event horizon without getting shredded. Around such a black hole, the spacetime is locally very euclidean, meaning that bigger and bigger objects can reside intact in stable orbits closer. So, small black holes are ‘sloppy eaters,’ while big ones actually attain something resembling table manners and would constitute better neighbors. How you go from being small to being big is perhaps a cloudy question since it isn’t clear if the process which typically makes stellar black holes is necessarily the same as the one which created the supermassive black holes that typically reside in the centers of galaxies.

Whatever you might think, the bottom line is simply this: a black hole in the core of a galaxy is probably not eating the stars in the sky around it. Galaxies do not shrink appreciably in size over time because of the black holes inside them per se. It simply doesn’t work like that!

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