How do black holes get close enough to merge? What causes them to emit gravitational waves, and where do the waves come from? What does the merger process look like? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPTION (AUTO GENERATED)

One of my favorite things about black holes is that they are so strange, so odd, so out of scale to everything else in the universe that their mere existence invites questions. In fact, it's more than invites. It demands questions, creates questions. Black holes just manifest questions. Like, when you're driving down the road and you see a really odd car painted a weird color as things sticking out of it.

You just you just have to start asking questions. It's like you don't get a choice. And black holes don't give us any choice. They're here. They exist.

They demand explanation. And so, they make regular appearances on this show because there's so much to ask about them. And today, we're asking how do black holes merge together. Can they merge together? What happens when they collide?

What about their singularities? And wait a minute. Nothing can escape a black hole. How can 2 of these objects become 1? I know I've talked about black hole mergers before, especially when it comes to the generation of gravitational waves.

But I've realized after surveying my list of questions of which there is a significant backlog, but please don't let that deter you from asking your own question. I've never gotten into the nitty gritty of the merger process itself and how it unfolds. And since this show is all about the nitty gritty, here we are with today's episode, how exactly do black holes merge? The first question we need to ask is, are we sure that black holes do merge, And how would we know? After all, black holes are black.

Space is black. If 2 black holes merge together, what evidence do we have that this process even happens in the first place? And, thankfully, that my friend says a very simple, very straightforward answer. Oh, yes. They merge, and we know it.

For decades, we had loads of circumstantial evidence that they merge, and that's mostly through the existence of super massive black holes. And the fact that there are these giant, super giant black holes inhabiting the universe, and galaxies generally have only a single one of these giant black holes in their centers. We know that galaxies merge. And so if black holes themselves never merge, we would expect the most massive galaxies, instead of having a single supermassive black hole, have many smaller ones all orbiting around each other. We don't see evidence of that.

We see evidence for only a single object per galaxy. And so, therefore, we're pretty sure we've been pretty sure for decades that black holes do merge, but that's not enough to satisfy everybody. So thankfully, the LIGO instrument came along and settled it once and for all. LIGO is the laser interferometer gravitational wave observatory. It's a thing that detects gravitational waves, and this has to do with black hole mergers because these invisible creatures, the black holes, living in the dark places of the universe, do emit a strange sort of signal when they merge.

It's like a final howling death scream in their last moments. But it's not made of sound. It's not made of light. It's not made of a shower of exotic particles. It's a scream of gravity.

When black holes merge, they create waves of gravity, ripples in space time itself. Deformations in space time like when you drop a big rock in the center of a pond and you see those ripples coming out of it. It's exactly like that except not like that at all. Now it turns out that just about everything in the universe is emitting some form of gravitational waves, but a black hole by itself does not emit gravitational waves. That's because gravitational waves can only be emitted by accelerating objects or by spinning objects that have some sort of asymmetry.

If you have a perfectly smooth featureless star that they exactly like the ideal perfect star platonic ideal of a star and it's a perfect sphere and it's spinning, it will not emit gravitational waves. But then if you add a lump to it, just one little protrusion, just even one atom out side of perfect sphericalness, then as that lump spins around and around, it will create gravitational waves. You'll imagine space time is like a soup and you're trying to stir it. If you take the the long end of your spoon, you know, the long, you know, wooden spoon with a long thin handle, and you stick the long thin handles in and you start to spin it around, you're not gonna get a lot of stirring action. You have to put the other end in, the lumpy bit in once you start spinning that around.

Now you got a stew going. And so black holes, because they're perfectly smooth, because they're perfectly featureless, black holes don't have any lumps, they're not going to generate gravitational waves on their own. They can only stir up space time when they're spiraling in towards each other. In this case, it's like you're taking 2 handles in the pot of soup and stirring the 2 handles around each other. That's going to stir up your soup.

That's going to generate gravitational waves. Suffice it to say, merging black holes release an enormous amount of gravitational waves. If you're within something like 10 light years of a black hole merger, you'll get literally ripped to shreds because the gravitational forces squeezing and stretching you are just going to tear you apart. It's even possible this is crazy. It's even possible to hear gravitational waves because the gravitational waves at their as they're washing over your body will stretch and squeeze your eardrum and you so you will hear it as a rumble as it's, you know, tearing you apart.

In fact, a typical black hole merger will release more energy than every single star in the entire universe. That's a lot of energy, and all of it is completely invisible without a flash or a spark or a particle to go along with it. It's all happening in complete silence except for the eardrum part if you happen to be nearby. But by the time these gravitational waves wash over the Earth, they've traveled for 1,000,000,000 of light years and have calmed down a bit, and so they're only capable of nudging a detector less than the width of an atom. But in 2015, the LIGO instrument became sensitive enough to discover those kinds of deflections and deformations, and they were able to find a gravitational wave signature that it matched exactly the predictions generated by general relativity of what happens when 2 black holes merge.

In fact, those gravitational waves play a critical role in the black hole merger process. It's not just a nice side effect. Gravitational waves are the very thing that make black hole mergers possible. So let's start the story of I know. I'm like 10 minutes in and we're now starting the story, but that's how the show works.

We're gonna start the story. We have 2 black holes, and they start very very far apart. And they somehow encounter each other. So maybe they were born together. You know, black holes are born from the deaths of massive stars.

A lot of stars, especially massive ones, are born in binary systems, so maybe these stars died and left behind 2 black holes. That's one case where you can end up with 2 black holes orbiting each other. Another case is if just black holes just wandering around the universe and getting gravitationally captured by a companion. Same deal. You end up with 2 black holes orbiting each other.

Now, to get these black holes closer together, you have to steal energy from the system. There's a lot of orbital energy contained. There's a lot of momentum in these black holes orbiting around each other. You have to take that momentum away. You have to take the energy away to get the black holes closer together.

Otherwise, they would just keep orbiting around each other forever and we know that black holes merge eventually. So, now, the question is how do they do it? How do we pull energy out? And the first thing that pulls energy out is something called dynamical friction, which isn't just any kind of friction, like, we think of friction of slowing things down. If if if you roll a car, eventually friction brings it to a stop.

Or if you slide something along a table, eventually friction brings it to a stop. Friction can steal energy from a system and and transform it into other things like like heat or sound or vibration. But the key point is it steals energy of of movement and brings something to a halt. Now, black holes orbiting around each other in space, they're not sliding against the table so it's not normal friction. This is dynamical friction.

What this means is that there's other stuff. Black holes aren't alone. There's bits of dust. If it's a stellar system, there might be planets still hanging around. There's just gas.

There's there's just junk. And this junk is going to interact with the black holes through gravity. Some of the junk is going to just get swallowed by the black hole, and it's never seen in this universe again. But some of that junk may just, like, randomly cross paths with one of the black holes. In which case, it gets a little bit of a boost and it moves on when it with its life, and it gets ejected from the system altogether.

When that happens, that energy to to give that particle a boost has to come from somewhere, and it comes from the orbital energy of the black hole itself which brings that black hole closer to its companion. We intentionally do something like dynamical friction. When we are sending spacecraft into the outer solar system, we'll we'll slingshot them gravitationally slingshot them around planets. We'll give them a very close orbit, and then the spacecraft gets a boost. It gets a boost in velocity.

It steals that energy from the orbital momentum, the angular momentum of the outer planets. So you bring if you slingshot around a planet, you're actually bringing that planet a tiny tiny bit closer to the sun, and you're giving a big energy boost to your spacecraft. So it's not spacecraft doing gravitational slingshots that bring black holes together. It's grains of dust. It's bits of hydrogen atoms.

It's it's random asteroids and maybe even entire planets that loop around these black holes just random intersections drawing energy out of the orbiting system of these 2 black holes. The next thing that kicks in is patreon. That's patreon.com/pmsutter. That is how, believe it or not, black holes merge together in our universe. I know it who knew?

But it's patreon.com/pmsutter for you to support this show and bring us closer together. Isn't that special? Anyway, I'm just kidding, of course. What comes after dynamical friction? Dynamical friction can bring black holes to within about a parsec of each other, you know, a few light years of each other.

But then there's not enough stuff to bring them even closer. You know, you can imagine these black holes starting off really far apart, and just slowly over time, there's enough junk in the system, enough gas and dust that dynamical friction steals energy from the orbiting black holes. The black holes get closer and closer together. But once they're within a few light years of each other, there's just not enough stuff. There's just not enough stuff.

If if we were to rely solely on dynamical friction, I I it would just take forever. You run out of stuff at these close distances. And so this leads to a problem. It's called the final parsec problem, which is we don't know how black holes close the gap to actually merge. We know how to get them.

We have simulations, models, the whole deal. We can get black holes from very very far away to about a parsec away from each other. But then to bring them even closer, it just doesn't work. Now what will eventually kick in to pull energy out of the system are the creation of gravitational waves. As the black holes orbit around each other, they stir up space time, they send out these ripples of gravity that steals energy from the orbiting system, that steals energy from the black hole system, and with that energy now gone, the black holes can get closer and closer together.

But gravitational waves are exceedingly weak. Gravity is by far the weakest force. Gravitational waves are just tiny little wrinkles on top of an already weak force, so it's, like, barely there. If we wanted to rely solely on gravitational waves to bring black holes together, we would have to wait multiples of the current age of the universe. And since we only have one age of the universe, like like, it might take a 1000000000 years for gravitational waves to pull 2 black holes together.

The universe hasn't been around that long, and we know that black holes are merging, so something else has to play the role, and we just don't know. So if anyone would like an episode dedicated to the final parsec problem, feel free to reach out, and I'll do an episode just on the final parsec problem. But we're gonna skip that. Something's gonna happen. We know something happens.

We just don't know what it is, and it brings black holes close enough that the gravitational waves that they're emitting can start to do a decent job and they can finish the job. That's because as the black holes get closer together, they orbit around each other faster and faster and faster. So they stir up space time even more. They send out even bigger gravitational waves, and so that gravitational waves can pull out even more energy, and that brings the black holes even closer together, and you get this cascading feedback scenario that goes from super slow with a dynamical friction to, like, medium fast with, like, the mystery process of the final parsec. And then black holes, they kick in in, like, the last few seconds.

A process that can take 1000000 of years to unfold, it's in the last few seconds that gravitational waves do the job. But who pays for the gravitational waves? You know, I keep saying the gravitational waves steal energy from the system, but where does that energy come from? Who pays for it? How do gravitational waves extract energy from this system?

Well, the answer is kinda weird. You know, something has to pick up the tab. Who's paying the gravitational wave bill at the black hole merger restaurant? There are no free lunches allowed in the universe. The answer is the black holes themselves.

Check this out. You remember our little friend e equals mc squared, Energy equals mass times the speed of light squared. The speed of light squared, that's just conversion factor. You can drop that. You can forget about.

The essential element of this equation is e equals m. Energy equals mass. Mass and energy are two sides of the same coin. There are two ways of approaching the same fundamental thing. And this means that you are free to convert between them.

You can change mass into energy and you can change energy into mass. You're allowed and and stuff particles do it all the time. The nuclear fusion happening in the sun is doing it right now, converting mass to energy and back and vice versa. The c squared that just tells you how much energy is in one unit of mass and vice versa. That's all it is.

Energy is mass. Mass is energy. If you have mass, you have energy. Black holes have mass. Black holes have energy.

Black hole mass means black hole energy. And get this, the final merged black hole mass. When these black holes finally do merge together and they create a single unified black hole, the mass of that black hole is less than the sum of the initial masses of the 2 black holes that merge together. Like, if you have a 10 solar mass black hole and another 10 solar mass black hole and you merge them together, you don't end up with a 20 solar mass black hole. You end up with around a 19 solar mass black hole.

The mass of those black holes gets converted into energy, and that's what powers the gravitational waves. It's true. It's it the gravitational wave emission that's happening in the last few seconds is more than just the orbital energy of the black holes. They're either even stronger than that. They're actually pulling from the mass of the black holes themselves, which is the weirdest thing in the world.

I mean, how can a black hole lose mass? Isn't, like, it all locked behind the event horizon never to escape? I mean, it's one thing for a star to explode and lose mass. It's one thing for a planet to lose an atmosphere and lose mass, but how does a black hole lose mass? Mass, but how does a black hole lose mass?

How do you make a black hole smaller? Yes. We have Hawking radiation, but this ain't Hawking radiation. This is the emission of gravitational waves. How do you make a black hole smaller?

I have to admit. I don't have a great answer for you. It's one of those weird cases where the underlying math just says it happens in one of those matter of fact physics ways. The same way the quantum mechanics just happens and it doesn't care how you feel about it. And I know there are a lot of explanations online, but they all fall a little short or miss something.

Every single explanation that I ever found available online is not quite correct and doesn't line up with the actual math. When you actually read the math of the generation of gravitational waves, it just says it. It just like falls out of the mathematics that, yes, the the black holes lose mass during the merger process and this mass gets converted to energy in the form of gravitational waves. And that just happens in the mathematics, and then when you try to put words around it, you can't. So I spent loads of time trying to come up with my own plain words explanation for what's really going on in this seeming paradox, How it could just walk around freely in the universe.

And I got nothing. It's one of these weird cases where the math is the math and our ability to describe what's happening with words, breaks down. The best I can do for you is that mass or idea of mass. If I say, that black hole weighs 10 solar masses, that's only cleanly defined for an isolated black hole. And that when 2 black holes are merging together, the definition of mass gets ambiguous and fuzzy during that process.

So, basically, there can be some cheating. There can be some wiggle room. Black holes can lose mass during the merger process because the word mass itself doesn't mean what we wanted to mean in this extreme case. You know, all the other times in the universe, you know, black hole by itself, you sitting on a chair or whatever, a planet orbiting a star, the concept of mass, what we understand as mass in like the Newtonian classical sense, lines up with what we expect. Well, once black holes start merging together, things get a little fuzzier.

The definition of mass gets a little looser and harder to bend down and so there's some wiggle room where some black holes black holes, when they merge, can lose mass. And I I know this isn't very satisfying. It's not very satisfying to me either. If I didn't have the mathematics in front of me telling me it's true and then the observational evidence backing it up, I would say this is this is nonsense, but it's not. It's one of those cases where we just have to follow the underlying math where it leads us even if that place that it's leading us to is a little bit uncomfortable.

So I know a a lot of of presentations, discussions of black hole mergers, they just kinda skip over this part because it doesn't make any sense. When you add up the orbital energy of 2 merging black holes, that's less than the energy emitted by gravitational waves by a lot. The only other source of energy is the black hole mass itself. And, yeah, black holes can lose mass during the merger process, and it's super weird. And it seems like it's a paradox, but it's not.

In the case of the first ever observed black hole mergers with LIGO, we had a 36 solar mass black hole and a 30 solar mass black hole merging together. That's a combined total mass of 66 solar masses. When they merged together, they became a 63 solar mass black hole. Last time I checked, 63 is less than 66. Where did that 3 solar masses go?

It got converted into energy, and it got converted into these immense gravitational waves that released more energy than all the stars in the universe combined. So we start with 2 black holes. Some dynamical friction brings them closer together. A mystery process gets them even closer. Then, this super confusing process of gravitational wave emission that is literally powered by the mass of the black holes themselves does the trick at the end.

And that trick in the end, the actual black hole merger is weird. Before I keep going, though, I want to mention that this show is sponsored by BetterHelp. And, you know, New Year's is right around the corner, and I gotta tell you, New Year's resolutions are kinda stressful. We set so much heavy expectations on ourselves, and then it just leads to disappointment, and it's kinda lame. So here's an idea for you.

Instead of setting New Year's resolutions for things you wanna change, why don't you use this time to take an inventory of things you're really rocking, things you're really good at, things you like about yourself, and then commit next year to maintaining those or expanding those or making sure those are a fundamental part of your life. Like, I don't know, listening to this podcast or or eating a wide variety of cheese. You know, the choice is yours, and therapy can help you get there. It's not just for those who have experienced major trauma. It's a part of everyday, you know, maintenance of your own life, your own mental health.

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Visit better help dot com slash spaceman today to get 10% off your 1st month. That's betterhelphelp.com/spaceman. We're used to thinking of, like, stars colliding or planets colliding, And we think of these physical objects touching each other. You know, if 2 planets collide, they have they have crusts and mantles, and they they crash together. When stars collide yeah.

You know, they don't have a solid surface, but they're they have atoms. They have plasma, and they're this like merge y, destructive thing that happens. We can envision the physical process. I don't want you to think about black hole mergers in the same way. I don't want you to think of them as 2 objects that are smashing together and that's because when it comes to black holes, we are dealing with geometrical objects.

The black hole itself is a singularity, a point of infinite density. It takes up no volume in space. And what we call the surface of the black hole, the event horizon is an invisible line in the sand. You you can't stand on it. You can't touch it.

You just pass through an event horizon, then you try to leave and you find you can't. That's how you know you that you're inside the event horizon, but that's that's like being in the center or, like, the the coming within, say, a whirlpool. You imagine a big pond, and there's a hole in the pond. The hole in the pond is the singularity, and the water is swirling around it and pouring into it. Wherever you go, you're in the water.

Nothing is different. You're in space time. But once you get close enough to the hole, and and the water is swirling in and you can't escape there, now you're quote inside the whirlpool. You're inside the the hole even though you're still surrounded by water. It's defined by the edge of that whirlpool is defined by the action of the water not by any physical boundary.

And it's the same with black holes. So the only way we can map out the merger process is by using advanced computer simulations that plot out the structures of the event horizons. Because they're not physical boundaries. They're invisible lines in the sand. They're like places of no return, and we want to know how the event horizons change during the merger process.

So I like to think of it more as like 2 soap bubbles gluing together rather than 2 planets crashing together. And event horizons, even though they're not physical boundaries, they still respond to the warping of space around them. If you if you're near a black hole and it's perfectly isolated and it's not spinning, you'll have a perfectly spherical event horizon. If it's spinning, then its event horizon will be stretched out. And if there's a large gravitational mass nearby it that's deforming space time in its own way, then the event horizon will distort around it.

It will follow those curves and hills and valleys in space time. So because an event horizon responds to the warping of space around it. When we usually think of black holes we usually think of a single solitary unit all by its lonesome, which is useful enough. But when we're here, like a millisecond before the merger event, we have to care about the wider universe. Each individual black hole is distorting space around it.

And once these 2 black holes which are about to merge are really really close together, they distort the space around the partner and this causes the event horizons to warp in response. Throughout the merger process, nothing is going to escape except some of the black hole mass, but we're not going to talk about that. If you were trapped inside of a black hole during the merger process, you can't get out. All we're doing is distorting the shapes of 2 event horizons which is totally 100% legit and fine. I can squeeze and stretch event horizons.

I can modify space and warp space around and the event horizons will will distort themselves in response. So that's fine. And eventually, I'm going to combine these event horizons together. The first thing that happens is an elongation. Just like the tidal forces that you would see with 2 regular merging objects.

Like the earth and the moon are close enough that the moon's gravity raises tides on the Earth. If you take 2 stars and bring them close to it together, these tidal gravitational forces will start to stretch the stars out. The exact same thing happens with event horizons. Gravity is gravity. And black holes are made of gravity, so you shouldn't be surprised that normal gravitational stuff happens to black holes.

But then something absolutely weird happens. Each black hole sends out a a tiny little tendril, almost like a tentacle. You ever watch that movie, the abyss? With that weird alien controlled water tentacle creature. If you're with me on that visual analogy, then I thank you.

If you're not, just just stick to, you know, generic tentacle of event horizon stuff. So, like, you have this event horizon that's elongated. Each one is elongated towards the other, and then there's this, like, little pinch point. The closest point on each event horizon, like, really stretch out, really reach out and form this little tendril. And when the 2 tendrils meet, they create a bridge, an incredibly thin bit of event horizon stretching between the 2 main black holes.

What this means is that if you were observing this black hole merger process and you were to slip into that tiny little thread and somehow survive, during the merger, you would be trapped. That's what an event horizon means. It's it's a it's a place that you can enter, but you can't escape from. And even if it's weirdly distorted and weirdly shaped and this long little tendril, bridgey thin thing, if you were to fall into that thin thing, you would not be able to get out. You would be a part of the merger process, and I guarantee it would not be pretty.

To me, this is by far the strangest part of the black hole merger process because it looks like a tiny thin umbilical cord stretching between the 2 black holes. It's not something you would intuitively predict would happen, but the simulation show that the extreme gravitational distortions lead to this exact case, but it doesn't last long. Less than a millisecond later, that bridge expands and the black hole swallow each other. And then there's only a single black hole left. As for the singularities themselves, well, we're not sure.

We're not sure what singularities are made of in the first place. So what happens inside of the newly merged event horizon? What happens to those singularities? Presumably, they merge together to form a single singularity, but, honestly, we don't know. I'll leave you with one more thing just to really make you need to lay down for the rest of the day.

That new black hole, the one that merged from 2 smaller ones that it took a 1000000 years to go from a great distance, then through dynamical friction get close together, then a mystery process brings them very, very close together, and then the emission of these terrible gravitational waves that suck mass out of the very black holes themselves to power, bring in in the last few seconds are able to merge these black holes together, the last millisecond this tendril bridge forms between 2 event horizons before they swallow each other. That new black hole, yes, its total mass is less than the combined mass of the original black holes. But with black holes, the radius is proportional to the mass which means that the area goes as the mass squared and the volume goes as the mass cubed. That means that even though the final black hole has less mass than the 2 black holes started with it has more surface area and more volume than the previous 2 black holes combined. So even though you're losing mass when you merge black holes, you're still increasing volume and increasing surface area.

There is less mass, but there is more black hole in the universe than what you started with. Like I said, this is what black holes do. They create questions. Thank you to Mark s, Timothy b at HB Shannon, Melvin n, Bartlett, Nylay v, Scott m, and Rusty w for all the questions that led to today's episode, and thank you to all my Patreon contributors. That's patreon.com/pmsutter.

I wouldn't be able to do this show without you. I really do truly appreciate all your contributions. I'd like to give shout outs to my top contributors this month. We've got Justin g, Chris l, Alberto m, Duncan m, Corey d, Stargazer, Robert b, Nyla, Samr, John s, Joshua, Scott, m, Rob, h, Scott, m, Louis, m, John w, Alexis, Gilbert, m, Rob, w, Dennis, a, Jules, r, Mike, g, Jim l, Scott, j, David, s, Scott r, Heather, Mike, s, Michelle, r, Pete, h, Steve, s, Watt Wotburg, Lisa, r, Koozie, Kevin, and Michael b. That's patreon.com/pm.

Sorry. Keep those questions coming. Come on. Ask a spaceman@gmail.com, or just go to the website, askaspaceman.com. Send me your questions even if they're about black holes in the final parsec problem or what exactly happens to the singularities, all those parts that I kinda sorta skipped over.

Happy to give a crack at those. And please keep those reviews going on iTunes and Spotify or your favorite podcast downloader thingy. I really do appreciate it, and I will see you next time for more complete knowledge of time and space.

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