Black Holes 5: Inklings & Obsessions

by Shane L. Larson

There are many exotic phenomena in astrophysics — some pervade the public consciousness, and others do not. Most folks have heard of the “Big Bang” and probably about “dark matter.” Fewer people have heard of the “Cosmic Microwave Background” or “neutron stars.” Perhaps even fewer have heard of “cosmic strings” or “radio jets.” But of all the strange and wonderful things astronomers and physicists have contemplated, the most universally known and recognized are probably “black holes.” Just about everyone has heard of black holes, and just about everyone has some cool science factoid they know about black holes and keep in their pocket — they pull the factoid out anytime the subject of black holes come up because the factoids typically MELT YOUR BRAIN.

On the left, an optical image from the Digitized Sky Survey shows Cygnus X-1, outlined in a red box. Cygnus X-1 is located near large active regions of star formation in the Milky Way, as seen in this image that spans some 700 light years across. An artist’s illustration on the right depicts what astronomers think is happening within the Cygnus X-1 system. Cygnus X-1 is a so-called stellar-mass black hole, a class of black holes that comes from the collapse of a massive star. New studies with data from Chandra and several other telescopes have determined the black hole’s spin, mass, and distance with unprecedented accuracy.

I find black hole factoids to be a curious mix of some things that are true, some things that are speculative but possibly true, and some things are are outright fiction. Where do all of the exotic facts about black holes come from, how do we all learn them, and why are some right and some wrong? Wondering about this led me to contemplate when I first heard about black holes.

Black holes have long been a passion of mine — my mom will tell you I was always kind of obsessed with them. But when did I first hear about and learn about them? I certainly can’t answer that question definitively, but I do know some things about my early exposure, so I can try to understand what strange and awesome ideas first attracted my attention.

The earliest encounter of which I am certain is during the 1979/1980 timeframe. This was the time that many people saw Disney’s epic space opera The Black Hole, replete with adorable robots, killer robots, really awful bad dialog, and archetypical mad scientists. It has often been derided for its scientific inaccuracies (most notably by Neil deGrasse Tyson [link]). I definitely saw The Black Hole. Multiple times. And I still watch it sometimes. Neil’s right, there is a lot of inaccurate science about black holes in The Black Hole, but there is a lot that I think was okay too (more on that later). There are definitely modern movies that get the science more uniformly correct (Interstellar), but I don’t mind The Black Hole — certainly not as much as Neil. The point here is this is a known anchor point in my love affair with black holes.

So what could a movie like The Black Hole teach me about real black holes? If you ask almost anyone, they know the correct fundamental thing: a black hole is an object whose gravity is so strong, not even light can escape — even The Black Hole got that right. Since nothing can travel faster than light, nothing can escape. If you fall into a black hole, your fate is sealed. It is this idea of being trapped forever, without recourse or hope of rescue, that lies at the heart of our fascination with black holes. They are strange; indubitably. But to be inescapable suggests a kind of absolute and infinite supremacy. 

Me in elementary school. I’m not sure what I’m doing, but I’m pretty sure I’m not getting into trouble! [Image: Pat Larson]

In 1979/1980 I was in fifth grade, and I was gobbling this stuff up left and right. I was a well known fixture in both my school library (Hygiene Elementary School, in Colorado), and in the Longmont Public Library, where my mom had gotten special dispensation for me to have an “adult” library card so I could prowl through all the science books in the grown-up section. My parents also exposed me to a steady diet of books at home, and while they were all nominally “family books,” some of them made it to the bookcase by my bed and never went through anyone else’s hands. In 1980 one such book was Roy Gallant’s lavishly illustrated Our Universe, published by the National Geographic Society.  I was certainly enraptured with outer space by then, steadily fed by the ongoing exploits of Viking and Voyager as they played out on the pages of National Geographic. But this book — this book. Blew. My. Mind.

It is a book filled with great pictures from an exquisite generation of space probes, and from the best telescopes the world knew in the pre-Hubble era. But the art and scientific illustrations are what sucked me in. Paintings of the surface of Venus. Speculations of what weird alien lifeforms evolution could have created. Stupendous cutaways of planetary interiors and atmospheres. All of it was linked together with Gallant’s trademark lucid storytelling.  This ode to the Universe captured my mind and imagination and never let go. That first copy my parents gave me was read cover-to-cover, and carried for miles and years everywhere I went, pulled out of my backpack in moments of wonder and curious indulgence.

Examples of the art and technical imagery in Roy Gallant’s “Our Universe.”

Near the end of the book, Gallant talks about black holes in just 4 short paragraphs, but accompanies the text with a lavish, full-page artist’s idealization of a black hole in space, tugging on a nearby star, bending the shape of spacetime, and absorbing a beam of light that was inexorably caught in its pull.

He asks in the caption of the picture, “Can you imagine a star so massive that its gravitation eventually crushes it out of existence, leaving only a black hole in the sky?” This is classic Gallant, imploring the reader to immerse themselves in the mystery, throw caution to the wind, and employ their imagination — take what little knowledge you have and simply speculate. That is where good ideas come from, and it is the basis for all science.

The artist’s representation of a black hole in “Our Universe.” [Image: Helmut K. Wimmer]

In many ways, the reason you and I are having this little blog conversation is precisely because astronomers know that black holes exist in Nature and are the central players in many astrophysical phenomena. But reading Gallant’s text it is clear that when he wrote Our Universe, the existence of black holes was still a subject of much debate among scientists. Today there are many ways that we have measured the properties of black holes and confirmed their existence, not the least of which are the many that have been detected via gravitational waves. But still, pictures of black holes remain elusive. The best we have so far is the Event Horizon Telescope picture, a silhouette of a black hole against the backdrop of stuff around it.

The picture in Gallant’s book is an attempt to show a black hole as a three dimensional object in real space, but how do you do that?  It was a noble attempt, and it is certainly not what a black hole looks like, but it served its purpose — it got my attention, it fueled my imagination, and it made me ask questions then go see if the answers were known. To this day I keep copies of Our Universe nearby — one in my office and one in my study at home. It is never far from my mind nor my fingertips, and I often pull it down and lose myself in the epic stories it tells.

The other thing I know happened to me in the fall of 1980 was my first exposure to Carl Sagan’s Cosmos. Starting in late September, every Sunday night, I sat rapt on my parents’ living room floor in front of the television, whisked away to worlds and places in the Cosmos I had only previously imagined, transported by the magic of film, the lilting and elegant soundtrack of classical music, and Sagan’s poetic and sonorous narrative. One of the most widely known episodes is Episode 9, “The Lives of the Stars” which famously begins with Sagan declaring, “If you wish to make an apple pie from scratch, you must first invent the Universe.”

Sagan uses his famous declaration about pies to introduce the concept of the chemical elements — the atoms from which all the beautiful and complex structures of Nature are built. Beyond the simplest elements — hydrogen and helium — very little was created when the Cosmos was born. Almost everything on the periodic table is created by stars during their lifetime, and a great deal of it (the heaviest elements) during the catastrophic death throes we call supernovae and gamma ray bursts. In telling us about the death of stars, Sagan uttered the magic words I had heard before — black hole. In his trademark penchant for poetic description, he called it “a star in which light itself has been imprisoned.”

Sagan’s Cosmos was the first place I was introduced to the ideas of black holes in the context of general relativity, beginning with masses curving space and affecting the motion of other masses, and also a discussion of the principles of black holes as tunnels [Images from Ep 9: “The Lives of the Stars”]

He had led us to the existence of the super-strong gravity of black holes through an imagined tea party with Alice and her friends in Wonderland, but then he hung on it all the modern picture of curved spacetime. It was, as far as I know, my first exposure to Einstein’s brilliant realization, and it has ever since dominated my destiny. Today, I have a doctorate in theoretical physics, earned for studying the magical mysteries of that self-same curved spacetime.

Me and J. Craig Wheeler. He’s one of the reasons you’re reading this blog right now!

For many of us, our interest in black holes might be piqued by these kinds of exposures, and then we go back to our lives as dental hygienists or soybean farmers or city managers. But this was all still swirling in my mind when I entered college, and in the true traditions of higher education, my exposures took those latent passions and exploded them into what would become my life. I was an undergrad at Oregon State University and at that time there was a stupendous class on campus called “Rocks & Stars,” run by the indomitable Julius Dasch. This was one of the most popular classes on campus, and had a regular stream of guest speakers who visited and talked to us about cool stuff.  I have strong memories of one visit from J. Craig Wheeler, a supernova expert from the University of Texas at Austin.

Supernovae are one of the pathways for making black holes in the Universe, and Wheeler gave us a spectacular talk that culminated with him reading to us from a science fiction book he wrote, called “The Krone Experiment.” I won’t give it away (go read it!) but what I remember from the talk was Wheeler talking us through what would happen if you were standing on a sidewalk and a micro-black hole came booming up out of the ground next to you. What would you see and experience? It’s the sort of question that just captures your brain and won’t let go. To be honest, it was the perfect question to ask a young scientist in the throes of deciding to commit their career to studying these enigmatic objects.

I think every one of these stories illustrates a key fact in my mind: it didn’t matter what I heard about black holes in my youth, only that I did hear about black holes. Exposure did what it should: it filled my head with all kinds of possibilities, all of them totally brain-melting, and made me pay attention and ask questions later.

This last point is the most important point here: we want people to ask questions. Either because they are confused, or because they are idly curious, or because they want to learn more. To that end, having mind bending movies like The Black Hole is stupendously important, and I don’t care if they get the science perfectly right! I have colleagues who often grouse about bad science in movies, complaining vociferously that the producers should have taken a basic science class, or gotten a good science advisor. They proclaim, “Is it really that hard to get the science right? The right science is just as cool!” 

But people aren’t watching The Black Hole to learn science (I certainly wasn’t) — they are being entertained, itching a part of their brain that wants to be asked “is that even possible or real?” And that serves its purpose, because eventually every one of them ends up in an audience somewhere at a public lecture and raises their hand and asks someone like me “is what happened in the movie real?”  THAT is where we get the science right. The movie’s job was to put a question in someone’s mind, to make them care enough to know what the right answer might be, and then in some other part of their lives have some discussions about science, what is known, what is not known, and what the other mysteries of the Cosmos might be.

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This post is the last in a series about black holes.

Black Holes 01: Imaging the Shadow of Darkness

Black Holes 02: What are black holes made of?

Black Holes 03: Making black holes from ordinary stuff

Black Holes 04: Singularities, Tunnels, and Other Spacetime Weirdness

Black Holes 05: Inklings & Obsessions (this post)

Black Holes 4: Singularities, Tunnels, and Other Spacetime Weirdness

by Shane L. Larson

I think one of the great things about the modern world is the propensity of information. Information is free and easy to come by, and it possible to learn about anything you want. More-or-less, the total knowledge of our civilization has been written down in books and documents, and disbursed to libraries, websites, and other mediums of communication. It is not always easy to discern what is authentic and what is not, as is clearly the case when one looks at the wild, apocalyptic wastelands of modern social media. But none-the-less, it is easy to indulge your desire to simply learn. We consume books and podcasts and documentaries, sacrificing time we could spend on woodworking or yardwork or binging TV shows in favor of trying to recapture how we felt in 2nd and 3rd grade, before school became about exams and homework and was just about how awesome all the far flung corners of the world and Nature could be. 

I think deep down all of us are lifelong learners; I’ve met many of you at public lectures or here at the blog. Some of you are quiet, and sit in the back with contemplative furrows on your brow; others of you are more exuberant and can barely contain your questions. Either way, you all show up, because you remember how cool it was when you were first learning. But I’ve noticed something interesting in my years talking to all of you: as a rough rule of thumb, I can usually triple the attendance of any talk if it is about sharks, volcanoes, dinosaurs, or black holes. Vast numbers of you succumb to your curious inner child if I talk about the right things. 

People’s minds, young or old, can be captured if we talk about science in ways that stimulate their interest and imaginations. [Image: Bill Watterson]

What is it about these topics that inspires deep interest in people? I think, at the heart, they are very real examples of the Universe’s ability to put you in mortal danger with implacable indifference. Never mind that it is unlikely you will encounter any of these dangers in your life. Pondering being faced with a highly improbably danger in the Universe allows us to ask ourselves, “what would I do?” in much the same way we watch super-hero films and imagine ourselves in the fray. 

Black holes are notable in this list because not only do they have the mystique of danger about them, but they are suffused with a long list of exotic, mind-bending phenomena that add to their mysterious nature.  

Let’s talk about some of the exotic things you have hard about black holes, and I often get asked about.

“Is everything is going to get sucked into black holes?” 

This is probably the most common question I get about black holes! The simple answer is “no” — black holes are not little Hoovers running around the Cosmos sucking stuff up. I’ve thought a lot about where this idea comes from, and I think it is a mis-extrapolation of the inescapability of a black hole. When you are far from a black hole, its gravity is exactly the same as the gravity produced by ordinary objects of the same mass. If you are orbiting far away from a billion-solar mass black hole, the gravity you feel is exactly the same as if you are orbiting around a dwarf galaxy that has a billion sun-like stars in it!  If we could magically replace the Sun with a one solar mass black hole, the Earth would continue along in its orbit as if nothing had happened because the gravitational influence is exactly the same! 

Far from the black hole, you cannot tell if you are orbiting a black hole or a star of the same mass — their gravity is identical unless you get close. [Image: S. Larson]

If you are silly (or unfortunate) and fall into a black hole, you are never going to get out. The gravity of a black hole is so strong that it can trap anything inside it; that is true. But it is not infinitely strong and able to influence everything outside it. 

“What does it mean to get spaghettified?” 

When you get close to a black hole, the gravity can become more intense than anywhere else in the Cosmos. Imagine you are jumping in feet first. The gravity is strongest close to the black hole, so your feet are pulled on more strongly than your head, which is farther away. The result of this dichotomy of gravitational strength is the black hole tries to pull you apart, much as you stretch a rubber band by pulling on opposite ends. Physicists call this difference in force a tidal force, and the process of pulling you apart is called tidal disruption. Stephen Hawking, in his famous book “A Brief History of Time” called this effect “spaghettification.”  

Some ways of falling into a black hole will feel less painful than others. [Image: S. Larson]

Somewhat paradoxically, the spaghettification effect is strongest near the event horizon of small black holes, and weaker near the event horizon of larger black holes. The spaghettification effect is also stronger when your head is farther away from your feet (so tall people will suffer more than us short people). The two rules of thumb for surviving spaghettification when you are jumping into black holes are this: 

1. Jump into the biggest black hole you can find; million solar mass black holes are much more fun to jump into than solar mass black holes.
2. Belly flopping into black holes is safer than jumping in feet first.

“Do black holes really bend time?” 

The movie Interstellar has revived broad interest in black holes and inspired wide-ranging conversations about what black holes are really like. One of the most common conversations we have is about time, which usually begins with “what was the deal with the guy who got old when he didn’t visit the black hole?” This plot device could just be accepted at face value, like we do with so much science fiction, but in this case it is rooted in the physics of the real world. General relativity predicts that the closer you are to a source of gravity, the slower your clock ticks compared to someone very far from the source of gravity. Here I use the word “clock” in the physics sense: anything that keeps regular time, whether it is a digital watch, a wind-up pocket-watch from your grandparents’ day, an hour-glass, or the steady beat of your heart.  

Consider two people, one close to the black hole and one farther from the black hole. Every clock ticks slower when you are close to the black hole — this could mean an actual clock that tells time, but it can also mean a regular biological clock, like your heartbeat. [Image: S. Larson]

The bending of time is definitely one of those counter-intuitive predictions of general relativity, but if space and time are one entity (“spacetime”), then bending space very strongly must necessarily also bend time. It doesn’t take much to bend time by a measurable amount — the bending of time is the central physical effect behind the Global Positioning System, which you use everyday on your phone to navigate to the nearest ice cream shop (or coffee shop — whatever). The difference between the bending of time around the Earth and the bending of time around black holes is the strong gravity near the black hole makes the effect much more pronounced. 

“Are black holes are infinitely dense? What does that mean?” 

Anything labeled infinity is, generally, an anathema to scientists. “Infinity” is a perfectly good concept in mathematics, but with respect to the natural world, it seems that the Cosmos is only filled by things that are finite and measurable. That is not to say there aren’t enormous, gigantic, mind-bogglingly huuuuuuge numbers, but they are all tiny compared to “infinity.” In the natural sciences, we have often encountered “infinity” in the mathematical ways we describe Nature, but we’ve found most of them were simply artifacts of our early poor understanding of how the world works, particularly on the microscopic scales of fundamental particles. Gravity is the last frontier in this regard, and there are many persistent “infinities” we encounter, and they often manifest themselves in the study of black holes. 

An example of your common experience with density. This cube of tungsten and this clown nose are about the same size, but the tungsten is significantly heavier. Why? because more stuff is packed into roughly the same amount of space. [Image: S. Larson]

To think carefully about this, let us be precise about what we mean. “Density” is a common concept in physics and chemistry. It is how much stuff (mass) is squeezed into a given amount of space (volume). Dense objects feel heavy in your hand, while less dense objects feel lighter.  As a matter of practical everyday experience, you most often encounter the notion of density when thinking about things floating or sinking in water (objects more dense than water, like rocks, sink; objects less dense than water, like styrofoam, float). 

So let us define the “density of a black hole” the way we define the density of any other object in the Universe: the mass of the black hole, divided by the volume of the black hole. Those of you who are practicing gravitational physicists will recognize that we should be careful when computing the “volume”, but for practical purposes here let us use the ordinary formula for the volume of a sphere where the radius of the sphere is the radius of the event horizon of the black hole. This is practical and intuitive, and will illustrate our point effectively.  

The first picture of the black hole at the heart of M87, formed by light being bent around the inner most regions of space outside the event horizon. This black hole has a diameter larger than the diameter of our solar system! [Image: Event Horizon Telescope Collaboration]

Imagine two black holes: one that is the mass of the Sun, and one that is one billion times the mass of the Sun (a bit smaller than the black hole in M87 that was the subject of the Event Horizon Telescope picture). The solar mass black hole only has a radius of about 3 kilometers, and a density of about 18 quadrillion times more the density of water (1.8 x 10¹⁹ kg/m³, for those calculating themselves). By comparison, a 1 billion solar mass black hole has a radius just under 3 billion kilometers (about the radius of Uranus’ orbit); it would have density of only 2% the density of water (numerical value: 18 kg/m³; slightly less than the density of styrofoam). If you could somehow drop it in a gigantic cosmic bathtub, its density suggests it should float. 

If black holes were solid objects and could interact with the world like ordinary “things,” a calculation of their density suggests some are less dense than water and could float in a cosmic wading pool. [Image: S. Larson]

It can’t float, of course — the event horizon is not a hard surface that water can act on and thus provide buoyancy in a ginormous cosmic pond. Water would flow right through the event horizon and disappear, so all the water in the cosmic pond would essentially flow into the black hole like some kind of drain.  But that’s not the point in the floating analogy. As a general rule, we think we understand the physics of things that have densities less than the density of water, so the idea that the density of a black hole is the same as materials that do float is a strange and discomfiting result. And it should be! Just remember your discomfiture is related to the odd nature of black holes — density defined in the classical way really doesn’t apply to black holes the way we’ve done it here, because as we’ve noted before, they are mostly empty space! This odd result has little to do with their overall size, and more with what lies at their heart… the singularity. 

“The Singularity” 

The real mystery of black holes lies at their heart, in the center of the space defined by the boundary of the event horizon. All the gravity of the black hole is concentrated there. All the matter that collapses to form the black hole is still being drawn together even after it falls through the area we call the event horizon. Gravity keeps pulling it inward, inexorably inward, squeezing it smaller and smaller with a force so great no known force in Nature can stop it. Everything that fell inward to create the black hole gets squeezed down smaller and smaller, becoming more and more dense. Eventually it gets squeezed into a space that is vanishingly small, or so general relativity predicts. This point of zero size with everything squeezed into it is infinitely dense, and is called the singularity. The laws of physics as we understand them break down before you ever really reach the singularity, at a distance away from it called the Planck length, about 10^-35 meters (0.00000000000000000000000000000000001 meters). This is the length where we expect the physics is governed by quantum gravity, a description of gravity, space, and time on the tiniest scales. We have searched for such a mathematical description of Nature for many years, but so far have been unsuccessful. 

How do physicists think about the singularity? It is an infinity, and infinities are anathemas to physicists. More often than not we are trying to understand what is happening far away from the singularity when thinking about the Cosmos. This is, more or less, what astronomers do because they are observing the Cosmos outside the event horizon, which is far from the singularity. Easy peasy — you don’t even have to waste one brain cell on the singularity if you don’t want to! Sometimes physicists pretend they are okay with the singularity being infinitely dense, and use the classical laws of physics (general relativity in particular) to understand the influence of the singularity around it. Gravitational physicists often do this, in particular because they are trying to understand how the world behaves under the influence of strong gravity. All the tales and imaginings you have heard about the inside of black holes are figured out by scientists thinking about the singularity this way. The last prominent group that thinks about the singularity are the quantum gravity squad. There are many ideas about what a complete description of quantum gravity will look like — all of them are clever, and elegant, and exotic. But we don’t yet have a way of experimentally testing any of them. Someday we will be able to test them. The day we understand quantum gravity, it will tell us something about the true nature of the singularity. 

“Are Black Holes Spacetime Tunnels?”

The last and most famous example of spacetime weirdness and black holes is the astonishing idea that for some kinds of black holes, if you jump in, they may in fact be tunnels. For the movie nerds out there, this is the central plot device in many science fiction stories. For perfectly spherical black holes, there are no tunnels — if you jump in a black hole, the singularity lies in your future; you will be crushed ruthlessly and mercilessly.  But for black holes that happen to have electric charge on them (expected to be few) or are spinning (most black holes found in Nature are expected to be spinning) there are trajectories inside the event horizon that do not end at the singularity. They end… somewhere.   

Scientists struggle to visualize black holes just as much as ordinary people, so we have developed a special map called a Penrose diagram. As you go up the diagram from bottom to top, time increases from the past to the future. As you go left or right on the map, you change where you are in space. Here the white areas are the ordinary Universe, and the yellow areas are inside a black hole. The one on the left is a Schwarzschild black hole that has no tunnel; if you are inside, the singularity lies to your future and there is no ordinary Universe you can get to. The one on the right is a charged black hole, which might have a tunnel. If you are inside, you can avoid the singularities on the left and right, and possibly emerge at the top of the diagram. [Image: S. Larson]

In these kinds of black holes, if you avoid the singularity you come out of something that looks mathematically similar to a horizon. The difference is you come out of this horizon, emerging from the inside to the outside. Such things are variously called “wormholes” or more commonly “white holes.” They are, in essence, the other end of the black hole, like it is some kind of giant culvert or tunnel that connects one place to another. 

Tunnels to where? you quite astutely ask. The truth is we don’t know, but there are several possibilities. One possibility is the tunnel emerges somewhere else in our observable Universe. As an astronomer this is a very intriguing possibility, because it suggests there may be something that could be observed with telescopes. Sadly, to date, we have not seen anything exotic and unexplained that might be a white hole.  

Another possibility is that it may emerge somewhere in our Universe, but outside the observable part of the Universe. This idea is a bit harder to wrap your brain around, because it hinges on understanding that the Universe can be larger than what we can observe and could, in principle, go on forever. The “Observable Universe” are just those parts of the Universe that are close enough for us to observe in a telescope because light has had time to reach us in the time since the Universe was born. An easy way to think about this is to think about your home state where you live. Most of us can walk only a few miles per hour — let’s say 3 miles per hour. That means in one day, you could only walk 3 miles per hour x 24 hours = 72 miles. If you started walking right now, by this time tomorrow you could be anywhere in the state within 72 miles. Does that mean the rest of the state isn’t there? Of course not — it just means the parts of the state you could get to at the fastest pace you could walk (the “Observable State”) is only 72 miles away in any direction. 

If I start at Northwestern University and walk for 24 hours at 3 miles per hour (average walking speed of a human) I can reach anywhere inside the red circle. I can get no farther, but that doesn’t mean there aren’t more places outside the circle! The Universe is the same, only the time is not 1 day, but the age of the Universe, and the speed is not walking speed, but the speed of light. Inside the circle is what we call the Observable Universe, but it is not the Entire Universe. [Image: S. Larson, Map by Google]

A third exotic possibility is that the white hole may emerge not in our Universe, but in some other Universe. A Universe that is not our own, but is somehow parallel to our own. It is an interesting possibility to ponder and imagine because it opens up all kinds of possibilities. Are the laws of physics the same there, or is the other Universe some weird place that doesn’t have stars and planets and galaxies? Do all of our black holes emerge as white holes in the other Universe? Where do black holes from the other Universe go? Do they emerge in our Universe, or do all white holes in all the other Universes emerge in only one of the other Universes? Some things we can imagine within the realm of science and do calculations and simulations about, but others are mere speculation that we have yet to ponder and consider seriously. It makes your head spin, but these are the things that great speculative science fiction about black holes are made of.  

The last possibility is that tunnels through black holes simply do not exist at all, that Nature somehow closes them off, or we have not fully understood the mysteries of black hole insides completely yet. There is much we still have to learn.

Which of course is the point. Black holes, on any given day, seem completely unfathomable, especially in the context of the weird implications about what they do to the world around them. But is precisely that mystery that draws our attention time and again. Partly because we like that feeling of being completely baffled by Nature, but also because some deep part of us knows that these inscrutable mysteries hide deep and precious secrets, secrets that lie at the core of how Nature and the Cosmos work. 

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This post is the fourth in a series about black holes.

Black Holes 01: Imaging the Shadow of Darkness

Black Holes 02: What are black holes made of?

Black Holes 03: Making black holes from ordinary stuff

Black Holes 04: Singularities, Tunnels, and Other Spacetime Weirdness (this post)

Black Holes 3: Making black holes from ordinary stuff

by Shane L. Larson

If you are exploring the Cosmos, and either by design or accident, find yourself plunging toward a black hole, on a beeline that takes you directly across the horizon, you don’t encounter anything along the way; all you feel is the inexorable pull of gravity pulling you farther and farther down. When you reach the event horizon, the nominal “surface” of the black hole, what do you encounter? 

Nothing.

The event horizon is simply the invisible line in space where gravity has become so strong that even if you were travelling at the speed of light, you could not escape; the event horizon is a boundary that once crossed, Nature says you are never coming back out — the inside of the black hole and only the inside of the black hole is in your future. That’s a big statement, but you cross this point in space without even an alarm to let you know you are trapped. It’s as easy as walking across a line drawn in the sand at the beach.

A black hole with the MASS of the Sun is not even close to the SIZE of the Sun! Here the approximate size of a solar mass black hole is shown near the city of Evanston, IL — only about 6 kilometers (4 miles) across. What is it made of? Nothing tangible — it is empty space, filled with nothing except gravity itself! [Map: Google; Image: S. Larson]

Through the horizon and as you fall inward you still encounter absolutely nothing. This has previously led us to ask, “What is the black hole made of?” Based on what you experience, we had concluded “a black hole is made of pure gravity.” But gravity, as we learned early on in our thinking about the world, is a consequence of mass (or energy if you take the modern understanding of mass and energy being related). That normally would imply that the black hole was made of mass of some sort, but as our gedanken experiments have paradoxically shown us, there is no mass to be encountered when travelling toward and into black holes! 

A thoughtful cosmic explorer (or astronomer) would take that bit of confusing information and ask a very pointed question: “how do you make a black hole, then?” The motivation for such a question is built out of our common experience. If you want to make something, whether it is a gallon of dandelion wine, a guitar, or a cinnamon roll, you take other things and transform them into the new thing.  So what are the other things that can be transformed into a black hole? And how do you change them from being ordinary things into pure gravity? Those are very good questions, and to be honest with you here at the beginning, we don’t know all the answers. We only know part of the story, the penultimate explanation for how it happens. Some of the story is still unknown, and lies beyond the boundaries of what we currently understand about the Cosmos. That is part of what astronomers and physicists investigate and attempt to understand every day.

Astronomers have seen many phenomena in the Universe that are explained by black holes. The question is where do they come from? [Image: Wikimedia Commons]

How do we start? Where ever you are, look around you and pick up the nearest thing you can see. Maybe it’s a rock, a bagel, a book, a Lego brick, your cat — whatever. Here I’ve picked up a fountain pen. Why does the fountain pen, or any other object, have form? What is it that makes it a solid tangible object? If you try to squeeze the fountain pen, it may deform slightly, but generally resists any effort to squeeze it out of shape. Why? Because as you press the fountain pen, the building blocks of which it is made, the molecules and atoms, fight to hold their shape. They press against their neighboring atoms, and when the pressure from your fingers tries to force them closer together, they press back against you in tandem, resisting your attempt to move them.

If you press hard enough, you can sometimes squeeze them together or change how they sit next to each other. Sometimes you are stronger than a material and break the object. Some objects are hard to compress, but they can certainly be deformed if you apply a force to them in specific ways. It’s hard to flatten a paperclip into something like a piece of foil, but it is not too difficult to bend it back and forth into a new shape. Ultimately what you can do physically to any object depends on how the building blocks of its structure respond to forces applied from the outside.

(L) Very solid objects, no matter how hard I squeeze them, retain their shape. The atoms that they are made of resist external forces. (R) Some objects can be deformed, bent, or broken, like these paperclips — their atoms resist some external forces, and yield to others. [Images: S. Larson]

Now consider a slightly different example. Go to your kitchen and find a party balloon in your junk drawer. Blow it up and tie it off so it is maybe 20 centimeters across. Take a couple of sheets of aluminum foil, and wrap the balloon up. What happens when you try to squeeze the foiled balloon? It deforms a little bit under the force of your hands, but when you let go the pressure from inside the balloon pushes it back into its round shape.

A balloon wrapped in foil as a heuristic model of a star. The balloon presses outward against the pressure from your hands that is trying to collapse the foil.

This simple balloon and foil model is completely analogous to a star. The foil is playing the role of the outer layers of the star that we see when looking through our telescopes (the “atmosphere” or the upper layers of the star). Your hands pressing down are like gravity, trying to pull everything that makes up the star into the center. Opposing the inward press of your hands, the balloon represents something inside the star pressing outward against the pull of gravity. We know the outward press is the energy released by nuclear fusion deep in the core of the star. This balanced state, where the inward pull of gravity is precisely counterbalanced by the outward push from the energy created by fusion, maintains the round and stable size and shape of the star. Astronomers call this state hydrostatic equilibrium.

When the balloon is popped, nothing prevents your hands from collapsing the foil. This is similar to fusion ending in the core of a star — nothing presses outward, and gravity collapses the star.

Now, gently hold the foiled balloon in the palm of your hand and have a friend pop the balloon with a needle. The support from the balloon vanishes, leaving you holding an unsupported shell of the foil. You are gravity, so squeeze the foil down. It should be easy — there is nothing to fight back against you. You can, and should, squeeze the foil down into a small, aluminum ball. Ball it up, and squeeze it into the smallest ball you can. Once you’ve squeezed it as hard as you can, stand on it trying to squeeze it smaller. If a member of your family is stronger than you, ask them to squeeze it even smaller.

How small did you make it? Can you make it any smaller? The answer is “probably not.” Why? Because all of the aluminum atoms in the foil are resisting being pressed together, far stronger than you can press them together with your hands or feet. This is not dissimilar to the fountain pen we discussed above — all the atoms that make up the aluminum are pressing out, resisting being pushed any closer together than they already are.

The exact same thing happens in Nature. Gravity takes collections of stuff — stars, planets, anything round — and tries to pull it together as strongly as it can. Eventually everything gets crowded together, and through a variety of interactions resists the inward pull of gravity. For stars in the middle of their lives, they exist in hydrostatic equilibrium, with the inward tug of gravity balanced against the outward push from the fusion in the core.

Squeeze the foil as hard as your possibly can. Eventually your strength will be matched, and the ball will get no smaller.

When a star reaches the end of its life, the fusion in the core shuts down. That moment is like you popping your balloon — the star suddenly finds itself without much outward pressure at all, and the inward pull of gravity takes over — the star collapses. The collapse is the beginning of a supernova explosion. 

For our interests here we are not interested in what gets blown out, but what happens in the innermost core. There, the titanic pressures of the collapse and explosion break apart the atoms, and breaks apart the nuclei of the atoms. You may recall from school that atoms themselves are made of smaller bits — the smallest bits are called electrons which orbit around a nucleus made up of bits called neutrons and protons. Like you standing on a wine glass, the inward force of gravity during the collapse crushes every atom, breaking every one apart into these shards called electrons, protons, and neutrons.

In the soup of protons and electrons and neutrons that results, the protons and electrons are forced together and turn into a neutron plus a small particle called a neutrino. This conversion process is called “neutronization” (really — sounds like something from a superhero movie, right?) — the conversion of most of the matter of the core into neutrons. 

A neutron star (diameter 20 km) scaled to the Chicago skyline. [Image: LIGO-Virgo/Nick Gertonson/Daniel Schwen/Northwestern]

This core that remains is called a neutron star when it settles down, and its gravity is extreme beyond belief.  It has about 1.5 times the amount of stuff in as the Sun, but squeezed down into something about 20 kilometers across — the size of a city.  At the surface, the gravity is 200 BILLION time stronger than the gravity you are experiencing right now on Earth. What are the consequences of such extreme gravity? Imagine you could take a walk on a neutron star (and you could certainly NOT walk, but go with me here) and you had the unimaginable misfortune of encountering a cliff only ONE MILLIMETER high. What would happen if you fell off? On a neutron star, falling off a one millimeter high cliff means when you reach the bottom you will be travelling about 227,000 kilometers per hour (141,000 miles per hour)!

The gravity of a neutron star is extreme, but a neutron star, like its parent star, maintains its shape as a round, spherical object — it is in hydrostatic equilibrium! Gravity is trying to press down, but something just as strong is pressing back. In this case, it is the neutrons that make up the star. Neutrons do not like to be near each other and push back when they are squeezed into small spaces — this is called “neutron degeneracy pressure” (for the quantum mechanics aficionados among you, this is a consequence of the “Pauli exclusion principle”). The reason gravity could not collapse the neutron star is because the neutron degeneracy pressure is enough to stop it.

But there is a funny truth about gravity. All four of the fundamental forces of Nature have a range of distances over which they act, and their strength varies over those distances. They also each affect only certain kinds of objects in the Cosmos. Gravity, however, is completely indiscriminate — it acts on and affects everything that has mass and energy, which as it turns out is everything in the Cosmos!

The consequence of that simple fact is if you make a big pile of anything, gravity always tries to pull it closer together, and will succeed in pulling it together until it is opposed by a stronger force (for example the hydrostatic equilibrium, and the neutron degeneracy pressure examples we noted above).

We only know the masses of a few neutron stars, most between the mass of the Sun, and two times the mass of the Sun. Can heavier ones exist in Nature, or do they all turn into black holes? Explore the stellar graveyard on your own with this interactive tool at CIERA. [Image: Frank Elavsky/Northwestern University]

Most of the neutron stars we have observed in the Cosmos up to now have masses between about 1.4 times the mass of our Sun, up to around 2 times the mass of our Sun. Why aren’t their bigger ones? We certainly see huge stars, up to 30 or 40 times the mass of the Sun — when they explode, they definitely have larger cores that should leave behind bigger remnants, bigger stellar skeletons. So can a neutron star bigger than the ones we’ve found in the Cosmos exist? You can imagine taking one of the known neutron stars, and slowly piling more and more mass onto it. Each jelly-bean or rock or bit of starstuff you drop on the neutron star increases its mass, which increases its gravity, which makes gravity pull inward more strongly. Eventually, gravity will get so strong that the neutrons cannot resist any more — gravity overwhelms the degeneracy pressure, and presses the neutrons closer together. 

Concentrating all the mass of neutrons together makes gravity even stronger, which pulls all the mass of the neutron star even closer in a never-ending cycle of just making gravity stronger. At this point, there is no known force in the Universe that is stronger than gravity. Nothing can oppose gravity’s inexorable inward pull, and everything that was a neutron star gets smaller, and smaller, and smaller, until the gravity is so strong that not even light can escape. We have a name for that.

A black hole.

So at last, we arrive at the answer to our question: we make black holes by squeezing matter together. Black holes are not stuff but they are made of stuff in the beginning. 

Where is all that stuff now? It is concentrated somewhere behind the event horizon, where we cannot see. Mathematically, the laws of gravity suggest it is concentrated into an infinitely dense point called a singularity. It is… … … something. Something that completely defies our understanding of the Laws of Nature, and is the subject of much consternation and study on the part of modern physics and astronomy researchers.

Now we are curious creatures, and it is completely natural to ask “what is inside the black hole?” or “what is inside the event horizon?” The answer quite pointedly is you can NEVER know unless you jump in yourself! The emphasis really is on the word UNLESS — nothing prevents you from jumping in and looking around; the only prohibition is on your ability to come back out to visit your friends who watched you jump in. The prohibition that the speed of light is the ultimate speed limit in the Cosmos, coupled with having to travel faster than the speed of light to get out of the event horizon, means you will never hear about anything that happens on the “inside” of a black hole second hand!

But we can use our mathematical understanding of gravity to predict what you would experience if you jumped in, and the predictions are weird and disconcerting. We’ll talk about some of that gravitational weirdness next time. 

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This post is the third in a series about black holes.

Black Holes 01: Imaging the Shadow of Darkness

Black Holes 02: What are black holes made of?

Black Holes 03: Making black holes from ordinary stuff (this post)

Black Holes 2: What are black holes made of?

by Shane L. Larson

In modern astrophysics, the study of black holes grows out of general relativity, the modern description of gravity written down by Einstein in 1915. As descriptions of Nature go, general relativity is among one of the most remarkable discoveries humans have ever made.

On the surface, general relativity seems extraordinarily complex and mathematical, and it can be. The governing equations that describe what general relativity explains and predicts about the Cosmos are what scientists call non-linear. Generally this means the equations cannot be solved with simple pen and paper calculations, using algebra skills you learned early in your mathematical training. This was something Einstein recognized early on. He had in fact abandoned the idea that there would ever be “simple” or “exact” solutions to his equations, and started working on “weak gravity” (“linearized” for the aficionados) cases where the equations of general relativity can be written in ways simple enough to work on.

Karl Schwarzschild [Image: Wikimedia Commons]

But, as if often the case in science, even the smartest of us sometimes don’t see the obvious. In 1915, barely a month after the first presentation of general relativity at the Prussian Academy, a young German soldier named Karl Schwarzschild wrote a letter to Einstein, showing that if you use general relativity to consider a situation which has symmetry, the equations become simple enough to solve directly. Schwarzschild considered the case of a source of gravity that was perfectly spherical, like a planet or star or other massive body. Today, we’ve named this solution after him, and the most extreme example of what Nature can do with it is called a Schwarzschild black hole.

Most of us have heard quite a few weird and exotic things about black holes, much of which defies our common experience and common sense. That exoticness comes from the sophisticated nature of the non-linear equations of general relativity, but also from the fact that the places where the Cosmos creates or harbors black holes are the most extreme environments imaginable, far outside anything you might encounter on Earth, either on a wilderness hike or in a physics laboratory. But the discomfitting exoticness of black holes belies a subtle truth: they are exceedingly simple objects.

Cars are complicated, which is why you see lots of magazines like the one on the left. Black holes are simple, which is why you don’t see magazines like the one on the right. [Image: S. Larson]

What do I mean by simple? Consider for a moment one of wonders of the modern age: the automobile. An average vehicle has maybe 20,000 parts that make it up. If you want to understand all the details about how a vehicle works, or make one yourself, you have to understand everything about all those 20,000 parts. What is each one made of, how is it shaped, where does it go in relation to other parts, does it move or is it held still, what kinds of environment will it encounter? These and many other questions are required to have a complete understanding of a “car,” so there are books and magazines and entire industries and trades dedicated to motor vehicles.

Unlike automobiles, black holes are simple. They are completely characterized by only three numbers: the mass, the spin, and the amount of electric charge they have. Black holes that have one or more of these properties are named for the scientists who first wrote down the mathematical descriptions that describe them in the context of General Relativity.

These three properties are all ones that seem familiar and quite ordinary, because they are used when we talk about most things in astrophysics. Mass, spin, and charge are all quantities that are more or less familiar. However, in the context of black holes what we mean by them is less clear.  Consider “mass.” What do we mean by the mass of a black hole? To understand this, we have to first be very clear what we mean by black hole and confront some of its exotic properties.

Our adopted definition for “black hole” is a very practical one — it’s an object whose gravity is so strong, not even light can escape. As scientific definitions go, I like this precisely because it is very practical — it captures an immutable way to identify what an object is based on a simple observation or experiment you can do, in this case you can test the gravity of an object to see if it is, in fact, a black hole or something else.

One of the things you may remember learning about gravity early on in your science classes is that gravity gets stronger as you get closer to an object, and gets weaker as you get farther away from an object. That means if you are far away from a black hole, the gravity you feel from it does not have to be very strong at all! More to the point, if you are far from the black hole and point a laser pointer directly away from the black hole, the laser light goes flying off minding its own business without consequence; the black hole is so far away its gravity has little or no measurable effect. But that it also means is as you get closer and closer to the black hole, the gravity must get stronger until it finally becomes so strong that the laser light cannot get away. That transition point, where gravity is finally strong enough to stop light, is called the “event horizon.”  It is NOT a physical surface — it is simply that place where gravity has gotten strong enough to overcome light.

We can represent gravitational influence with a figure that shows lines along which an object feels the gravitational force. The number of lines emanating from an object is related to the mass. The strength of gravity you feel is related to how many lines are around you (how many lines cross into the little red circles). Stick Spock, far away, feels weaker gravity than Stick Picard, who is somewhat closer. Stick Geordi, who is very close to the source of gravity, experiences much stronger gravity. [Image: S. Larson]

This transition point is important, especially in terms of astrophysics, because it defines which places in space we can detect signals from (for example, light emitted by atoms which can be seen with telescopes), and which parts of space we cannot. Quite literally, the event horizon is an invisible boundary in space that defines “inside” and “outside” the black hole. It’s kind of like putting a line of tape across the bedroom you shared with your sibling when you were growing up — there’s nothing to indicate where the boundary is when you walk across it, but there are definite sides.  On the outside, atoms are free to create light which can move away from the black hole and be seen in telescopes. On the inside, the gravity has passed the tipping point, and light can no longer get out. Atoms can still go about their atomic business and make light, but that light cannot go sailing across the Universe — like everything else on the “inside,” the light is subject to the inexorable pull of the black hole, dragging it deeper into the interior. For this reason, we treat the event horizon as if it is the surface of a black hole, and for all intents and purposes it is — anything that crosses the event horizon disappears and vanishes into the black hole forever. Every black hole has an event horizon — it is what defines them.

The question that set us along this line of reasoning is “What do you mean by mass?” If the black hole has an inside and an outside, then that seems like an impossible question to answer because the mass lives inside the event horizon — how do you know it has mass? That is an eminently reasonable question to ask! It’s an important one to ask because of the way we talk about black holes. In most contexts, mass is a code word that means “the amount of stuff that makes up an object.”  For astronomers, a practical way to think about what we mean by mass is it defines “how much gravity a black hole creates.”

To imagine what we mean by that, try to think about how you measure the mass of the Sun. Has anyone ever taken the Sun and plopped it down on a scale at the doctor’s office? No. We’ve measured the mass of the Sun by observing how its gravity has influenced other objects around it. If I look at the orbit of a spaceship or a small asteroid at a known distance from the Sun, the time it takes to complete the orbit tells me how massive the Sun is. We didn’t “measure the mass” of the Sun (how much “stuff it has” in it), we inferred the mass by measuring the gravity of the Sun. When we state the mass of a black hole, we are doing exactly the same thing — we’re using a number (that we call “mass”) to express how much gravitational influence the black hole would have on things that might fly around it in space. 

One way to “measure mass” is to look at how long it takes to complete an orbit of a given size. You can do this around the Sun or around a black hole, and they will give the same answer if they “have the same mass.” Compared to the Sun, the gravity of the black hole is only extremely strong when you are close to the hole, seen here in this figure by comparing how close the lines are near each of the objects. [Image: S. Larson]

If you’re scratching you head, you’re doing okay — this is probably one of the hardest things to wrap your brain around. If the black hole has gravity, doesn’t that mean it “has mass?”  Not necessarily.  Consider trying to get as close to the black hole as you can, without crossing the event horizon. As you get closer and closer to the black hole, all you encounter is empty space. In fact, if you fly right through the event horizon to the inside of the black hole, all you encounter is MORE EMPTY SPACE. The black hole has gravity but it is comprised entirely of empty space.

Wait — what? That’s right, a black hole is completely empty space. It isn’t tangible, there isn’t stuff you can scoop up and collect in a little plastic bag. It is empty space. So what is it? It is pure gravity. Now it seems weird to think about it that way, because you are used to thinking that things in outer space are made of stuff — stars, galaxies, nebulae, comets, asteroids, and planets are all made of stuff. But black holes are not. You’ve encountered that idea before — if we go dig a big hole in your garden then lean on our shovels to admire our work, we point at a big empty space, full of nothing, and we call it a hole. This is kind of the same idea.

Now you rightfully might be inclined to ask what is making the gravity? After all, in the rest of the Universe, to make gravity you have to have stuff. Isn’t that the point in why we have orbits around the Sun? The Sun has stuff it is made of, that stuff makes gravity, and gravity is what makes stuff move in orbits. But gravity isn’t a substance that massive objects make and throw out into the Universe — gravity is an effect they have on the Universe around them. Einstein’s great realization is that what you and I think about as a “force” of gravity is really our response to the shape of the Universe around us (more properly, the shape of “spacetime”), which is forcing us to move in certain ways.  A black hole’s “gravity” is just a statement of how the black hole has bent spacetime outside of it.  Let’s imagine a simple example.

Paths ants take when walking along a flat surface. [Image: S. Larson]

Imagine I show you the paths some ants are walking along, but I’ve gotten some of my Hollywood special effects friends to remove the objects they are walking on, and all you can see is their path.  The only rule is an ant always walks on a straight line, directly where its head is pointing, never turning to its left and never turning towards its right. What do you think the ant paths in the figure above are showing?

You might have said a “table” or a “piece of paper” or the “ground” or a “wall.” It could be any of these things! You can’t tell the difference between them from the paths, only that whatever it is is FLAT.  Now consider the ant paths shown below.

If the surface has an interesting shape, the paths ants take walking across it, even though they are walking “in straight lines,” look interesting. One path will tell you the surface is interesting (left), but many paths will reveal what the surface really is (right). In this case, a sphere. [Image: S. Larson]

What is that ant walking on? The path the ant took was straight as far as the ant was concerned, never turning left and never turning right. But eventually the path came back to itself not because of something the ant did, but because of the shape of the surface it was walking on! So what was the surface? From a single path, you can’t tell, but if you have multiple ant paths you begin to see what the underlying shape might be, and there are many possibilities that include the first circular ant path we noted above, but in the end we would conclude it was a ball.

Now consider the more complicated collection of paths below. The more paths you have, the more likely it is you can understand the underlying shape of the space. The ants aren’t feeling any force that makes them change directions they are moving. As far as they are concerned they are walking freely in straight lines, and the shape of the surface they walk on determines what that path looks like. The end result shows you the shape of the space, and sometimes it is flat, sometimes it is spherical, and sometimes it looks like a bottle!

If the surface has some exotic shape, the ant paths can have a wide variety of different behaviours, but with enough paths you can understand the surface they are walking on. [Image: S. Larson]

So what should you take away from this parable of the ants? You should know that how something moves can be understood as moving along the shape of something. Gravity bends the Universe, and how we move can be understood as us moving along the bends, along the warps and weaves, of that bent Universe. When a planet or a star is sitting off by itself in the Universe, it bends spacetime around it, and black holes do the same thing. When we move along an orbit around a black hole, when we “feel its gravity pulling us in an orbit” we are really just moving along the bent Universe around the black hole. 

So what’s the difference between how a star bends spacetime and how a black hole bends spacetime? Only how strongly it does so. The Earth bends spacetime pretty strongly — if you try and jump straight up  you can’t get away. A rocket has to travel just over 11 kilometers a second (25,000 miles per hour) to get away. A black hole bends spacetime more strongly, so strongly that you’d have to travel faster than the speed of light, or 300,000 kilometers a second (671 MILLION miles per hour) to get away!  Exotic, to say the least!

But despite their exotic nature, black holes had to come from somewhere. Next time we’ll talk about how to make black holes in the Cosmos. 

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This post is the second in a series about black holes. 

Black Holes 01: Imaging the Shadow of Darkness

Black Holes 02: What are black holes made of? (this post)

A Cosmic Collection

by Shane L. Larson

The Cosmos wheels above our heads, far out of reach but well within our powers of perception. Always we wonder, what’s happening now and what does it mean? [Image: S. Larson]

The Cosmos is vast beyond ordinary comprehension, and it is always up to something. Astronomy is our most valiant attempt to observe everywhere all at once, to discover all that is discoverable, to know all that is knowable. We are exceptionally good at it, by any standard you can imagine. The store of cosmic knowledge we have amassed just since recorded human history began (only a few millennia) is extraordinary, and has helped push mathematics, physics, and technology forward in dramatic and unexpected ways. In just the last century and a half, technology has expanded our capabilities by leaps and bounds, allowing us to collect exquisite data that is perplexing and mysterious and revealing. Today we live in an era where we can collect so much data, and collect such complex data, that it cannot be absorbed, analyzed, nor understood with only brief consideration. It requires long and sustained study, intense scrutiny, and expansive modeling.

[L to R] Hubble Space Telescope, the ATLAS detector at the Large Hadron Collider, and LIGO-Livingston. Exquisite technology expands our ability to observe the Universe around us.

Modern science, particularly at the frontiers of knowledge, requires a lot of human brains to make great discoveries. It begins with the great machines themselves. Building something like the Hubble Space Telescope, or the Large Hadron Collider, or LIGO and Virgo requires vast teams of engineers, physicists, materials scientists, construction engineers, titanium welders, chemists, geologists, and a thousand other professions just to build the experiments. Once we start collecting data, there are thousands of others in physics, computer science, signal processing, image analysis, information technology, visualization, and a thousand other professions needed to understand the data!

Big discoveries emerge almost immediately, because the Universe is always up to something, and always up to something that is dramatic and stunning to behold. If you build an exquisite experiment, you’re going to discover something. Such was the case of Hubble’s discovery of the existence of other galaxies, when we constructed the 100-inch Hooker Telescope on Mount Wilson. Such was the case of Rosalind Franklin’s discovery of double-helix structure of DNA with the development of x-ray crystallography. Such was the case of the discovery of the Higgs Boson with the construction of the Large Hadron Collider. Such was the case with LIGO and Virgo, which over the past three years have witnessed six different gravitational wave events.

My personal accounting of every known gravitational wave event, accurate and complete up through GW170817. When we announced GW170608, my page was too narrow to include it!

Today, the LIGO-Virgo Scientific Collaboration announced our first catalog of gravitational wave events — GWTC-1 (Gravitational Wave Transient Catalog). It is the current complete list of every event we’ve discovered in our data. Some of them you know about, because we have talked about them before (even here on this blog: GW150914, GW151226, GW170104, GW170814, GW170817). But since then, we’ve been sifting through the data, looking at every feature, comparing it to our astrophysical predictions, cross-checking it against monitors that tell us the health of the instruments, determining if it appears in all the detectors, and using our most robust (but slow-running) super-computer analysis codes. 

The result is the catalog before you (if you’re curious, you can see the catalog at the Gravitational-wave Open Science Center), that has improved values for the properties of all the previously announced sources, and four new binary black hole sources that were in the data: GW170729, GW170809, GW170818, and GW170823. Additionally a source previously known as LVT151012 (“LIGO-Virgo Trigger“) has been renamed GW151012.

A screen cap of GWTC-1, the first “Gravitational Wave Transient Catalog of Compact Binary Mergers” as it appeared today. The number of events, the amount of data about what the Cosmos is doing, is growing. [Image: LIGO-Virgo Collaboration]

Astronomers are collectors. Every event has an identity, and a long list of everything that we know about it, but there are always going to be a few that are well known and remembered above all the others. GW150914 is always going to be “The First.” GW151226 (“Boxing Day“) was the second and will always represent the moment we all realized this endeavour really was going to be astronomy, not just a single one-time experiment. GW170817 is always going to be remembered as the first multi-messenger gravitational wave detection of a binary neutron star.

But today when you look at the long list of events it strikes me, for the first time, that this is a huge and ever-growing collection. We’ve always known that would be the case, but there is something viscerally pleasing about watching it happen right before your eyes. It is clear that the list is now long enough that it would be challenging to memorize!

We don’t have images of the gravitational wave events, but our artists can imagine what the members of our collection might have looked like at the moment we observed them. [Images: Aurore Simonnet/LIGO-Virgo Collaboration/Sonoma State University]

From the perspective of astronomy, this is a good thing. Having a collection of events is how we learn things about the Universe that can’t be learned from just a few observations. Let’s examine an analogy to explain the necessity of collections. Suppose you were an extraterrestrial visitor who landed on Earth to learn about “humans” and visited someone’s book-club, perhaps five people. What could be learned by just observing five people? A few obvious things might pop out immediately. Humans have five projections from their bodies (two arms, two legs, a head). They have two eyes and two ears. But depending on the five people you may not learn that there is a wide range of hair or eye colors (any redheads in your reading group? anyone with grey hair? what about blue or green eyes?). You may or may not know that there are multiple sexes, nor that there are smaller and larger humans.  Your knowledge would be completely defined by the size of your collected observations.

This is absolutely the case in astronomy — sometimes we have many observations, sometimes we have only a few, but we always want more. Having many observations is paramount to understanding the Cosmos because observations are the only things we have. We are confined to observing the Universe from this small world on which we live, and what we know is built completely on our few, meager observations.

What stands out the most in the new LIGO catalog? We are still letting the implications settle in, but the most important thing the new events do is it makes our estimate of the popuatlion of black holes in the Universe more accurate, and we’ve started to examine those implications is a new study that is being released in tandem with this announcement. But let me highlight the things that personally catch my attention the most.

This shows all the known masses of black holes and neutron stars, detected both by traditional telescopes and using gravitational waves. I’ve highlighted the new black holes in the catalog in green. You can explore this plot with an interactive we’ve created at CIERA. [Image: LIGO-Virgo/Frank Elavsky/Northwestern]

First, remember that every gravitational-wave detection by LIGO-Virgo is not just one black hole, but three — the two black holes that came together, and the black hole that resulted from their merger. That is very important because it means we have three new measurements of the possible masses that black holes can have. If you look at our black hole mass plot you see that black holes come in all masses between five solar masses and 80 solar masses. In fact the new event, GW170729, produced the heaviest stellar origin black hole known to humans, at 80.3 times the mass of the Sun!

Second, it is interesting to look at the black holes that merged and consider how they are different from one another. From the existent data, it looks like the black holes that merge are always close to the same mass. So far, we’ve never seen a smaller black hole fall into another black hole that is five or ten times larger. Does that mean it never happens in Nature? Or does it mean it happens rarely? Or does it mean we’re not good at seeing or recognizing such events yet? The answer is an important one because the sizes of the black holes before they merge tells us something about how they form and grow together. That question is of intense interest to astronomers since black hole formation is tied to stellar evolution, and stellar evolution is tied to how all the stuff around us is made.

Lastly, the trend continues to show that LIGO and Virgo are sensitive to heavier black holes than those that have been previously known from traditional telescopes. The dramatic demonstration that there are stellar-origin black holes near 100-solar masses is stimulating dramatic conversations among astronomers (particularly theoretical astronomers like my group, who study stellar evolution) about how the Cosmos creates these large black holes. 

Left to Right: LIGO-Hanford (Hanford, Washington), LIGO-Livingston (Livingston, Louisiana), and Virgo (Pisa, Italy). All three detectors are currently working toward the start of our new observing run (“O3”) in the Spring of 2019. When new data begins to flow, the catalog is going to start growing once again.

Perhaps the most exciting thing to me, is this is just the beginning. LIGO and Virgo are currently in a maintenance phase, but our third observing run (“O3”) will begin in the spring of 2019. The instruments will be performing at higher precision than ever before, and there are going to be more detections that will make this catalog grow even larger. Our questions are swirling, the anticipation is palpable. But even more importantly, there is a dedicated group of scientists, particularly those who work in signal analysis, computer science, and machine learning, who are developing new and improved techniques for finding signals in data. There are great practical applications to such endeavours (like how do you separate the 25 zillion text messages sent by teenagers every five minutes), but it will once again help grow our gravitational wave catalog, expanding our understanding of the stellar graveyard of the Universe.

Once new data is being collected, the data from our previous observing runs will sit there in the open data archives, waiting for someone to come back and look at it again. Historically, there have always been discoveries made in archived astronomical data long after it was collected. Data is simply too complex to understand everything in it, and we are simply too naive about everything that is going on in the Universe to recognize everything in our data the first time we work with it. There is certainly more in the LIGO-Virgo data than even this catalog. But progress is slow, and only the future will show us what is yet to be discovered, in an every growing tree of knowledge, dividing and growing from our previous discoveries.

Examples of Lichtenberg figures, created by electrical discharges and discovered by the father of experimental physics, Georg Christoph LIchtenberg. Knowledge, like these figures, branch and grow continuously from each other. [Images: Wikimedia Commons]

One of the great physicists of the 16th Century was Georg Christoph Lichtenberg, widely recognized as the first great designer and builder of experiments in physics, our distant ancestor in this game. Today he is most well known for an artform known as “Lichtenberg figures”, the branching shapes burned in materials by surges in electricity — a most suitable metaphor for our growing branches of knowledge. Lichtenberg fully understood the staggering and surging process of scientific discovery, writing “Nothing puts a greater obstacle in the way of the progress of knowledge than thinking that one knows what one does not yet know.” Today’s announcement is just the beginning of what we do not know.

So today, please join us in basking in the glow of new discovery, reveling in the joy that this is just the beginning, and there is no end. Congratulations to my colleagues and friends in LIGO and Virgo; we’ll do this again sometime soon!

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Several of my colleagues in LIGO and Virgo have also written about the new catalog — please check out their posts as well!

• Christopher Berry — The O2 Catalogue – It goes up to 11
• Mark Hannam — Digging in the Stellar Graveyard

The Cosmic Classroom on Boxing Day

by Shane L. Larson

The seas of the Cosmos are vast and deep. From our vantage point here on the shores of Earth, we have seen much that is beautiful, awe-inspiring, frightening, humbling, confusing, and enigmatic. The simple truth of astronomy is that it is a spectator sport. The only thing we can do, is watch the skies and wait for the next Big Thing to happen. We collect events, like bottle-caps or flowers, and add them to our collection. Each new addition is a mystery, a new piece of a puzzle that takes shape ever-so-slowly over time.

On 14 September 2015, the LIGO-Virgo collaboration announced that they had detected the first gravitational waves ever, and that those waves had been created by a pair of merging black holes far across the Cosmos.

Today, we have some more news: LIGO has detected the second gravitational wave event ever, and those waves were also created by a pair of merging black holes far across the Cosmos. But as is often the case with astronomy, we know what we’ve observed, but we still don’t know what it means.

The name of the event is GW151226 (the date of the event), but within the collaboration, we call it “The Boxing Day Event.” On 26 December 2015 (Boxing Day in Europe), the two LIGO detectors responded to the faint ripple of gravitational energy washing across the Earth, the signature of two black holes merging to form a new larger black hole.

LIGO detected the black holes merging at 3:53 UTC in the morning on Boxing Day (it was late in the evening on Christmas Day in the United States, 9:53pm Central Standard Time). The event happened 440 Megaparsecs away — almost 1.4 billion lightyears! As with GW150914 before it, this titanic merger of black holes happened long, long ago, in a galaxy far, far away. It happened before multi-cellular life had ever arisen on Earth, and for a billion years that information has been sailing through the void, until it washed across our shores.

Learning to do astronomy: We can’t do experiments in astronomy, not the way we all learned to do them in middle school. Experiment. Observe. Fail. Learn. Repeat.

The timeline of LIGO’s first Observing run (called O1). The first detection (GW150914) and the second detection (GW151226) are marked. There was also a candidate that looked like a gravitational wave, but was not strong enough for astronomers to confidently say a detection was made. [Image: LIGO Collaboration]

In astronomy, all we can do is observe, and hope that when we see something interesting happen, it happens again. Or something similar happens again, so we can start trying to make connections. Since the first LIGO detection, we have been patiently waiting for more detections. It could have been anything: merging neutron stars, a gamma-ray burst with an associated gravitational wave signal, a supernova explosion in the Milky Way, or perhaps other pair of black holes similar to GW150914.  As it turns out, it was the merger of black holes, but somewhat different than the one we observed before. Excellent! A chance to learn something new about the Cosmos!

When you look at the pile of gravitational wave events we’ve seen before (it’s a very small pile — there is only one event there, GW150914), we do the most obvious thing you can imagine: we start to compare them.

Strictly in terms numbers, you see that the Boxing Day black holes are less massive than the GW150914 black holes, by a substantial amount. This tells astronomers something very important: black holes can and do come in a variety of masses. That certainly did not have to be the case; there are many instances in the Cosmos where almost every example of an object is similar to every other object. People are all roughly the same height; grains of sand are almost all roughly the same size; yellow-green stars like the Sun (“Type G2” in astronomer speak) are all roughly the same mass. Though we did not expect it to be true, it could have been the case that all black holes were about the same mass; LIGO is happy to report that black holes come in many different masses.

But this, in and of itself, inspires new questions and new mysteries. The question for astronomers now is where do black holes of different sizes come from? The Boxing Day black holes are “normal size” — we think we understand how black holes in this mass range are made in supernovae explosions. The GW150914 black holes are a much grander mystery — they are larger (by a factor of 2 or 3) than any black holes that we expect to form from stars today. We have some interesting ideas about where they may come from, but those ideas can only be tested with more gravitational wave observations.

Comparison of the size of black holes observed by LIGO, as well as other candidates detected with conventional telescopes. (L) The physical size of the black holes overlaid on a map of the eastern United States. (R) The same image showing the masses on the vertical axis, and the black holes that combined to make larger black holes. [Image: LIGO Collaboration]

Gravitational wave astronomy: Every observation is different, because every source is different. Every set of waves is a unique fingerprint that encodes the physical properties of the objects that made the waves: their masses, how fast they are spinning, what kind of object they are,  how physically big they are, the distance to them, and so on. It’s like looking at the pictures in your high school yearbook — every picture is the same size, and is what we all call a “picture,” but each one uniquely identifies you or your friends. It encodes the color of your hair and eyes, whether you were smiling and wearing braces, the sweater you wore on picture day, and so on.

A typical visualization of a black hole binary. They emit no light, so there are no pictures! [Image: SXS Collaboration]

When we look at our data, we don’t usually show pictures. LIGO is not a telescope, so it does not generate images like we are used to seeing from the Hubble Space Telescope. Most “pictures” you see are simulations or realizations of the data. Instead, we show our data as graphs and plots that represent our data in ways that tell astronomers what LIGO is measuring and how that relates to quantities in physics we understand, like orbit size or energy.

A stereo equalizer display.

One common picture we use is something called a “spectragram” — you may have encountered something like a spectragram on a stereo. The equalizers on your stereo tell you how loud the music in terms of whether it is more treble sounding or bass sounding.  In LIGO, we look at our data by looking a spectragram and how it changes over time.  The fact that the Boxing Day black holes and GW150914 are different is immediately obvious when comparing their spectragrams — the fine details of the shape and duration is different in the two cases, but they have the same basic swoopy shape to them. Think about your high school yearbook: the pictures are all kind of the same, but different in the details.

The comparison of spectragrams from GW150914 (top) and the Boxing Day event (bottom). The blue swoop is the gravitational wave signal as it evolves in time (early in the event on the left, and the final merger in the tall swoop on the right). [Images: LIGO Collaboration]

The difference in the gravitational waves LIGO detected is even more obvious if you look at the waveforms themselves. Imagine you are standing on the beach watching waves roll in and crash on the sand. In between waves, the water is calm and relatively low, but at the moment the wave is washing ashore, the height of the water increases subtantially; if you happen to be standing in the wave as it washes by, you might not be able to stand up because the energy carried by the wave is enough to knock you over. In a very similar way, the waveforms illustrate the strength of the gravitational waves as they wash past the Earth. The size of the “up and down” in the waveforms we plot tells us how strong the waves are.  If you compare the Boxing Day black hole waveforms with the GW150914 waveforms, you see they both have a lot of up and down (a measure of strength — they were strong enough for LIGO to detect!), but their overall shape and duration is different.

Comparison of the “waveforms” for GW150914 (top) and the Boxing Day black holes (bottom). The signals are considerably different, and longer in the case of the Boxing Day event. [Images: LIGO Collaboration]

Gravitational wave astronomers at LIGO are most excited about the long chain of up-and-downs in the Boxing Day waveforms. This is a part of the black hole evolution we call the insprial — the long, slow time where the orbit is shrinking, the black holes drawing inexorably closer, creeping toward their ultimate fate: the coalesence into a new, single, spinning black hole. The longer the inspiral is visible to LIGO, the longer we can study the black holes with gravitational waves. Once they merge to form a new black hole, they very quickly become quiet, much like a bell fading into silence after being struck by a hammer. The inspiral, and the merger, are the only chance we have to take the measure of these tremendous astrophysical entities.

What now? LIGO has now made two detections of gravitational waves, both during our first observing run (what we call “O1”). In mid-January 2016, we turned LIGO off and have spent the ensuing months combing over the machine and addressing all the problems and difficulties we encountered in O1. In late summer 2016, we’ll start up for “O2.” We’ll turn up the lasers a little bit, and LIGO will be able to see a bit farther into the Cosmos. If our first stint as gravitational wave astronomers is any indication, we will likely see something new; we don’t know, all we can do is observe.  After a few months, we’ll shut down again, tune things up, think hard about how we are working with the machine, and in 2017 expect to come back online with everything at full design specifications.  We are like toddlers, learning to walk. We’ve taken our first few steps, and have discovered there is a tremendous world just waiting to be explored. We’re learning to keep our balance and do things right, but in the not too distant future will be confident and excited in our new found ability to observe and discover a Cosmos that up to now, has been completely hidden from us.  Carpe infinitum!

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Many of my colleagues in the LIGO Virgo Collaboration have also written excellent blog posts about the Boxing Day event, and the work we do to make gravitational wave astronomy a reality. You should visit their blogs!

• Christopher Berry [Birmingham] – The Boxing Day Event
• Mark Hannam [Cardiff] – Black holes rule!
• Matthew Pitkin [Glasgow] – Yes, we’ve found another one
• Amber Stuver [LIGO] – Merry Christmas, LIGO: Another Gravitational Wave!
• Daniel Williams [Glasgow] – The wave that stole Christmas

The Harmonies of Spacetime — GW150914

by Shane L. Larson

I have a good friend, Tyson, whom I don’t get to see nearly often enough. We are both privileged to be among the first generation of scientists who will know the Universe by observing the faint whisper of spacetime, bending under the influence of massive astrophysical systems. We are “gravitational wave astronomers.”

Picking crab with Tyson (far right) and family. [Image: Sabrina Savage]

A while back we were sitting on his back porch late into the evening, picking crab and talking about everything. It was the kind of common, easy conversation among friends that ranges over movies, politics, family, childhood memories, inside jokes, and so on. But at one point, the conversation drifted back to science and to the near future. Tyson said something that really just kind of made us all stop in shocked silence: “If we’re really going to detect gravitational waves in the next 3 or 4 years, they are already closer than Alpha Centauri and heading right for us.”

Whoa.

Little did we know then how prescient that observation was. We are both part of a project called LIGO — the Laser Interferometer Gravitational-wave Observatory. And this morning our collaboration made the big announcement.

Frame from a visualization of the binary black hole merger seen by LIGO [Visualization by “Simulating Extreme Spacetime” (SXS) Collaboration]

On 14 September 2015, the two LIGO observatories detected a very loud gravitational wave event. Our analysis since that day has told us that it was the merger of two black holes — one 29 times the mass of the Sun, the other 36 times the mass of the Sun. The two black holes merged, forming a new, bigger black hole 62 times the mass of the Sun. We named the event after the date: GW150914.

All of this happened about 400 Megaparsecs from Earth (1.3 billion lightyears). If you are adding up the numbers, you see that there are 3 solar masses missing. That is the equivalent mass that was radiating away from the system in the energy of the gravitational waves.

Make no doubt about it — this is one of the most momentous discoveries in the history of astronomy. It will be up to historians of science to place this within context, but I would rank it right up there with the discovery of the nature of the spiral nebulae and the discovery of the Cosmic Microwave Background.

There are many important and stunning parts of this story. Let’s me tell you just a small slice of how we got to today.

LIGO: LIGO is two gravitational wave observatories that work together as a single experiment. The are located 3002 kilometers apart, with one in Hanford, Washington and the other in Livingston, Louisiana. They are enormous, 4 kilometers to a side — so large, they can be seen in satellite photos.

(L) Aerial view of LIGO-Hanford Observatory [top] and in Google Maps [Bottom]. (R) Aerial view of LIGO-Livingston Observatory [top] and in Google Maps [Bottom].

The observatories are “laser interferometers” — laser light is injected into the the detector, and split so it flies up and down each of the two arms. When the light returns back to the splitter, it is recombined. When you combine laser light in this way, it can be combined such that the beams cancel out (making what we call a “dark fringe”) or they combine to make a bright spot (making what we call a “bright fringe”); in between combinations have a full range between bright and dark. We sit on a “dark fringe.”

Schematic of the LIGO interferometers, showing the basic layout of the lasers and optics locations. The lasers travel up and down the two 4 kilometer long arms, and are recombined and detected at the photodetector. [Image: S. Larson & LIGO Collaboration]

When a gravitational wave hits LIGO, it stretches and compresses the arms. The result is that it changes how long it takes the lasers to travel from the splitter to the end mirror and back. If that happens, when the lasers are recombined the brightness of the fringe changes.

What Happened? Both the LIGO detectors run more or less continuously, and we get our primary science data when they are on at the same time. In the early morning hours of 14 September 2015, at 4:50:45am Central Daylight Time, a signal was detected in the Livingston detector. 7 milliseconds later, a signal was also detected in the Hanford detector. These detections are sensed automatically by sophisticated software that looks for things that are “out of the ordinary.” Notable events are logged, and then humans can take a look at them. In this case, we knew almost immediately it was significant because it was in BOTH detectors, and it was a strong signal (we use words like “loud” and “bright” to mean strong, but we don’t really “hear” or “see” the signals in the usual sense; these are descriptive adjectives that are helpful because of the analogy they make with our normal senses).

Spectrograms of the event at Hanford and Livingston. The darker areas are what a “typical” spectrogram might look like; the bright swoops are the (very noticeable) signal! [Image: LIGO Collaboration]

One of the easiest ways to see the signal is in a diagram called a “spectrogram” which shows how the signal in the detector changes in time. Once we had the first spectrograms, the emails began to fly.

Finding Out: We all get LOTS of email, so it took a while before everyone in the collaboration actually realized what was going on. I didn’t hear until the night of September 15. AT 9:35pm CST I got an email from Vicky Kalogera, the leader of our group, that said “have you caught any of what’s going on within LIGO?” We had a round of email with unbearably long delays between them, but by 11:35pm, I had our initial understanding/guesses in my hands. That was enough to do what we all do in science — we make some calculations and extrapolations to understand what we have seen, and to plan what we should do next. We want to figure out what the new result might mean! Here’s the page out of my Moleskine, where I started to compute what a detector in space, like LISA, might be able to see from a source like this.

My journal page from the hour after I first found out about the event. [Image: S. Larson]

The Importance: There are all kinds of reasons why this discovery is important. If you take your favorite gravitational physicist out for pizza, they’ll talk your ear off for hours about exactly why this is important. But let me tell you the two I think the most about.

First, this is the first direct detection of gravitational waves. It is the first time we have built an experiment (LIGO) and that experiment has responded because a gravitational wave passed through it. This is the beginning of gravitational wave astronomy — the study of the Cosmos using gravity, not light.

Second, this is the first time that we have directly detected black holes, not observed their effects on other objects in the Universe (stars or gas).

The Astrophysics: The two black holes, caught in a mutual gravitational embrace, had spent perhaps a million years slowing sliding ever closer together, a long and lonely inspiral that ended with their merger into a single, bigger black hole. This is the first time we know conclusively of the existence of black holes that are tens of solar masses in size. Such black holes have been predicted in theoretical calculations, but never seen in the Cosmos before.

A more technical simulation of the binary black hole merger; gravitational physicsists and astronomers will be comparing the data to their simulations to examine how well we understand “real” black holes. [Image: SXS Collaboration]

Our next big question is “how often does this happen?” If it happens a lot, that is a potential clue pointing to where such black holes come from. If it is a rare event, that also tells us something. So now, we wait — this is just the beginning of LIGO observations, and after a few years of listening for more, we’ll know how common these are.

The People: Science is a way of thinking about the Universe, and so often when we talk about science we talk about Nature — all the wonder, all the mystery, the rules of the Cosmos. But science is a uniquely human endeavour and every momentous discovery is the culmination of countless hours of sweat, uncountable failures, and equally uncountable tiny moments of success that culminate at a profound moment of knowing something new. It would not be possible without the dedication of enormous numbers of people. The world gravitational wave community has been working toward this day for decades. More than 1000 authors appear on the discovery paper, and there are thousands of others who have worked and are working on the project, who are not in that list of authors. It has been a heroic effort on the part of physicists, astronomers, optical engineers, data and computer scientists, technical and support staff, professors and students.

Just some of the thousands of people who have made LIGO a reality and the detection of GW150914 possible. [Images from the LIGO Collaboration]

Teasing out the secrets of Nature is hard. Since before recorded history began, our distant ancestors  have plumbed the mysteries of the Cosmos using tools that Nature gave us — our five senses. Astronomer Edwin Hubble once opined “Equipped with his five senses, man [sic] explores the universe around him and calls the adventure Science.” (Harper’s Magazine 158: 737 [May, 1929]).

Today, we add a new sense to our quest to understand the Cosmos. TODAY the Era of Gravitational Wave Astronomy opens. Within the next few years, we will no longer live in a world where our view of the Cosmos is limited to what light alone can tell us. TODAY, we see the Cosmos anew, with senses attuned to the fabric of space and time itself!

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I’ve written about gravitational waves here at WriteScience before. In many of those I’ve explored what the physical description and meaning of gravitational waves are, and what the endeavour to detect them is all about. If you’d like to take a stroll down memory lane, here are links to those old posts:

• An early post about what it takes to build a machine like LIGO. “Knowing something about everything”
• When the BICEP2 results were first announced, I wrote a three part series about what they were looking for, what gravitational waves are all about, and how scientists were going to move forward after their announcement.
  • “Behind the Curtains of the Cosmos 1: Inflation and the Microwave Background”
  • “Behind the Curtains of the Cosmos 2: Gravitational Waves”
  • “Behind the Curtains of the Cosmos 3: Keys to the Cosmos”
• I wrote a long, 13 part series for the GR Centennial year. As part of that series, I wrote two posts about gravitational waves. At the bottom of each of these posts are links to little 3 minute YouTube videos I did to accompany them.
  • “Gravity 11: Ripples in Spacetime”
  • “Gravity 12: Listening for the Whispers of Gravity”
• I work on another gravitational wave experiment called LISA, and we just launched a spacecraft to test our ideas called LISA Pathfinder, so I wrote a bit about that too. “This is just the beginning”

Many of my colleagues in LIGO are also blogging about this momentous discovery. I will add their links here as they appear, so you can read their accounts as well:

• Christopher Berry (Birmingham)
• Rebecca Douglas (Glasgow)
• Sean Leavey (Glasgow)
• Matt Pitkin (Glasgow)
• Brynley Pearlstone (Glasgow)
• Amber Stuver (LIGO)
• Daniel Williams (Glasgow)
• Roy Williams (Caltech LIGO)
• Andrew Williamson (Cardiff)

 

Gravity 8: Black Holes in the Cosmos

by Shane L. Larson

When I give talks about black holes, I usually lead with a question for the crowd: “You’ve all heard about black holes. What do you know about them?”  The responses are varied, but can be succinctly summarized as this: black holes mess things up!

This little chat captures the essential truth about black holes: if you fall inside, you are without question doomed.  That notion is a bit horrifying, and one of the reasons why these enigmatic objects are so fascinating to us — there exist objects in the Cosmos that have the ability to utterly destroy anything. No amount of human ingenuity or heroics by Bruce Willis can ever spare your fate if you fall down the throat of a black hole.

People’s intuitions are all (more or less) based on solid science, and can help us understand how astronomers find and study black holes. One of the classic thought experiments is often posited to me as a question: what would happen to Earth if you replaced the Sun with a black hole (of equal mass)?  The answer is simple: absolutely nothing!

Oh sure, 8 minutes after the transformation it would get dark on Earth because there would be no more sunlight, and eventually Earth would turn into a snowball and all life as we know it would die. But in terms of the orbit nothing would change! The Earth would continue to happily speed along its appointed path, obeying Kepler’s laws of orbital motion, with nary a concern that it is orbiting a black hole instead of a friendly star. Far from a black hole, the gravity is not extreme at all.

That doesn’t sound very interesting, but as is often the case in the Cosmos, the most innocuous of ideas are often hiding a deeper, more profound notion, if you open your mind to it. This is the case here.

A binary star is a pair of stars that orbit one another, just like a planet orbits our Sun. They are often roughly the same mass, so they both move around a common center that astronomers call the “center of mass.” The stars more or less continue with their lives as if they lived alone, but if they are close enough together their interactions can have profound consequences for their evolution.

We know that a large fraction of stars in the galaxy are actually binary stars — two stars mutually orbiting one another the way planets orbit the Sun. So what would happen if we replaced one star in a binary with a black hole? This is eminently reasonable because we think black holes are one of the possible skeletons of dead stars.

In terms of the binary orbit, if the star and it’s black hole companion are far apart, nothing would change! The star that remains a star would continue to happily speed along its appointed path, obeying Kepler’s laws of orbital motion, with nary a concern that it is orbiting a black hole instead of the friendly star that was once its gravitational partner in the Cosmos.

Even though the orbit of the companion star is not dramatically affected by the presence of a black hole, there is an important consequence for astronomers: if they are watching this star system they will see the single star apparently orbiting … nothing! The star will continue to trace out its orbital path, appearing in our telescopes to wobble back and forth for no discernible reason.  This is something we have looked for, and it is something we have found!

Cygnus, the Swan, is a constellation in the northern sky. Three bright stars (Deneb in Cygnus, Vega in Lyra, and Altair in Aquila) make up “The Summer Triangle.” The black hole system, Cygnus X-1, lies near the center of the Triangle, in the neck of Cygnus.

In the northern sky, the Milky Way can be seen high in the sky on clear summer evenings. Prominent along the faint, diaphanous band is the constellation of Cygnus, the Swan, flying south along the great river of the galaxy. In the neck of Cygnus, near the naked eye star Eta Cygni, astronomers have found a bright blue-supergiant known as V1357 Cygni (also known as HD 226868 — there are a lot of stars, so astronomer names for them are not always the most pleasing for idle conversation!). It is bright enough to see in a telescope from your backyard, but there is little else you or I can discern. But in 1964, astronomers flew an x-ray detector on a rocket to the edge of space, and discovered this star is one of the strongest sources of x-rays in the sky. We now call it Cygnus X-1.  Since then, astronomers have watched this star closely, and note that ever so slightly it is wobbling back and forth once every 5.6 days, suggesting its unseen companion is about 14.8 times the mass of our Sun; the orbit between the two is about half the size of Mercury’s orbit.

An artist’s impression of Cygnus X-1. The strong stellar wind blowing off the supergiant is captured by the black hole and pulled down to form an accretion disk. [ESA/Hubble image]

But what about the x-rays? Ordinary binary stars don’t spew off as many x-rays as Cygnus X-1. What gives? This is another clue pointing toward the companion being a black hole. The blue supergiant blows off a strong stellar wind, much like the solar wind from our own Sun, but stronger. That material is captured by the gravitational pull of the companion and pulled down onto a turbulent maelstrom of material called an accretion disk. The accretion disk swirls just above the black hole, and is subject to intense gravity. Heuristically, the picture is this: the intense gravity makes the gas move very fast. When gas moves fast, it gets hot. When gas gets hot, it emits light. The faster it moves, the hotter it gets, and the more energetic the light. X-rays are very energetic, so the gas must be moving very fast. Why? The extreme gravity of a black hole.

So black holes can do crazy stuff to gas that streams down close to them. But what will the extreme gravity do to a solid object that gets too close? Imagine you (unwisely) decide to jump into a black hole; not being much of a diver, you jump in feet first. As expected, far from the black hole you don’t notice anything; the gravitational field looks perfectly normal, like any Newtonian gravitational field. Space and time are only distorted and stretched by noticeable amounts when you get close.

Tidal forces are a difference in the strength of gravity across your body. In the extreme gravity near a black hole, the side closest to the black hole is pulled on more strongly than the far side. As you get closer and closer to the black hole the effect is to stretch you out (“spaghettify” you) until you are pulled apart (“tidally disrupted”).

As you get closer, the strength of gravity increases — general relativity tells us the curvature, the warpage of spacetime is increasing. As you approach, the black hole pulls more strongly on your feet than your head. As you get closer and closer, this difference in force (what your physicist friends call a “tidal force”) can become quite strong! The net result — it stretches you out — provided you can withstand the strain, you’ll stay together, but get longer, like a rubber band.

Stephen Hawking has dubbed this effect “spaghettification” — the turning of you into a long piece of spaghetti. It is more extreme if your head is farther from your feet — short people have a better survival probability than tall people!  If you really want to survive the dive into a black hole, your best choice is to belly flop or cannonball — both greatly reduce the distance between the side of you close to the black hole, and the side of you farther from the black hole.

Astronomers observe tidal disruption flares. Here is an artists conception (top) and telescope observations (bottom) of a star being tidally disrupted by a 100 million solar mass black hole in galaxy RXJ1242 in 2004. [NASA]

Imagine now it wasn’t you diving into a black hole, but a star.  The exact same effects occur. Imagine a star falling toward a black hole. As it closes the distance, the strength of gravity grows inexorably stronger. The side of the star closest to the black hole feels the tug of the black hole more strongly than the far side. Despite the fact that it’s own self-gravity is strong enough to keep it together, as the influence of the black hole grows, it begins to overcome the self-identity of the star, and distorts it into a oblong caricature of its former self.  If the star strays too close, the black hole’s gravity will overcome the star’s gravity, and tear it apart. The star will be tidally disrupted.

When this happens, the guts of the star are violently exposed in an energetic event called a tidal disruption flare. Generally, the remains of the star, now a seething, turbulent cloud of gaseous debris, collapses down toward the black hole, forming an accretion disk that heats up and, for a time, becomes very bright. Slowly, the gas falls down the throat of the black hole, vanishing forever, and all evidence of the star is erased.

Two decades of observations have shown the orbits around the 4 million solar mass black hole at the center of the Milky Way. [NCSA/UCLA/Keck]

So what are these black holes that eat stars? They are the great monsters of the Cosmos. Lurking at the centers of spiral galaxies, like Charybdis in the Straits of Messina, these “supermassive black holes” have grown on a steady diet of stars and gas to enormous sizes. Our own Milky Way harbors a massive black hole that is 4 million times heavier than the Sun; even though it is millions of times more massive, the horizon is only about 17 solar radii across. But the consequences of its existence are profound. For the last two decades or so, astronomers have been watching a small cluster of stars in the center of the galaxy. We’ve been watching them long enough now, that they have traced out significant pieces of their orbits, and in some cases completed an entire orbit, allowing us to measure the mass of the black hole.

Despite being 4 million times more massive than our Sun, the black hole at the center of the Milky Way has an event horizon diameter only 17x larger than the Sun’s diameter!

Astronomers have looked for and found supermassive black holes in many other galaxies. In the course of those observations, we have discovered a tantalizing and interesting connection between galaxies and the massive black holes they host. Galaxies often have a part of them astronomers call “the bulge.” In the Milky Way, and other spiral type galaxies, the bulge is the large spherical bubble of stars that sits over the center of the galaxy. Some galaxies, like elliptical galaxies, are “all bulge.”  Astronomers have discovered an interesting relationship: the bigger a bulge, the bigger the black hole that lies at the center of it.

The black hole in the center of M87 powers an enormous, energetic jet of material spewing out from the galactic core. (L) I was one of the first amateurs image this jet in 2001. (R) HST image of the jet, for comparison. 🙂

An example of galaxies that are “all bulge” are ellipticals, like M87 in Virgo. M87 has a 2 BILLION solar mass black hole in its core that has launched an enormous jet that shoots out of the galaxy, extending nearly 5000 light years out from the core. No one knows exactly how black holes launch jets, but the best observations and models lead astronomers to believe that a spinning black hole can twist up magnetic fields into galactic sized magnetic tornadoes. Hot gas is very easy to convince to follow strong magnetic fields, and as it plummets toward the black hole, some of it is redirected up the jets.

But even among galaxies, some black holes are larger than others. In the northern sky, just below the Big Dipper is a smattering of faint stars known as Coma Berenices — “Bernice’s Hair.”  The stars of Coma Berenices are in our own Milky Way galaxy, but behind them, across 320 million lightyears of the void, lies the Coma Cluster of galaxies. A group of about 1000 galaxies, the center of the cluster is ruled by two super-giant elliptical galaxies known as NGC 4874 and NGC 4889 (both of which can be seen with backyard telescopes; NGC 4889 is easier than NGC 4874!). Both show strong evidence for massive central black holes, including enormous jets emanating from the centers. But astronomers have attempted to mass the black hole in NGC 4889 and found the black hole could be as massive as 37 billion solar masses. If true, the event horizon would be 24 times larger than Neptune’s orbit. That size boggles the mind — a void of nothing, almost 25 times larger than the solar system; anything that goes in is lost. Forever.

Coma Berenices is a pretty splatter of stars beneath the Big Dipper (which is part of Ursa Major). The Coma Cluster of galaxies, and NGC 4889, lies 320 million lightyears behind the stars of Coma Berenices.

The idea that black holes and galaxy bulges are related is a new one in astronomy, only having been proposed in 1999.  A diligent padawan of the Cosmos would ask the obvious question: if a galaxy has no bulge, does it then have no super-massive black hole? The answer may be “yes.” A classic example of this is the Triangulum Galaxy (M33), right here in our own Local Group. A beautiful, classic spiral galaxy, M33 is only marginally tipped to our line of sight and can be easily seen and studied with a backyard telescope. Curiously, M33 has no bulge; so far, no massive black hole has been found.

M33, the Great Galaxy in Triangulum. There is almost no bulge surrounding the bright core seen here; astronomers have yet to find any evidence of a supermassive black hole there.

And so the search continues. The number of galaxies for which we know the bulge-black hole relation works is still small — we have seen enough to understand the implications and possibility, but we still haven’t seen so many that we are confident stating, without equivocation, that “all bulgy galaxies have black holes.” Time and diligent observations of new galaxies will help resolve this question.

The fact that you and I can have conversations like this about black holes, dealing with what astronomers see and not (too much) about what we speculate is a mark of how far astronomy has come. When general relativity was first penned, black holes started as a curious, if somewhat suspect mathematical solution to the equations of gravity. Repeated, careful observations of the Cosmos have, however, led astronomers to the inescapable conclusion that black holes do in fact exist. They are part of our understanding of the machinery of the Universe. Now, the questions are different than what they were a century ago. Instead of asking “do they exist?” and “are they real?” we instead noodle our brains on the questions of “how many are there?” and “how big are they?” and “what are they doing to the Cosmos around them?”

And a lot of us still wonder, “what would happen if I jump in one?”

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This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015).  You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru.

Gravity 7: Recipe for Destruction (Making Black Holes)

by Shane L. Larson

Black holes emit no light, by definition. For many years, the only hope astronomers had of detecting these enigmatic objects was to look for how they interact with other astrophysical objects, like stars and gas. Astronomers have been around the block a few times — they’ve studied a lot of stars, and seen a lot of gas in the Cosmos. What should they be looking for that would clue them in when the stuff they can see has drifted near a black hole? What do black holes do to things that fall under the influence of their gravity?

If you’ve ever heard about or read about black holes, you’ve learned that their gravity can be strong — extremely strong. This leads to a somewhat deceptive notion that black holes are like little Hoovers, running all over the Universe sucking things up.  The reality is that a black hole’s gravity is strong and can have a profound effect on the Cosmos around it, but only up close.

To get a handle on this, it is useful to go back to the way we first started thinking about gravity — in terms of a field. In the field picture, the strength of gravity — what you feel — is given by the density of field lines in your vicinity; gravity is stronger when you are surrounded by more field lines. There are two ways to increase the strength of the gravitational field.

The easiest way to make gravity stronger is to have more mass. Mass is the source of gravity; when we were drawing gravitational fields, the number of field lines we drew depended on the mass of the object.  The Sun is much more massive than the Earth, so we draw many more field lines to represent its gravitational field.

Two observers (Stick Picard, top; Stick Spock, bottom) are the same distance from objects. For the person near the smaller object, they feel weaker gravity (evidenced by fewer field lines around them).

Another way to increase the strength of gravity is to make an object more compact. You can see this by considering two stars of equal mass, but one smaller than the other. How do their gravitational fields compare? Far from either star, the gravitational fields look identical. There is no way to distinguish between the two based on simple experiments, like measuring orbits. But suppose you were down near the surface of each star. Here we notice something interesting. Both stars have the same number of field lines, because they have the same mass. But down near the surface of the smaller, more compact star the lines are much closer together. This was the signature of gravity being stronger.

Imagine two stars with exactly the same mass, but one is larger in size (top) than the other (bottom). Observers far from either star (Stick Spock, both panels) feel the same gravity if they are the same distance away. For close-in observers (Stick Geordi, both panels) the gravity is stronger. But for the compact star (bottom) the observer can get closer, and when they do, they feel even stronger gravitational forces. The gravity is much stronger near a compact object.

The field picture of gravity is associated with the idea of forces (it is a “force field”), which is the foundation of Newton’s approach to gravity. But one of the requirements of general relativity when it was developed was that it correctly describe situations where we would normally use Newtonian gravity, as well as any situation that required relativistic thinking. We’ve seen in these examples that gravity gets stronger if an object is more massive, or if it is more compact. In the language of general relativity, we would say “there is stronger curvature” in both these cases. Remember our mantra: “mass tells spacetime how to curve.” Spacetime is told to curve more where the masses are bigger, or when the mass is very compact.

So what does this tell us about black holes? It says that to make an object whose gravity is so strong that the escape speed is the speed of light, I can do one of two things: I can dramatically increase the mass, or I can make the object more compact.  This is the first clue we have to where black holes might come from — they have to be either very massive, or extremely small. We actually encounter both in the Cosmos, as we shall see, but for the moment let’s focus on the small ones. So how do you make things extremely small?

Wrap a balloon in aluminum foil. The foil is like the stuff of the star; the balloon is an outward force, keeping the star from collapsing.

Let’s do an experiment to think about this. Go find a balloon and some aluminum foil. Blow the balloon up (it doesn’t have to be huge) and wrap it in aluminum foil.  This is a mental model of a star at any given moment in its life. Gravity is always trying to pull everything toward the center. But the star is not collapsing — why not?  Deep in the cores of stars, the temperature and pressure is so high that nuclear fusion occurs — through a series of interactions with all the nuclei that are packed together, hydrogen is “burned” into helium. This process releases energy — it’s nuclear fusion power! In your balloon and foil model, the foil is stuff in the star — all the churning roiling gas and plasma that make up the body of a star. What is keeping it from collapsing? In this case it is the balloon, pushing the foil outward — the balloon is acting like the fusion energy bursting out from the core, supporting the star and keeping gravity from collapsing it.

Gravity (turquoise arrows) is constantly trying to pull the star inward on itself. The pressure from the nuclear fusion generating energy in the core presses outward (yellow arrows) preventing the star from collapsing.

As a star ages, the fusion process in its core evolves, slowly burning the core fuels into heavier and heavier elements, until a large core of iron builds up. There are no effective nuclear reactions that can sustain the burning of iron into heavier elements.  The iron is effectively ash (that’s what astronomers call it!) and it settles down into the core.  The iron is not burning, so there is no fusion energy pushing outward against gravity’s desire to collapse the core — what’s stopping it?

In addition to the iron nuclei, the core is also full of the other constituents that make up atoms, electrons.  Electrons are a particular kind of particle we encounter in the Cosmos called a fermion. Fermion’s are okay to hang out together, provided they all think they are different from one another (in the language of the physicists — the fermions all have to have different “quantum numbers”); this is a well known physical effect known as the Pauli Exclusion Principle. If you do pack fermions together they dislike it immensely. They start to think they are all looking the same, and they press back; this is called “degeneracy pressure”, and it is what keeps gravity from being able to crush the iron core of the star.

When gravity overcomes the electron degeneracy pressure in the iron core (pop the balloon), there is nothing pushing outward against gravity, so the core can collapse.

High above, the star continues to burn, raining more and more iron ash down on the core. The mass of the core grows, and the gravity grows with it. When enough iron amasses in the core, the gravity will grow so strong not even the degeneracy pressure of the electrons can oppose it. When that happens, gravity suddenly finds that there is nothing preventing it from pulling everything down, and the iron core collapses.  In your model, this is equivalent to popping your balloon — you’re left with a lot of material that is not being supported at all, so it collapses.  Collapse the foil shell in your hands — you are playing the role of gravity, crushing the material of the star down into a smaller and smaller space.

When the collapse occurs, the iron nuclei are the victims. The compression of the iron core squeezes down on the iron nuclei, disintegrating them into their constituent protons and neutrons. The extreme pressure forces protons and electrons to combine to become more neutrons (a process creatively called “neutronization”). In less than a quarter of a second, the collapse squeezes the core down to the size of a small city and converts more than a solar mass worth of atoms into neutrons. We call this skeleton a neutron star.

Gravity wants to compress all the matter, to pull down as close together as it can get. The explosion helps gravity move toward its goal by applying astronomical pressures from the outside, squeezing and squeezing the matter down. What stops it?

You hands act like gravity to crush the foil into a small remnant of its former self. There is a minimum crushing size, because the foil presses back against your efforts.

Let’s go back to your model. The balloon has been popped — that’s gravity overcoming the supporting pressure of the electrons. The foil has collapsed — that is gravity pulling as hard as it can to get all the material down into the center. Now squeeze that lump of foil as hard as you can; make the smallest, most compact ball of foil you can. Odds are there is some minimum size you can make that ball of foil. What is keeping you from squeezing the foil smaller? The foil itself is getting in the way! It is pushing back against the force that is trying to crush it — you — and you are not strong enough to overcome it!

This is the case with the neutron star. When neutrons are so closely packed together, their interactions are dominated by the strong nuclear force, which is enormously repulsive at very short distances. As more and more neutrons are packed into a smaller and smaller space, they become intensely aware of one another and the pressure from the strong nuclear force grows until it is strong enough to oppose gravity once again.  The collapse stops, suddenly.

The iron core is heavy (more than a solar mass) and moving fast (between 10-20% the speed of light) — it is not easy to stop so suddenly. When the center of the core stops, the outer layers of the core are unaware of what lies ahead. In the astrophysical equivalent of a chain-reaction traffic pile-up, the layers crash down on one another; the outer layers rebound outward.  This rebounding crashes into the innermost layers of the star above the core, setting up a shock wave that propagates outward through the star.  The wave begins to tear the star apart from the inside.

The Western Veil Nebula (NGC 6960), just off the wing of the constellation Cygnus. Visible in amateur telescopes, it is one of the most exquisite supernova remnants in the sky. [Wikimedia Commons]

Energized by an enormous flux of neutrinos produced by the newly birthed neutron star, the shock is driven upward through the star, until it emerges through the surface, destroying the star in a titanic explosion known as a supernova.  It is an explosion that would make Jerry Bruckheimer proud — the energy released is enormous, for a time making the exploding star brighter than all the other stars in the galaxy combined. The material of the star is blown outward to become a supernova remnant, a vast web of ejected gas and atoms thrown out into the Universe. We see many, many supernova remnants in the galaxy — every one of them is unique, they are all exquisite and beautiful in ways that only the Cosmos can create.

Left behind, slowly settling down into a well-behaved stellar skeleton, is the neutron star.  At the surface of the neutron star, the gravity is enormous — about 200 billion time stronger than the gravity at the surface of the Earth. The escape speed is 64 percent the speed of light. If you fell just 1 millimeter, you would be travelling at 61,000 meters per second (136,400 miles per hour!) when you hit the surface!

Lego Neil deGrasse Tyson and Lego Me visit the surface of a neutron star. [click to enlarge]

But this is still not the extreme gravity of a black hole. If a star is massive enough, the crushing force of the collapsing star and the ensuing explosion is so strong it cannot be stopped even by the protestations of the neutrons. In fact, the infalling matter crushes the matter so strongly that gravity becomes triumphant — it crushes and crushes without bound. The strength of gravity — the warp of space and time — soars. At some point the escape speed at the surface of the crushing matter reaches the speed of light — the point of no return has been reached, but the matter keeps falling right past the event horizon, continuing to fall inward under the inexorable pull of gravity. All the matter is crushed into the smallest volume you can imagine, into the singularity, at the center of the empty space we call the black hole. No force known to physics today is strong enough to overcome this event.

Different effects in astrophysical systems fight against gravity’s inexorable pull. If the gravity gets strong enough, nothing can prevent the collapse to a black hole.

The process just described is known as core-collapse and is just one way that astronomers think black holes might be made. Similar explosive events that lead to collapse include the collision of two neutron stars, the parasitic destruction of a small star by a compact companion that grows its mass large enough to collapse, and possibly even the collision of smaller black holes to make larger black holes.

So how compressed do you have to be to become a black hole? The answer for a perfect ball of matter is called “the Schwarzschild radius.” If you squeeze an object down to a ball that fits inside the Schwarzschild radius (that is, it fits inside the event horizon) then no known force can stop gravity from collapsing that object into a black hole. For the Sun, the Schwarzschild radius is about 3 kilometers — if you shrink the Sun down into a ball just 6 kilometers in diameter, the size of a small city, it will be a black hole. For the Earth, the Schwarzschild radius is about 1 centimeter — if you shrink the Earth down to the size of a marble, it will be a black hole.

What it would take to make the Sun or the Earth into a black hole. The Sun as a black hole would cover your town, but you could carry the Earth in your pocket (though this is NOT recommended).

Given a notion of how black holes form, astronomers can start probing the Universe, peering into places that should give birth to black holes. The same physical effects that we used to understand their formation can be used to understand how they interact with the Cosmos around them, giving astronomers clues about how to detect them. Next time, we’ll use this information to find out how black holes influence the Universe around them, and use that information to go black hole hunting in the Cosmos.

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This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015).  You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru.

[9 March 2015] This is revised version of the original post. I owe many thanks to a colleague who pointed out that my original explanation of core-collapse followed very old ideas about how stars die. In this revision, I have endeavoured to present a correct but still clear picture of what is going on. Any inaccuracies that still persist are my own.

Gravity 6: Black Holes

by Shane L. Larson

There are many topics that set the mind afire with wonder, wild speculation, and imaginative ramblings into the unknown and the unknowable. Particularly popular, especially among human beings less than about 12 years old, are dinosaurs, volcanoes, alien life, and black holes. “Grown-ups” will often rediscover a bit of their childhood wonder when these topics come up, and have been known to engage in deep question-and-answer marathons to try and understand what it is that we, the humans, have learned and understood about these enigmas of Nature.

There are many things in science that spark our imaginations in dramatic ways, no matter your age, like dinosaurs, volcanoes, alien life (or freaky life on Earth, like octopuses), and black holes.

While most of us lose our penchant for crazy trivia factoids as we age, there is still a lingering desire to think about dinosaurs, volcanoes, alien life, and black holes. These topics can be understood quite well on a heuristic level, and from those simple descriptions emerges a rich tapestry that serves as a playground to let our imaginations run wild.  All four topics are particularly interesting because they in a very real way represent the frontiers, the boundaries of our understanding of what is possible in the Cosmos. The dinosaurs were among the largest lifeforms ever to walk the Earth. Volcanoes are among the most violent, explosive, destructive natural phenomena on Earth, the planet vomiting its guts onto the surface for us to see. A single instance of alien life would transform our parochial view of life in the Cosmos.  But even among these grand mysteries that are so enjoyable to speculate and dream about, black holes hold a special place. Black holes are the ultimate expression of Nature’s power to utterly erase anything from existence.

What are these enigmatic black holes? Where do they come from, and what do we understand about them?

Imagine Stick Picard, Stick Geordi, and Stick Spock are throwing apples in the air. If Picard throws an apple up, it comes back down. If Geordi throws an apple up faster, it goes higher, but still comes back down. If Spock throws an apple fast enough, at escape speed, it will not come back down — it will break free of the Earth’s gravity.

Fundamentally, a black hole is an object whose gravity is so strong that not even light can escape its grasp.  What does that mean?  Imagine we go stand out in the middle of a field. You take a baseball, and throw it up in the air as fast as you can.  What happens? The ball rises, but gravity slows it down until it turns around and falls back to Earth.  If you have a friend do the same thing, but she throws her baseball even faster, it goes higher than your baseball, but still it turns around and falls back to Earth.  The faster you throw the baseball, the higher it goes. As it turns out, there is a certain speed you can throw the ball that is so fast, the ball will escape the gravity of the Earth and sail into deep space. That speed is called, appropriately enough, the escape speed.  On Earth, that speed is 11.2 km/s — if a rocket reaches that speed, it will make it into space, slipping free of the Earth’s gravity forever.

(T) The fasted “plane” ever built was the rocket powered X-15, which attained a speed of 2.02 km/s, far short of the escape speed of Earth (11.2 km/s). (B) Rockets, like the Apollo 15 Saturn V, have broken free of the Earth’s gravity. [aside: Apollo 15 famously tested the Equivalence Principle on the Moon.]

Our operational definition of a black hole is this: a black hole is an object whose escape speed is the speed of light. You may notice that this definition has nothing related to relativity in it. Black holes are a natural consequence of any description of gravity. The first ponderings about black holes were made in 1783 by the Reverend John Michell. A graduate of Cambridge University, Michell was by all accounts a genius of his day, an unsung polymath who pondered the mysteries of the Cosmos as he went about his duties as the rector of St. Michael’s Church in Leeds. He made many contributions to science, including early work that gave birth to what we today call seismology, and the idea for the torsion balance that Henry Cavendish later employed to measure the mass of the Earth and the strength of gravity. But here we are interested in Michell’s mathematical work on escape speed.

At the time Michell was thinking about escape speed, the speed of light was the fastest speed known (it had been measured to better than 1% accuracy more than 50 years earlier by James Bradley), though no one knew it was a limiting speed. Michell asked a simple and ingenious question: how strong would the gravity of a star have to be for the escape speed to be the speed of light?

No known picture of John Michell survives. But he still speaks to us from the past, through his scientific writings.

He described his result to his friend Henry Cavendish in a letter, noting that light could not escape such a star, assuming “that light is influenced by gravity in the same way as massive objects.” A prescient statement that ultimately turns out to be true, as Einstein showed when he proposed general relativity 132 years later. Michell called such an object a dark star.

Michell’s ideas were published in the Proceedings of the Royal Society, and then more or less faded into history until they were revived by the publication of general relativity. Most of us associate the idea of black holes with relativity and Einstein, not Newtonian gravity and Michell. Why?

Because special relativity adds an important constraint on Michell’s dark stars: there is an ultimate speed limit in the Universe. Nothing can escape from one, because nothing can travel faster than the speed of light. General relativity has this idea built into it, together with the idea that light responds to gravity just as matter does, completing the picture. The first true black hole solution in general relativity was written down by Karl Schwarzschild in the months after Einstein first announced the field equations to the world.

So how can we think about black holes in general relativity? An easy heuristic picture is to appeal to our notion of curvature. Imagine flat space — space with no curvature, thus no gravity. If you give an asteroid a little nudge, it begins to move, and continues to move on a straight line. It will do so forever, in accordance with Newton’s first law of motion: an object in motion stays in motion (until acted up on by an external force). Now imagine that same asteroid in an orbit a little ways down inside a gravitational well. If you give the asteroid a little nudge outward, its orbit will wobble around a bit, but still remain confined to the gravitational well. If you give it a bigger nudge, it can climb up out of the well and escape into the flat space beyond — this is escape speed.

Weak orbits, far from a source of gravity, are not deep in a gravitational well (top orbit); a small nudge will give a rock in these orbits escape speed and it will break free. Strongly bound orbits, deep in the gravitational well (bottom orbit) require much larger nudges to reach escape speed and break away.

But what happens if the asteroid orbit is in a deep gravitational well? A deep well is indicative of strong curvature — what a Newtonian gravitational astronomer would call a “strong gravitational field.” If you are going to nudge the asteroid so it can climb out of the gravitational well, it will require a BIG nudge — objects strongly bound by gravity need BIG escape speeds.

For a black hole, the gravitational well is infinitely deep. Imagine you are orbiting far from the black hole. This is just like any orbit in any gravitational well; you are somewhere down in the well, and with a big enough nudge, you will have the escape speed to break free and climb out of the well. As you go deeper and deeper in the well, you have to climb further out, so the required speed to break free is higher. But there will come a point of no return. At some point deep down in the well, the escape speed becomes the speed of light. At that point, no matter what speed you attain, you will never be able to climb out of the gravitational well. That point, is a point of no return — we call it the event horizon.

Around a black hole, there is a point, deep in the gravitational well, where the escape speed is the speed of light. This is called the event horizon, and is the point of no return. Outside the event horizon is outside the black hole — you can still escape. Inside the event horizon is inside the black hole — you are trapped forever, being pulled inexorably toward the singularity.

This is an overly simple picture of the event horizon, but is a perfectly good operational definition. General relativity predicts that time and space behave weirdly inside this surface, but for those of us on the outside, we’ll never know because that information can never be carried up the gravitational well, past the event horizon, and to the outside Universe.

The existence of the event horizon as a one way membrane, as a point of no return, means black holes are exceedingly simple — they are among the simplest objects in the Cosmos. What does that mean?

Think about an average automobile, like my prized 1990 Yugo GVX. What does it take to completely describe such an object? You have to describe every part of it — the shape and size of the part, what it is made of, where it goes on the vehicle, what it touches and is attached to. All told, there may be 10,000 parts — bumpers, windshields, lugnuts, u-joints, battery leads, spark plug cables, fuses, windshield wiper blades, turn signal indicators, and on and on and on.

Magazines devoted to cars and black holes may look the same. There may be a LOT to talk about in a car magazine. In a black hole magazine, there are only 3 things to talk about, but those 3 things have tremendous influence on the Cosmos, which is quite interesting.

What about a black hole? There are only THREE numbers you need to specify to completely characterize all the properties of a black hole. Those numbers are (1) the mass, (2) the spin, and (3) the electric charge. If you know these three numbers, then general relativity tells you everything you can know about the black holes.

What does that mean everything? The idea that you only need 3 numbers to describe a black hole is a central feature in general relativity, known as the “No Hair Theorem.” Here the word hair hearkens back to our idea of a “field” as being some invisible extension that spreads out from an object in every direction (like hair). General relativity says that if the black hole has any properties besides mass, spin, and electric charge, there should be other kinds of hair emanating from the black hole.

Now, that statement should incite the little scientist in the back of your brain to start jumping up and down. This is a prediction of general relativity. Predictions were meant to be tested — that is what science is all about. One could pose the question “are the black holes we find in Nature the same ones predicted by general relativity?” Are black holes bald (described only by mass, spin, and charge) or do they have some kind of external hair that affects the Universe around them?

For astronomers to address questions like this, they have to understand what happens to things that get too close to a black hole. How do black holes appear in and influence the Cosmos? This will be the subject of our next chat.

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This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015).  You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru.