Gravity 11: Ripples in Spacetime

by Shane L. Larson

We have travelled far in our journey to explore gravity, far from home and into the deep reaches of the Cosmos. But all that we know, all that we have learned, has been discovered from our home here, on the shores of the Cosmic Ocean. Today, let us return home.  In the words of the space poet Rhysling,

We pray for one last landing
On the globe that gave us birth
Let us rest our eyes on the fleecy skies
And the cool, green hills of Earth.

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Imagine yourself in a soft green meadow, far from the hub-bub of everyday life. What do you hear? What do you see? The gentle rustle of the trees, and the whisper of the long grass. The tall flowers of spring rocking gently back and forth, and the dark shadows of a bird of prey soaring effortlessly against the blue sky. All these sights and sounds are the signature of something unseen — the atmosphere of the Earth, the blanket of air that protects us and supports all the life around us.

How do we know the air is there? We can’t see it. All of these observations, infer the existence of the air by recognizing its influence on other things. If we want to measure the air directly, to detect it, then we need to construct controlled experiments where we understand the physical effect of the air and how it interacts with the experiment we design to elucidate its presence. Consider a simple experiment you can do right at home.

An experiment to convince yourself air exists. (TopL) If you just dip a straw directly in water and lift it out, then (TopR) all the water runs out.  (LowerL) If instead you put your finger over the straw before dipping it, then (LowerR) no water gets in the straw. Something invisible got in the way -- air!

An experiment to convince yourself air exists. (TopL) If you just dip a straw directly in water and lift it out, then (TopR) all the water runs out. (LowerL) If instead you put your finger over the straw before dipping it, then (LowerR) no water gets in the straw. Something invisible got in the way — air!

Take a drinking straw and a glass of water.  Dip the straw in the water, then place your thumb over the top of the straw, and remove it from the water.  If you take your thumb off the straw, you find that you had trapped some water in the straw.  Now do a slightly different experiment. Put your thumb over the end of the straw first, then put it in the water. If you take the straw out of the water and remove your thumb, you find that there is no water in the straw!  Why didn’t water go in the straw? There must have been something in the way, something invisible you couldn’t see. It is, of course, the air. This seems completely obvious to us now, thinking about it with 21st century brains, but two millenia ago, when we were just beginning to speculate on the nature of the world, this was a remarkable and marvelous observation of the world.

Today, astronomers find themselves in a similar brain loop with respect to gravity. One can “measure the force of gravity” through experiment. But when Einstein developed general relativity, he did away with gravitational forces in favor of motion on the curvature of spacetime. We can use this idea to describe everything we see in Newtonian gravity — objects freely falling to the ground, orbits of astrophysical bodies, and the weightlessness of astronauts in space. There have been exquisite tests of general relativity confirming its unique predictions beyond Newtonian gravity, and we rely on it every single day.

But is there a way to directly measure spacetime? Can we confirm that gravity is no more than the curvature of spacetime itself?  This is a question that has occupied the minds of gravitational physicists for a century now, and many ideas have been proposed and successfully carried out.

The most ambitious idea to directly measure spacetime curvature was first proposed by Einstein himself, and has taken a century to come to fruition. One of the motivations to develop general relativity was famously to incorporate into gravitational theory the fact that there is an ultimate speed limit in the Cosmos. If the gravitational field changes (for instance, due to the dynamical motion of large, massive objects like stars), that information must propagate to distant observers at the speed of light or less. If gravity is no more than the curvature of spacetime, then changes in the gravitational field must must be encoded in changing spacetime curvature that propagates from one place to another. We call such changes gravitational waves.

The opening pages of Einstein's first two papers on gravitational waves in 1916 (L) and 1918 (R).

The opening pages of Einstein’s first two papers on gravitational waves in 1916 (L) and 1918 (R).

If you want to build an experiment to detect an effect in Nature, you need a way to interact with the phenomenon that you can unambiguously associate with the effect. For the first 40 years after Einstein proposed the idea of gravitational waves, physicists were vexed by the detection question because they were confused as to whether the phenomenon existed at all!  The problem, we now know, was our inexperience with thinking about spacetime.

The International Prototype Kilogram (IPK).

The International Prototype Kilogram (IPK).

Scientists spend their lives quantifying the world, describing it precisely and carefully without ambiguity, as much as is possible. To this end, we use numbers, and so need a way of agreeing on what certain numbers mean. For example, we measure mass using “kilograms.” What’s a kilogram? It is the mass of a reference body, made of iridium (10%) and platinum (90%), called the “International Prototype Kilogram” (IPK). The IPK, and six sister copies, are stored at the International Bureau of Weights and Measures in Paris, France. Scientists around the world agree that the IPK is the kilogram, and can base numbers off of it. Nature doesn’t care what the IPK is; the Sun certainly has a mass, expressible in kilograms, but it doesn’t care one whit what the IPK is. The kilogram is something humans invented to quantify and express their knowledge of the Cosmos in a way other humans could understand.

Example coordinates that can be used to describe the screen or paper you are reading this on. They are all different because humans invented them, not Nature. They are not intrinsic to the surface they are describing, though they are often chosen to reflect underlying shapes of the surface.

Example coordinates that can be used to describe the screen or paper you are reading this on. They are all different because humans invented them, not Nature. They are not intrinsic to the surface they are describing, though they are often chosen to reflect underlying shapes of the surface.

In a similar way, when spacetime physicists describe spacetime, we have to have a way of identifying locations in spacetime, so we make up coordinates. Like the kilogram, coordinates are something we humans create to enable us to talk with each other; Nature cares nothing, Nature knows nothing about coordinates. But sometimes we get so used to think about Nature in terms of coordinates, that we begin to ascribe physical importance to them! This was the case during the early decades of thinking about gravitational waves. Physicists were confused about whether or not the coordinates were waving back and forth, or if spacetime itself was waving back and forth.  Arthur Eddington, who had led the 1919 Eclipse Expedition to measure general relativity’s prediction of the deflection of starlight, famously had convinced himself that the waves were not real, but only an artifact of the coordinates.

At the poles of the globe, all the lines of longitude come together, and there is no well defined value. There is nothing wrong with the sphere; the coordinates that humans invented are not well suited there!

At the poles of the globe, all the lines of longitude come together, and there is no well defined value. There is nothing wrong with the sphere; the coordinates that humans invented are not well suited there!

Sometimes coordinates behave badly, giving results that might seem wrong or unphysical. For instance, you can see one example of badly behaving coordinates at the top of a sphere — if you are standing on the North Pole of the Earth, what is your longitude? You can’t tell! Longitude is a badly behaving coordinate there! There is nothing wrong with the sphere, only our coordinates.

And so it was with spacetime. In the early 1930s, Einstein and a collaborator, Nathan Rosen, had discovered a gravitational wave solution that appeared unphysical and claimed this as a proof that gravitational waves did not exist. Their result was later shown to be coordinates behaving badly, and Einstein pivoted away from denying gravitational waves exist, though Rosen never did.

The argument of the reality of the waves persisted for decades; in the end, the questions were resolved by a brilliant deduction about how to measure gravitational waves. As with all things in science, the road to understanding is a slow and steady plod, ultimately culminating in a moment of  understanding. In the early 1950s, our thinking was progressing rapidly (or so we know now, with 20/20 hindsight). The watershed came in January of 1957 at Chapel Hill, North Carolina, at a now famous conference known as “The Role of Gravitation in Physics.” There were 44 attendees who had gathered to discuss and ponder the state of gravitational physics. It was barely 19 months after Einstein’s death, and the question of the existence of gravitational waves had not yet been resolved.

The community had slowly been converging on an important and central issue in experimental physics: if you want to detect something in Nature, then you have to know what the phenomenon does to the world around it. You then need to design an experiment that focuses on that effect, isolating it in some unambiguous way. At the Chapel Hill Conference, the realization of what to do was finally put forward by Felix Pirani. Pirani had settled on the notion that an observable effect of a passing gravitational wave is the undulating separation between two test masses in space (something gravitational physicists called “geodesic deviation” or “tidal deviation”). This idea hearkens back to the idea that the trajectories of particles is a way to measure the underlying shape of gravity, which was one of the original notions we had about thinking of gravity in the context of curvature.

The Sticky Bead argument was a thought experiment that convinced physicists that gravitational waves were real and could carry energy. (TOP) Imagine two beads on a smooth rod. There is a small amount of friction that keeps the beads from sliding freely. (BOTTOM) When a gravitational wave passes by, it pushes the beads apart. The friction stops the motion of the beads, heating the rod up. Measuring the heat in the rod constitutes a detection of the gravitational waves, since they were the source of the energy.

The Sticky Bead argument was a thought experiment that convinced physicists gravitational waves were real and could carry energy. (TOP) Imagine two beads on a smooth rod. A small amount of friction keeps the beads from sliding freely. (BOTTOM) When a gravitational wave passes by, it pushes the beads apart. The friction stops the motion of the beads, heating the rod up. Measuring the heat in the rod constitutes a detection of the gravitational waves, since they were the source of the energy.

Also present at the conference was Richard Feynman, by then a professor at the California Institute of Technology. Feynman took Pirani’s notion and extended it into what we now call “the sticky bead argument.” He imagined a smooth rod with two beads on it. The beads were a little bit sticky, unable to slide along the rod without being pushed. When the motion of the beads was analyzed under the influence of gravitational waves, they moved back and forth, but their motion was arrested by the friction between the beads and the rod. Friction is a dissipative force, and causes the rod to heat up, just like your hands do if you rub them together. In the sticky bead case, what is the origin of the heat? The heat energy originated from the gravitational waves and was deposited in the system by the motion of the beads.

This idea was picked up by Herman Bondi, who expanded the idea, fleshing it out and publishing it in one of the leading scientific journals of the day. As a result, Bondi is generally credited with this argument.

(L) Richard Feynman (C) Hermann Bondi (R) Joseph Weber

(L) Richard Feynman (C) Hermann Bondi (R) Joseph Weber

Confirming that the beads move validated the idea that gravitational waves not only carry energy, but can deposit it in systems they interact with. This was the genesis of the notion that an observational programme to detect them could be mounted.  That challenge would be taken up by another person present at the Chapel Hill conference, named Joseph Weber. Weber had spent the previous academic year on sabbatical, studying gravitational waves at Princeton, and left Chapel Hill inspired to begin a serious search. Weber’s entrance to gravitational wave astronomy happened in the early 1960s with the introduction of the first gravitational wave bar detector.  This was the foundation that led to the great experimental gravitational wave experiments of today; we will start our story there in our next chat.

I am indebted to my colleague Peter Saulson (Syracuse) who first made me aware of Pirani’s talk at the 1957 Chapel Hill Conference. That Conference is part of the folklore if our discipline, though details are often glossed over usually going directly to the Bondi Bead story. I am also indebted to Carl Sagan, who introduced me to the idea that one can detect the air with water experiments (in “The Backbone of Night,” episode 7 of Cosmos: A Personal Voyage).

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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 10: Signatures of the Big Bang

by Shane L. Larson

Science has two interlocking pieces that always work together. One part is “describing the world to predict the future and explain the past.” This is the part that many of us remember from science class, involving pen and paper and mathematics and the Laws of Nature. Another part is “observing the world and seeing what Nature is up to.” This is also a part that many of us remember from science class, involving doing experiments and recording numbers and making graphs. These two pieces are called theory and experiment respectively, and they constantly validate and reinforce each other in a never-ending cycle of upgrading and refining our knowledge of the Cosmos.

All science is a combination of theory and experiment. In Cosmology, theory is an application of general relativity embodied in the Friedmann Equations (left); experiment is captured in astronomy (right).

All science is a combination of theory and experiment. In Cosmology, theory is an application of general relativity embodied in the Friedmann Equations (left); experiment is captured in astronomy (right).

Cosmology has seldom had both theory and experiment walking hand in hand. Instead one or the other has been out in front — sometimes way out in front — waiting for the other to catch up. This was certainly the case when general relativity was announced to the world — as a description of the machinery of the Cosmos, it was perfectly capable of making predictions that were so far beyond our ability to observe and verify that we didn’t recognize the truth for what it was. This famously happened early on, in 1917 when Einstein published one of the earliest papers about relativistic cosmology entitled “Cosmological Considerations in the General Theory of Relativity.”

As city dwellers, it is often easy to forget that the sky is full of stars. This fact leads to the most natural assumptions about the Universe based on experience: the Universe is full of stars.

As city dwellers, it is often easy to forget that the sky is full of stars. This fact leads to the most natural assumptions about the Universe based on experience: the Universe is full of stars.

At that time, we were profoundly ignorant about the nature of the Universe. The prevailing view was that the Cosmos was full of stars, and that the Universe was static. It’s the most natural assumption in the world based on your experiences when you step out the door every night — the sky is full of stars and they change little, if at all, night to night.

Einstein considered a Universe simply filled with stars, and asked what general relativity predicted. He found it only predicted one thing: the Universe must collapse.  Preconceptions are a powerful force in science, and Einstein believed strongly in the static Universe, so much so that he supposed maybe he had not gotten general relativity completely correct. So he introduced a mathematical addition to general relativity that pushed back against the collapse, called the Cosmological Constant.

Before 1924, the nature of galaxies was unknown. They were grouped with the "nebulae" -- wispy, cloud like structures that could be seen through the telescope. These included Messier 31, the Andromeda Nebula (L) and Messier 51, the Whirlpool Nebula (R). The Whirlpool was the first nebulae that spiral structure was detected in, by Lord Rosse in 1845.

Before 1924, the nature of galaxies was unknown. They were grouped with the “nebulae” — wispy, cloud like structures that could be seen through the telescope. These included Messier 31, the Andromeda Nebula (L) and Messier 51, the Whirlpool Nebula (R). The Whirlpool was the first nebulae that spiral structure was detected in, by Lord Rosse in 1845.

But science is always on the move. Telescopes in that day and age were getting larger. In 1917 the 100-inch Hooker telescope first saw starlight on its mirror, as it embarked on a long and storied history of astronomical discovery. Telescopes gave us the capability to probe deeper into the Cosmos, and we had started to discover vast diaphanous complexes of light that showed no stellar qualities. These were called nebulae, Latin for “cloud.”  A few of the nebulae, the “spiral nebulae,” perplexed astronomers — some thought they were simply odd nebulae (vast complexes of gas and dust), and others thought they were island Universes (other galaxies, like the Milky Way).

The 100-inch Hooker Telescope on Mount Wilson, used to discover the expansion of the Cosmos.

The 100-inch Hooker Telescope on Mount Wilson, used to discover the expansion of the Cosmos.

The discovery of the distances to the spiral nebulae, using Leavitt’s Cepheid variable method, was a watershed moment in the history of cosmology. It put on the table two  important facts: first, the Universe was vast — enormously vast — with distances far beyond the boundaries of our own galaxy.  Second, the major constituent especially on large scales, was not stars, but galaxies (which are agglomerations of stars). These two simple facts suddenly and irrevocably changed the way we thought about the Universe. In the first years after the discovery of the nature of galaxies, Friedmann and Lemaître used general relativity to imagine a Universe filled with galaxies, and discovered the idea that the Universe was expanding. This notion, discovered on paper, was bourne out in 1929 when Humason and Hubble, once again using the 100-inch telescope on Mount Wilson, found all the galaxies in the Universe were receding from one another.

At that time, Lemaître made a great leap of imagination — it was a thought that was well outside the comfort zone of astronomers of the day, though today we may view his leap as completely obvious. From the mindset of the future, it is difficult to imagine just how hard it was to think different. Lemaître supposed that if the Universe was expanding, then in the past it would have been smaller, and hotter. The idea was met with incredulity and derision, sparking enormous debate for decades to come. But science is the blend of ideas on paper with observations of the Universe. If Lemaître’s ideas were right OR wrong, the evidence could be found by looking into the Cosmos.

There are many lines of evidence that confirm the basic idea of the Big Bang, but there are three major pillars of support. The first, is the expansion itself. The Universe is not like a sports car, starting and stopping on a whim, braking and accelerating at random. Its evolution is driven by the Laws of Nature, in a smooth and predictable fashion. If we see expansion today, that expansion started in the past. The rate and trends in the expansion are a function of the amount of matter in the Universe, and the initial conditions of the expansion. These quantities can be determined from astronomical observations, and are consistent with the Big Bang picture.

A popular T-shirt meme about atoms, a clever science pun!

A popular T-shirt meme about atoms, a clever science pun!

The second and third pillars of evidence for the Big Bang have to do with what happens to the Universe as it expands and cools, and the consequences for matter.  Everything you and I see around us here on Earth — rocks, trees, candy bars, platypuses — is made of atoms. Atoms are a composite structure. The center is a compact heavy core called the nucleus comprised of protons and neutrons. It is surrounded by a cloud of electrons, equal in number to the protons in the nucleus.

The fact that the atom holds together is a manifestation of the forces at work. The electrons are held to the atom by virtue of attractive electrical force between them and the nucleus. If you bang two atoms together hard enough, they break apart into free nuclei and free electrons.

The nuclei, built of protons and neutrons, are held together by a very strong force that acts over short distances called the nuclear force. The nuclear force is tremendously strong, but if you bang to nuclei together hard enough, they too can be broken up into free protons and free neutrons.

In the distant past, shortly after the Big Bang, the Universe was very compact: everything in it was closer together, and extraordinarily hot. As the Universe gets smaller, it’s a bit like being squished together in the mosh pit at a concert — you can’t really move anywhere without crashing into something else. The enormous temperatures mean that everything was moving extremely fast — the hotter the temperatures, the faster the motion, the harder the crashes. If you go far enough back in time, the Universe gets so hot you can’t have atoms. If you go even farther back, it gets hotter and the Universe can’t even have atomic nuclei.

The basic constituents made during Big Bang nucleosynthesis.

The basic constituents made during Big Bang nucleosynthesis. Protons (red) and neutrons (green) bind to form the simplest atomic nuclei.

The second pillar can be understood by going back to a time in the first minute after the Big Bang. Up to this point, the Cosmos was a primordial soup of free electrons, free neutrons, and free protons, all swirling around in a maelstrom of churning energy. The Universe had started its inexorable expansion, and was cooling as a result.  By the time the Cosmos was 10 seconds old, it had cooled from its hot beginnings down to a temperature of about 2 billion degrees Celsius. At this temperature, protons and neutrons begin to stick together to form the first atomic nuclei. This process of formation is called primordial nucleosynthesis — it makes hydrogen, deuterium, helium, and small amounts of lithium and beryllium.

Big Bang theory predicts how much of each of these was synthesized in the first 15-20 minutes, a delicate balance astronomers call the primordial abundances. What astronomers can see agrees with the predictions of Big Bang nucleosynthesis.

But perhaps the most important observational signature of the Big Bang has to do with light. After the formation of the atomic nuclei, the Cosmos was still too hot to form proper atoms. Every time a nucleus tried to bind with an electron, a collision would knock the electron free. So, for the next 400,000 years, the Universe remained a seething fluid of atomic nuclei, free electrons, and energy.

When light is packed in so tightly with charged particles, like the electrons and atomic nuclei, it is not free to travel about of its own free will. It travels only a short distance before it encounters an electron, and it scatters.  Light simply can’t go very far.

(L) Before recombination, light cannot travel very far because it encounters free electrons, which interact with it causing it to scatter. (R) After the electrons bind to nuclei to make atoms, the light decouples from matter, and is free to stream through the Universe unimpeded by scattering interactions.

(L) Before recombination, light cannot travel very far because it encounters free electrons, which interact with it causing it to scatter. (R) After the electrons bind to nuclei to make atoms, the light decouples from matter, and is free to stream through the Universe unimpeded by scattering interactions.

But, after 400,000 years, the Universe cools to a balmy 3000 degrees Celsius, cool enough that each time an electron bumps into a nucleus, it binds together to form an atom. This process is called recombination. From the point of view of the light, all of the charged particles suddenly disappear (atoms are neutral, having no overall electric charge) and the Universe becomes transparent. The light can travel anywhere it wants without being impeded by the matter; astronomers call this decoupling.  The Cosmos is full of freely streaming light.

A recreation of the 1965 Cosmic Microwave Background map, covering the entire sky (Penzias and Wilson could not see the entire sky from Bell Labs). The band of stronger microwave light is the signature of the Milky Way Galaxy.

A map of the Cosmic Microwave Background across the whole sky. First detected by Penzias and Wilson in 1965, this light is the signature of ever cooling Universe after the Big Bang. The band of stronger microwave light along the center of the map is the signature of the Milky Way Galaxy.

For the next 13 billion years, the Universe continued to expand to the present day. All the while the streaming light — the signature from the birth of atoms — surfed right along.  Spacetime is stretching as the Cosmos expands, and the light from that early, hot, dense state had to give up energy to fight against the expansion, shifting to longer and longer wavelengths as time progressed. By the time light reaches the Earth today, it should appear as microwave light.  And indeed, it is. In every direction we look on the sky, we see a uniform background of microwave light called the Cosmic Microwave Background. This is the third, observational pillar, the evidence, that tells us our thinking about the Big Bang is on the right track.

This is the basic picture of the Big Bang that was developed since the late 1920’s — decades of careful comparison of observations with theoretical calculations. The refinements and developments — of both theory and experiment — continue to this day.

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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.

Getting there from here…

John C. Armstrong:

This is a post I made for my HNRS2030 students, reblogging to Write Science

Originally posted on HNRS 2030 - Our place in the Cosmos:

“The surface of the Earth is the shore of the cosmic ocean. On this shore, we’ve learned most of what we know. Recently, we’ve waded a little way out, maybe ankle-deep, and the water seems inviting. Some part of our being knows this is where we came from…We are a way for the cosmos to know itself.”

― Carl Sagan, Cosmos

As Carl says, most of what we know we’ve learned from the surface of the planet. All of what we know has been gleaned from instruments sent by humans to the near and far reaches of our solar system. The sun is 93 million miles from Earth. α Centauri is 4.4 light years further. Andromeda, our nearest large galactic neighbor, is a 2.5 million light years away.

But only careful application of the scientific method to observations of the solar system, the galaxy, and our Universe has allowed us to deduce the…

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Gravity 9: The Evolving Universe

by Shane L. Larson

Of all the fundamental forces in Nature, gravity is the weakest. What do we mean by that? Let’s forego our usual thought experiments, and do something real to demonstrate this idea.

pizzaFirst, go eat a piece of pizza (or any other food you enjoy). This is the process by which you accumulate the eenrgy needed to make your body go. Without pizza, you wouldn’t be able to do anything.  Second, go stand in the middle of the room (where you won’t hurt yourself) and jump straight up in the air, as high as you can.

Using the chemical energy from some Dr. Pepper, I can overcome the gravitational pull of the entire planet.

Energy from pizza, gives me the power to defy the gravitational pull of the entire planet.

What happened? Since I’m pretty sure most of you reading this aren’t superheroes and can’t fly, you probably ascended up in the air a bit, and then came back down to the floor. It’s an everyday sort of thing, completely ordinary. But this is science, and there are remarkable and deep truths hiding in the simplest of circumstances. So consider this:

Using some simple chemical energy, which your body gleaned by breaking down some food you ate, you were able to (momentarily) overcome the gravitational pull of the ENTIRE EARTH.

This is what we mean when we say gravity is weak. But despite this fact, it is fundamentally the most important force of Nature if we want to think about the Cosmos as a whole. It has no competitor on the largest scales imaginable, meaning that even with its weak ability, gravity is able to change the Cosmos over the long, inexorable flow of time. It made sense that general relativity could and should be used to consider the past, present and future of the Universe itself.

The night sky over the Pando Forest in central Utah. Pando is an 80,000 year old aspen grove -- it has seen almost 30 million nights like this one, but very little has changed. The constellations change over thousands of years, but the sky is still full of stars, and the Milky Way still arches over the sky, giving the impression that the Universe is unchanging. [Image: Shane L. Larson]

The night sky over the Pando Forest in central Utah. Pando is an 80,000 year old aspen grove — it has seen almost 30 million nights like this one, but very little has changed. The constellations change over thousands of years, but the sky is still full of stars, and the Milky Way still arches over the sky, giving the impression that the Universe is unchanging. [Image: Shane L. Larson]

In 1915, when Einstein first presented general relativity to the Prussian Academy of Sciences, there was precious little we knew about the Universe, though perhaps we didn’t realize it at the time. The only objects outside the solar system that we knew a lot about were stars, and many scientists (including Einstein) supposed the Universe was comprised entirely of stars. Einstein himself made one of the first attempts to use general relativity to describe the Universe. He considered the case where the Universe was uniformly filled by stars, and found a result that disturbed him — no matter what he tried, general relativity predicted the Universe would collapse. To counteract this, Einstein modified general relativity through the introduction of a “Cosmological Constant” that made the Universe slightly repulsive. The result was precisely what Einstein hoped to find, what he and most scientists thought the Universe was: static, unchanging in time. But great changes were afoot, being driven by our ability to see the Universe better than ever before.

Henrietta Swan Leavitt, in her office at the Harvard College Observatory. She made one of the most important discoveries in the history of astronomy: how to measure distances to a common type of star, known as a Cepheid variable.

Henrietta Swan Leavitt, in her office at the Harvard College Observatory. She made one of the most important discoveries in the history of astronomy: how to measure distances to a common type of star, known as a Cepheid variable.

In 1915, the largest telescope of the day was the 60-inch reflector on Mount Wilson, though it would be eclipsed two years later by the 100-inch Hooker Telescope, also on Mount Wilson. Enormous telescopes such as these were enabling us to probe the size of the Cosmos for the first time. The key to making those measurements was discovered by a pioneering astronomer at the Harvard College Observatory, Henrietta Swan Leavitt.

Delta Cephei is a naked eye star, in the lower corner of the constellation of Cepheus ("The King").

Delta Cephei is a naked eye star, in the lower corner of the constellation of Cepheus.

Leavitt was studying a class of stars known as Cepheid variables. Named for the archetype, delta Cephei, these stars are “radial pulsators” — they grow and shrink over time in a regular pattern over the course of many days. The observational consequence, if you are watching, is the brightness and the temperature the star changes. What Leavitt discovered was a regular pattern between the time it took a Cepheid star to change its appearance (its “period”), and its true brightness (its “luminosity”).

The brightness of Cepheid variables goes up and down over the course of many days. The curve here is for Delta Cephei, which changes brightness every 5.4 days. (TOP) The observed change in brightness is a direct result of the stars size pulsating in time.

The brightness of Cepheid variables goes up and down over the course of many days. The curve here is for Delta Cephei, which changes brightness every 5.4 days. (TOP) The observed change in brightness is a direct result of the stars size pulsating in time.

How does that help you measure distances? Let’s imagine a simple example here on Earth. Suppose you have a 100 Watt lightbulb and a 10 Watt lightbulb side by side.  The 100 Watt bulb looks brighter — way brighter. This is the intrinsic brightness of the bulb — it is clearly putting out more energy than its smaller, 10 Watt companion, which you can easily discern because they are right next to each other.  This intrinsic brightness at a known fixed distance is what astronomers call absolute luminosity or absolute magnitude.

Is there any way to make the 100 Watt bulb look dimmer? Yes! You can move it farther away — the farther you move it, the dimmer it appears. In fact, you could move it so far away that the 10 Watt bulb you leave behind looks brighter! By a similar token, you can make it look even brighter by moving it closer! How bright something looks when you look at it is what astronomers call apparent luminosity or apparent magnitude.

Disentangling distance and brightness is one of the most difficult problems in astronomy. Observing how bright an object is depends on two things: its intrinsic brightness, and its distance. (TOP) A bright light and a dim light are side by side at a fixed distance; one is obviously brighter than the other. (BOTTOM) If the brighter light is farther away, it can look dimmer than the closer light!

Disentangling distance and brightness is one of the most difficult problems in astronomy. Observing how bright an object is depends on two things: its intrinsic brightness, and its distance. (TOP) A bright light and a dim light are side by side at a fixed distance; one is obviously brighter than the other. (BOTTOM) If the brighter light is farther away, it can look dimmer than the closer light!

By comparing apparent brightness (how bright something looks in a telescope) to absolute brightness (how bright something would look from a fixed distance away) you can measure distance. The biggest problem in astronomy is we don’t know what the absolute brightness of objects are.

What Leavitt discovered was if you measure how long it takes a Cepheid to change its brightness, then you know its absolute brightness. Comparing that to what you see in the telescope then let’s you calculate the distance to the star! This discovery was a watershed, arguably the most important discovery in modern astronomy: Leavitt showed us how to use telescopes and clocks to lay a ruler down on the Universe. Leavitt died of cancer at the age of 53, in 1921.

Harlow Shapley.

Harlow Shapley.

Despite her untimely death, astronomers rapidly understood the power of her discovery, and began to use it to probe the size of the Cosmos. Already by 1920 Harlow Shapley had used the Mount Wilson 60-inch telescope to measure Cepheids in the globular clusters in the Milky Way. What he discovered was that the globular clusters were not centered on the Earth, as had long been assumed, but rather at some point more than 20,000 lightyears away. Shapley argued quite reasonably that the globular clusters are probably orbiting the center of the galaxy. This was the first indication that the Copernican principle extended far beyond the Solar System.

In 1924, Edwin Hubble, who Shapley had hired at Mount Wilson Observatory, made a stunning announcement — he had measured Cepheid variables in the Andromeda Nebula, and it was far away. At 2.5 million lightyears away, the Andromeda Nebula was the farthest object astronomers had ever measured the distance to. In fact, it wasn’t a nebula at all — it was a galaxy. Here, for the first time, some of the long held, cherished beliefs about Cosmology that were prevalent when Einstein introduced general relativity began to unravel. (Historical Note: Hubble’s original distance to the Andromeda Galaxy was only 1.5 million lightyears. Why? Because there are two different kinds of Cepheids, both of which can be used to measure distances, but calibrated differently! Astronomers didn’t know that at the time, so Hubble was mixing and matching unknowingly. Eventually we learned more about the Cosmos and arrived at the current known distance — science is always on the move.)

The Hubble Ultra Deep Field (UDF), showing what is unseen but can be found if you stare at an empty part of the sky for long enough.

The Hubble Ultra Deep Field (UDF), showing what can be found if you stare at an “empty” part of the sky for long enough. Virtually every object in this image is a distant galaxy.

The Universe was not full of stars…. it was full of galaxies, and those galaxies were further away than we had ever imagined. This was a dramatic discovery that shook astronomers deeply. But it was only the beginning. A scant five years later, Milton Humason and Hubble, using the 100-inch telescope at Mount Wilson, made another astonishing discovery: every galaxy they looked at was receeding away from the Milky Way, in every direction. Furthermore, the farther away the galaxy was, the faster it was receding from us.  This result is now known as “Hubble’s Law.” Humason and Hubble had stumbled on one of the great secrets Nature — the Universe was not static, as a casual comparison of the night sky from one year to the next may suggest.  But what was going on? Why were all the galaxies flying away from us, in every direction we looked? This would seem to contradict the Copernican principle that we weren’t the center of everything!

(L) Alexander Friedmann. (R) Georges Lemaître.

(L) Alexander Friedmann. (R) Georges Lemaître.

As it turns out, the answer was already in hand. It had been discovered several years before Humason and Hubble by two scientists who had sought to use general relativity to describe the Cosmos: Alexander Friedmann, a Russian physicist, and Georges Lemaître, a Belgian priest. Friedmann had used general relativity to describe a Universe that was homogeneous (the same everywhere) and isotropic (looks the same in every direction). The “Friedmann Equations,” as they are now known, describe the evolution of such a Universe as a function of time. Lemaître derived the same result in 1927, two years after Friedmann’s death. In the mid 1930’s, American physicist H. P. Robertson and UK physicist A. G. Walker showed that the only solution in general relativity describing a homogeneous and isotropic Universe as that of Friedmann and Lemaître. This is now called the FLRW (“Friedmann-Lemaître-Robertson-Walker”) Cosmology.

What the FLRW cosmology tells us is that the galaxies aren’t really flying apart from one another — if the Universe is homogeneous and isotropic, then spacetime itself is changing, stretching and deforming. The reason the galaxies are receding from one another is the spacetime between them is expanding — the Universe is getting larger, expanding all the time.

Imagine the galaxies floating in spacetime, unmoving with respect to one anther (they are stapled down to their location in spacetime). General relativity predicts that the galaxies don't move, but that spacetime itself expands, it stretches, so the distance you measure between galaxies increases.

Imagine the galaxies floating in spacetime, unmoving with respect to one anther (they are stapled down to their location in spacetime). General relativity predicts that the galaxies don’t move, but that spacetime itself expands, it stretches, so the distance you measure between galaxies increases.

Lemaître was the first person to think differently about this problem. He had the presence of mind to ask, “We see the Universe is expanding, but what if I run time backward? What did the Universe look like in the past?” In 1931, he argued that the expansion seen in every direction suggested that the Universe had expanded from some initial point, which he called the “primeval atom.” If today we see everything expanding away, and you look backward in time, it must have all been much more compressed and compact, a state which would have made it hot, and dense. Lemaître didn’t know what might have initially caused the expansion of this primeval atom into the Cosmos we see today, but he did not see that as a reason to suppose the idea was invalid.

Lemaître with Einstein in California, 1933.

Lemaître with Einstein in California, 1933.

Change in science is hard, especially when data is new and our ideas are undergoing a dramatic evolution from past modicums of thought. Einstein is widely known to have critically panned both Friedmann’s and Lemaître’s work before the discovery of the expansion, still believing in the notion of a static Universe. Once the scientific community had come to understand and accept the expansion data, it required another great leap of faith to contemplate Lemaître’s notion of a hot dense initial state. Einstein again was skeptical, as was Arthur Stanley Eddington. For more than a decade, the arguments about the idea raged, and in 1949 during a BBC radio broadcast, astronomer Fred Hoyle coined the term by which Lemaître’s “primeval atom” idea would forever be known as: the Big Bang.

All ideas in science stand on equal ground — they are valid for consideration until they are proven wrong by observations. If the Universe did indeed begin in a Big Bang, then the obvious question to ask is what signatures of that dramatic event would be observable today? As it turns out, there are many observational consequences of the Big Bang, and they all have been observed and measured by astronomers, lending confidence to Lemaître’s initial insight.  This will be the topic 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.

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.

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.

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]

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").

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]

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]

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!

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. :-)

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.

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.

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?

1280px-Black_hole_consuming_star

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).

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.

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 nuclear fusion, keeping the star from collapsing.

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.

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 fusion stops (pop the balloon), there is nothing in the star pushing outward against gravity, so the star can collapse.

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.

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]

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]

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.

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).

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 my colleague, Christian Ott, who pointed out that my original explanation of core-collapse was seriously flawed, following very old (and wrong!) 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.

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.

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 tested the Equivalence Principle on the Moon.]

(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.

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?

speedLimitBecause 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 escapse 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.

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.

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.

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.