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The Poetry of LIGO’s Gravitational Waves

Yesterday the LIGO scientific collaboration announced that they had detected the gravitational waves from the in-spiral and merger of two black holes, shown in figure 1. It would not be an overstatement to say that this result has changed science forever. As a gravitational physicist, it is hard for me to put into words how scientifically important and emotionally powerful this moment is for me and for everyone in my field. But I’m going to try. This is my attempt to capture some of the science—and the poetry—of LIGO’s gravitational wave announcement.

To read this post in blog form, see here:

The Source

About 1.3 billion years ago and as many light years away, two spinning black holes, each about thirty times the mass of the sun (one a bit bigger, one a bit smaller) ended their lives as separate entities. These two monsters had probably lived out many separate lives together: first as a binary system of two massive stars and most recently as two black holes orbiting each other. Somewhere in between, each one probably briefly outshone the entire galaxy as a core-collapse supernova.

But nothing lasts forever. Einstein tells us that mass distorts spacetime, warping distance and duration. And an accelerating mass (like a black hole in an orbit) releases some of its energy in ripples of this distortion. And so, over the billions of years of their shared lives, our black holes lost energy to these gravitational waves and their orbit decayed. They slowly, inevitably, spiralled towards each other.

As the partners approached, their orbit sped up and their slow, stately waltz gradually transitioned into a frantic tarantella toward coalescence. Eventually the partners came within about 10 kilometres of each other (people RUN that distance!). By this time, they were orbiting each other about thirty-five times per second!

The black holes spiralled towards each other at roughly the same rate about five more times before they suddenly plunged together, spinning around their shared centre of mass 250 times per second. But this stage didn’t last that long. Before even one second had passed, the black holes’ event horizons overlapped, and they merged into a single rapidly rotating object. This new single black hole oscillated wildly as it settled down into its final configuration, emitting gravitational waves all the while.

In-spiral. Merger. Ringdown. After (possibly) millions of years in a slowly decaying orbit, the final plunge took less than a fifth of a second. In those last moments, gravitational waves carried away 1.8x10^(47) Joules. That’s three times the energy contained in our Sun. Three suns, released as ripples in spacetime.

This is a computer simulation of the in-spiral and merger of two black holes much like the ones I described, produced by my friends and collaborators in the Simulating Extreme Spacetimes collaboration:

(Note that I previously had a  rough calculation of the distances involved. However, I found the real data in the paper and updated my post.)

Gravitational Waves

But what of the gravitational waves emitted by our ill-fated dance partners? These ripples in distance, in the very fabric of space and time, travel outwards from their source at the speed of light. Space is large and empty and it is mostly a lonely journey. Perhaps they pass through a cloud of gas and dust. Perhaps they don’t. If they do, the distortions of distance move the gas. Some gas particles move apart, some together. The gravitational waves might move a ring of gas particles, as shown in figure 2.

The effect is small; if the gas cloud were a few kilometres in width, the gas particles would move a distance less than one one-thousandth of the width of a proton. But they would move. And if they moved enough (they don’t) they would make a sound—the sound of the merging black holes:


Eventually, after about 1.3 billion years, on September 14th, 2015, the gravitational waves reached Earth. They were too weak to make a sound, but we could detect them. A gravitational wave is a distortion in distance, one that travels. So we can measure this distortion with a very precise ruler. And light is one of the best possible rulers.

Actually, we used two gigantic, perpendicular light-rulers, each several kilometres long. As a gravitational wave passed the rulers, it shrank distance in one direction and grew it in the other. The scientists who use these light-rulers call this discrepancy a “strain.” The paired light-rulers themselves are called “interferometers.”

We’ve built several interferometers to detect gravitational waves. There’s one in Livingston, Louisiana (, which is shown in figure 3, and one in Hanford, Washington ( There’s another in Sarstedt, Germany ( and another in Cascina, Italy ( One, destined for India, is in storage ( And another is under construction underground in Kamioka, Japan (

On that fateful day, only the detectors in Livingston and Hanford were active. (Some of the others aren’t even sensitive enough for their intended purpose. When people first started building gravity-wave detectors, it wasn’t clear how far away the sources would be.) The waves hit Livingston first, at exactly 3:50:45 AM local time. About seven-thousandths of a second later, they reached Hanford and distorted the light-ruler there, too. And a fifth of a second after that, they were gone. The sound of the black holes had passed us by and continued its journey into the void.

But they did not pass without a trace. No, the Livingston and Hanford detectors recorded their passage, shown beautifully in figure 4. The 1.3 billion-year-old waveform passed through our world and changed us forever.

Learning from the Waves

We already knew gravitational waves exist. That measurement took 30 years and won the Nobel prize ( And we had a pretty good idea of what they should look like. But the only way to confirm that they looked like we expected was to observe them. So the first thing the LIGO team did was to use sophisticated statistical techniques, without any assumption about the final waveform, to extract the true wave from the noisy signal shown in figure 4.

They then compared that waveform to the wave predicted by general relativity. The two agree spectacularly. Score one for Einstein! Of course, there are possible modifications of general relativity such that a black hole in-spiral wouldn’t look any different. So only time, and more gravitational waves, will tell if those modifications are wrong. But for now, this result is a triumph of relativity.

Independently, the LIGO team matched the raw data to a “template bank” of possible gravitational waves, each generated for a different configuration of the black holes—different masses, different rotation rates, different orientations, et cetera. Eventually, they found a match. (Actually they found several, all of which were very similar.) And, fantastically, this match agreed perfectly with the wave extracted using the statistical technique. The extracted waveforms from the two detectors, calculated in both ways, are shown in figure 5.

As a huge bonus, matching the waveform in this way told the LIGO team the masses and rotation rates of the initial black holes and the final black hole that they became.

From the ripples in spacetime, they had extracted astrophysics!

Two Detections

I want to emphasize that one reason we can be so confident in the LIGO detection is that it happened twice, once for each detector. Both detectors are extremely sensitive—they could easily see an earthquake or a car driving down the highway and misinterpret it as a gravitational wave. But the gravitational wave was seen at both detectors, and the odds of them both getting exactly the same false positive are extremely low.

What We’ve Learned

In this one detection, we’ve learned a tremendous amount…some of it very definitive, some of it not. But at the very least, we now know the following:

1. Gravitational waves look very much like we expected.

2. Black holes definitively exist. No other two objects in the universe could have been so close before colliding. Of course, we had pretty good evidence that black holes existed before now (see:

3. Binary black hole systems definitely exist. A few years ago, it was not obvious that these systems formed. To get a pair of black holes orbiting each other, you need a pair of supernovae. And that could easily destroy the orbit.

What We Stand to Learn

For most of the history of astronomy, humans relied on their unaided eyes to look at the stars. In the early 1600s, telescopes were invented and the universe opened up. Suddenly the twinkle of stars and planets resolved into gas giants and moons, clusters and nebulae and galaxies. In the 1930s, we discovered a new kind of telescope: the radio telescope. Once again, we saw space in literally a whole new light. Suddenly objects we thought we understood looked very different. And wild new things appeared, like radio pulsars. Every advance in telescope technology sparked a huge leap in our understanding of the universe. We could, essentially, see a whole new side of the universe.

This is just as big. Now we can hear the universe. We’re going to learn so, so much.

Related Reading

If you enjoyed this post and want to learn more about general relativity and gravitational waves, you may be interested in my series on #howgrworks :

1. In Galileo Almost Discovered General Relativity, I explain the motivating idea behind general relativity and how Galileo almost figured it out.

2. In General Relativity Is the Dynamics of Distance, I explain how simple arguments can tell us that gravity stretches or shrinks space and time.

3. In General Relativity Is the Curvature of Spacetime, I describe how the distortion of distance and duration from gravity translates into curvature, and how this bends the path of light (and other stuff).

4. In Distance Ripples, I explain how gravitational waves work.

5. In Our Local Spacetime, I present a visualization of the curvature of spacetime near Earth.

6. In Classical Tests of General Relativity, I explain a little history.

7. In the Geodetic Effect, I talk about how we can use gyroscopes to directly measure the curvature of spacetime.

Further Reading

Here are some nice lay resources on the recent LIGO discovery. (Thanks to +Johnathan Chung​  for finding some of these.)

1. This is LIGO’s online press release. It contains, for example, a number of fantastic videos.

2. In this video, Brian Green explains the take-home message.

3. This is a great explanation of gravitational waves by quantum gravity physicist +Sabine Hossenfelder

4. This is the lay article about the discovery by the American Physical Society:

5. +Yonatan Zunger​ wrote up this nice explanation:

6. This is a nice article by +Brian Koberlein​  on the existence of black holes.

7. This is the press release for the Nobel prize awarded for the indirect discovery of gravitational waves:

8. This Nature article talks about several questions we can answer with gravitational waves:

9. +annarita ruberto​ provides a nice blue-by-blow of the detection:

Scholarly Reading

For the very brave, here are my academic sources.

1. This is the LIGO detection paper. Already peer reviewed. Kudos to the LIGO collaboration for going through peer-review before announcing their result!

2. This is the LIGO paper describing how they extracted the mass and spin of the black holes.

3. This paper describes the LIGO team’s investigation of whether or not the December detection could have been a mistake. (Obviously, they concluded it was real, or I wouldn’t be writing this blog post…)

4. This paper describes the LIGO team’s model-agnostic approach to measuring the wave. This is how they know they’re not falling victim to wishful thinking.

5. This technical paper describes how the LIGO team estimated their noise and error

6. This paper discusses how we’ve tested general relativity with this observation.

7. This is an assessment of the rates of black hole binary mergers in the universe based on the measurements LIGO has made so far.

8. This is a related paper on what that means for detectors.

9. This paper is a search for neutrinos from the black hole merger that LIGO observed. (None were found.)

10. This is the population model for binary black holes which may be wrong.

#howgrworks #physics #science #ScienceEveryDay #gravitationalwaves #astronomy #astrophysics 
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If we can't predict the weather next month how can we predict climate change?

The answer is hidden in chaos theory.

This is a common misconception about how climate models work and this post is inspired by a question in the +Science on Google+​​​ community.

The climate is a so-called "chaotic system." See:

One simple example of a chaotic system is the Lorentz attractor:

In a chaotic system, the behaviour of the system at any given time is very hard to understand. This is why we can't predict the weather very well.

But look at the movie of the Lorentz attractor below. Notice anything?

The particle moves all over the place. The motion is very hard to predict. But it's usual or average position is predictable! The particle is usually along those curves!

This is typical of chaotic systems and the climate is the same way. We can't predict the weather next week. But we can predict the general behavior of the average weather over many years. And this is why you should trust predictions about climate change.

The science is definitive. Global average temperatures are getting warmer and this is caused by human activity.

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An Explanation for the EM Drive? Probably not.

This news is a little old, but you may have seen an article claiming that scientists might have come up with an explanation for the EM drive. One such article, which does a good job summarizing the situation, is this one:

The paper it references is peer-reviewed and open-access. You can find it here if you're interested. I worked through it.

As the article (and Google plus's very own +Brian Koberlein​​​​​​​​​​) say:

the new paper re-interpret's the quantum vacuum in such a way that the em drive is not reactionless, it emits light.

So what does this mean?

The vacuum

Empty space isn't really empty. Rather it's buzzing with all sorts of particles that appear and disappear very quickly, as permitted by the Heisenberg uncertainty principle. These particles are always created in pairs of particles and antiparticles so that momentum, for example, is conserved.

In essence, the claim is that the electric field provided by the em drive pushes some of these particles out the back of the drive and leaves others inside, breaking up the pairs.

+Brian Koberlein​​​​​​​​​ ​mentions the "Unruh effect," where this happens because of acceleration. And most people know about Hawking radiation where this happens because of the gravity due to a black hole.


So if the claim is true, this would mean the device does not violate Newton's laws. And it's not "impossible" after all.

On the other hand, it would also mean a more efficient form of thrust would just be to attach a bunch of LEDs to the back of your spaceship.

This would also put an upper bound on the power and efficiency of the drive to be the same as other light-based devices. It could not get us to mars in 40 days.

The claim would, in other words, explain the em drive but also immediately make it obsolete.

Reasons to be Sceptical

The journal article in question is not even a little bit quantitative. There are no calculations in it whatsoever. It's essentially just an argument, in words that the em drive could be caused by an effect like this.

That's not how science is done and, to be honest, I'm annoyed this article got through peer-review. If I had reviewed this article, I would not have recommended it for publication. It's not a theory until it makes a quantitative, testable prediction.

And even if the prediction isn't testable, the authors should back up their ideas with some kind of calculation. Mathematics are how theoretical physicists keep themselves honest. It's much harder to fool oneself with maths than with words.

It's plausible that an effect like the Unruh effect and Hawking radiation could, maybe create an effect like the em drive, but the only way to tell is to do some math and make a prediction. And the authors of this paper did not do that.

So let me be clear.

This paper is interesting but it is neither an authoritative explanation for the em drive nor proof that it works. This isn't even a theory.


As the article said. If something seems too good to be true, it probably is.

In my opinion, the EM drive probably doesn't need an explanation because it probably doesn't work. We don't ask people to explain how broken chairs work.

Other stuff

Thanks to +Derek Adjei for linking to this article in the +Science on Google+ community.

Full disclosure, my discussion here is a copy-paste of my comment in the original post:

Image is the EM drive inventor, Roger Shawyer. Credit due to Roger Shawyer, Satellite Propulsion Research Ltd via IBTimes (

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The Worst Prediction in the History of Physics and How Astrophysics can Help us Understand Quantum Gravity

So I did an interview for the podcast "Tilting at the Universe." The interviewer asked me about dark energy, modified gravity, and numerical relativity.

It was a lot of fun I think I conveyed a lot of what excites me about astrophysics and cosmology these days. So check it out!

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The Direction of LIGO's Gravitational Waves

On September 14th, 2015, the LIGO gravitational wave observatory network [1] detected the gravitational waves from the merger of two black holes [2]. In moments, the LIGO team estimated (very broadly) where the black holes were located in the sky; these regions are highlighted in figure 1. Today I tell you how they figured this out. And why it's important.

(Those who wish to read this post in blog form can do so here:

Electromagnetic Counterparts

First, let's talk about why the direction of the waves is important. When LIGO detects gravitational waves, those waves can tell us an awful lot about their source. Just from the waveform, LIGO learned that the waves from September 14th came from the merger of two black holes, each about thirty times the mass of the sun, about 1.3 billion lightyears away [3]. And from that information, the LIGO team was able to extrapolate a surprising amount about the astrophysics of the stars that became those black holes [4].

But we'd like to learn more. Are the black holes immersed in a disk of hot gas? Or are they alone, as we expect? What about other systems? Most astrophysicists expect that the merger of two neutron stars [5] (or a black hole and a neutron star [6]) will produce both a short gamma ray burst [7] and a burst of gravitational waves. A detection of both at the same time would confirm this hypothesis. We know that when a star runs out of fuel, it may undergo a core-collapse supernova [8]. Unfortunately, the precise mechanisms of the supernova explosion are unknown.

To extract this information, we can't rely just on gravitational waves. We need electromagnetic waves, too. And this means looking at the source with optical telescopes, infrared telescopes, radio telescopes, gamma ray and X-ray telescopes, basically any telescope we can get our hands on. We even try to look with neutrino detectors. But looking means we need to know where to look. And that's where LIGO's skymap in figure 1 comes in.

So how did LIGO generate that? In the sections below, I'll tell you about several pieces of information that LIGO can use to estimate the direction from which the waves came.

Time of Arrival

The most important piece of information LIGO has is the time the wave arrives at the detector. Or, more precisely, the times the waves arrive at the different detectors. LIGO currently has two gravitational wave detectors, one in Livingston, Louisiana, and one in Hanford, Washington. They're about 3000 kilometers apart (through the ground), as shown in figure 2.

At normal human walking speed, it takes 758 hours to get between the two observatories. If you could travel at the speed of light and through the ground (like gravitational waves), then you could make it from LIGO Livingston to LIGO Hanford in about 10 milliseconds. But there's another reason why you can't travel like a gravitational wave: You're finite. You can only bet on Livingston OR Hanford, not both at the same time. Waves, on the other hand, are spread out. Just as, when you stand on the beach, an incoming wave can both tickle your toes and destroy your sister's sand castle a few meters down the shore, the same gravitational wave can be present at both LIGOs Livingston and Hanford. This means that, if the waves came from "above" North America (or indeed any direction perpendicular to a straight line drawn between the two detectors on a map), as shown in figure 3, LIGOs Livingston and Hanford would detect the waves at exactly the same time, with no delay.

But this depends very much on the direction. If you draw a line between LIGOs Livingston and Hanford, and if a gravitational wave comes from a direction parallel to that line, as in figure 4, one of the detectors will measure the waves a full 14.4 milliseconds before the other!

The waves that LIGO detected on September 14th arrived at Livingston about 7 milliseconds before Hanford. So their direction of origin lies somewhere between the two extremes I've outlined. And this piece of information helped LIGO narrow down where they came from. Indeed, for the September 14th detection, this was the most significant directional hint by far.

Detector Sensitivity

We can't point the LIGO detectors the same way you would point a telescope: they're what we call "all-sky" detectors. However, they are most sensitive to waves coming from overhead. This is baked into how the detectors are built and how gravitational waves work. As I've described in the past [9], a gravitational wave is a distortion in distance [10] that travels. But, and this is very important, the distortion is perpendicular to the direction of motion, as shown in figure 5. Just as an ocean wave travelling inland makes the water rise and fall, a gravitational wave travelling to your left might make you alternatively taller and shorter.

The LIGO detectors are designed to measure this distortion. They're essentially two huge, perpendicular rulers. But this means that, for them to see anything, the distortion must be aligned with the arms of the detector. Figure 6 compares the two most extreme possibilities. If the gravitational wave (purple) comes from directly above LIGO, it is most sensitive. If the wave comes from a direction in the same plane as the two arms of the detector, LIGO will be significantly less sensitive.

Since LIGO Livingston and LIGO Hanford are at different places on the surface of the Earth (which is round), they have slightly different orientations with respect to an incoming gravitational wave. The LIGO team can use this information and the relative signal strengths at each detector to help infer the direction of the wave. With only two detectors, this piece of information is less significant than the delayed time of arrival, but every little bit helps. And in the future, when there are more gravitational wave detectors around the world (Virgo turns on next year [11]!), orientation will help much more.


There is a complication to the orientation story I told you above. The complication is, of course, that there is more than one way to orient a gravitational wave. The wave has a direction of motion, but it's also possible to rotate the distortion that it produces around that direction. Gravitational waves have two fundamental "polarizations," called "+" and "x" respectively. And you can get one by rotating the other. Figure 7 shows the action of a gravitational wave on a ring of test particles for the + and x polarizations of a gravitational wave. The motion is the same, but the direction differs by 45 degrees.

The wave can also be a combination of the two polarizations, in which case the rotation rotates around the axis, either clockwise or counter-clockwise, as shown in figure 8. These are called the "left" and "right" polarizations respectively.

If a wave is left- or right-polarized, LIGO will be able to see it. But if a LIGO detector is oriented for + polarization and the incoming wave is x-polarized, sensitivity would be reduced in a way that has little bearing on the direction the wave came from. It's hard to distinguish loss of sensitivity from polarization to loss of sensitivity from orientation... especially with only two detectors. In the future, when we have more detectors, it will be easier to distinguish polarization from orientation.


The LIGO team takes all this information (and more, such as the masses of the originating black holes) and plugs it into sophisticated computer codes that, given times of arrival and detector sensitivity, assign a probability to each piece of the sky indicating how likely it is that the gravitational waves came from that direction. Some of the codes (essentially) randomly generate a huge number of possible waveforms and directions and see which combination yields times of arrival and sensitivities that match the physical measurement. This is called a Monte Carlo algorithm [12] and it has applications everywhere in physics. For example, I've used it in quantum gravity simulations [13]. Other codes invert this question and ask what the probability of a direction is given the measurements we have. This is called a Bayesian algorithm.

To ensure accuracy (and to avoid putting their eggs all in one basket), the LIGO team uses several algorithms. The Bayesian algorithm is extremely fast, so the LIGO team can use it to inform telescopes where to look immediately. One of the Monte Carlo algorithms is almost as fast. Finally, there is a much slower algorithm which uses astrophysics information extracted from the waveform (such as the masses of the black holes) to make an inference. This algorithm is run later.

It is in these algorithms that the magic lies--magic which took many years of hard work by the LIGO team to develop. But that hard work was more than worth it.

The Results

Figure 1 shows the locations in the sky from which the gravitational waves most likely came from, as determined by LIGO's algorithms. What it doesn't show you is the more than sixty teams that used this information to search the sky for counterparts to the gravitational waves, optical or otherwise. Their efforts are summarized in figure 9. The green panes represent measurements by optical or infrared telescopes. The red, radio. The blue, X-ray. Two gamma ray detectors and the world's most sensitive neutrino detectors, which are all-sky like LIGO, searched their data for correlations with LIGO. They didn't find anything definitive. But with LIGO detecting gravitational waves and the search infrastructure in place, it's only a matter of time until we see something amazing.

The LIGO collaboration consists of more than nine hundred scientists. But the combined search for counterparts, optical and otherwise, consists of at least as many. The team that looks for neutrinos is more than 300 people. [14] (The neutrino team doesn't need this sky map, since their detector is all-sky.) Figure 9 therefore captures the beginning of one of the biggest-ever collaborations in science. During a LIGO science run (when LIGO is actively taking data), scientists all over the world are poised, ready to aim their telescopes at the sky and search the sources of gravitational waves. It's a stunning tribute to the collaborative spirit of science and to the things we can accomplish when we work together.

A Possible Gamma Ray Burst Counterpart?

All this hard work might already be bearing fruit. As I've discussed before, we believe that the merger of a neutron star and a black hole (or two neutron stars) will produce a gamma ray burst [15]. Now, it's hard to imagine that the merger of two black holes, which is what LIGO measured on September 14, could produce such a thing. But people were looking anyway. (They didn't yet know that LIGO had seen a black hole merger... just that LIGO had seen something. And anyway, you never know.) And one of the gamma ray detectors, Fermi's GBM, thought they saw something.

When LIGO announced their detection, the Fermi team went back through the data their detector had collected and looked for excess power from the detector. They found what looked like an event and, after much analysis, concluded that the probability it was a false alarm was approximately 0.22%. This is certainly exciting, but physicists are a cautious lot and the false alarm probability isn't low enough to claim a definitive detection... especially when the other gamma ray detector looking for signal didn't see anything.

To explain this event, there have been some crazy ideas, like the possibility that both of LIGO's black holes emerged from the collapse of a single enormous star [16]. I'm excited that something exotic might be happening... but I also urge caution. We need more gravitational wave detections to understand what's going on.

We've entered the age of gravitational wave astronomy. It's only a matter of time.


Thanks to +Greg Roelofs and David Shoemaker(!) for their corrections.

Related Reading

If you enjoyed this post, you may enjoy some of these, too:

1. In this post, I describe some of the astrophysics we extracted from LIGO's detection of gravitational waves.

2. In this post, I attempt to capture some of the science--and poetry--of LIGO's detection of gravitational waves.

3. In this post, I describe how gravitational waves work.

4. In this post, I describe research efforts to simulate a short gamma ray burst.

5. Astronomy using gravitational waves, light, and subatomic particles is called multi-messenger astronomy. I wrote about that, and why it's exciting, here.


Here are the papers I summarized in this post:

1. This is the paper summarizing the generation of the skymap and the efforts to look for electromagnetic counterparts.

2. This is the paper summarizing the search for neutrino counterparts of LIGO's gravitational waves.

3. This is the paper by the FERMI team describing their possible detection of a gamma ray burst counterpart.

4. This is the original LIGO detection paper.

5. There is a large body of literature on localizing the source of gravitational waves. This paper is on LALInference, the tool that uses astrophysics inferred from the gravitational waves to help pinpoint direction.

6. This paper is on the fast Bayesian inference library that also searches for direction.

7. This paper discusses two the performance of two algorithms: coherent WaveBurst and LALInference.

8. This paper discusses extracting the polarization and including detector orientation in the inference.

9. This paper contains the crazy idea of two black holes emerging from a single star.

10. Astrophysicist Ethan Siegel evaluates the single star proposal in this popular article. Both Siegel and I think this proposal is pretty unlikely to be true.



#Science #physics #astronomy #ScienceSunday +ScienceSunday #LIGO #GravitationalWaves  
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The Black Holes that Created LIGO’s Gravitational Waves

A little over a week ago, the LIGO collaboration detected gravitational waves [1] emitted during the in-spiral and merger of two black holes. And the world's scientists, myself included, collectively went bananas [2]. Last week, I attempted to summarize the event and capture some of the science, and poetry, that has us so excited [3]. In short, gravitational waves provide us a totally new way to look at the universe. LIGO's one detection has already provided us with a wealth of information about gravity and astrophysics. Today, I summarize some of what we've learned.

(Those who want to read this post in blog form can find it here:

Black Holes As We Knew Them

In the dark ages before LIGO's detection, we expected black holes to fall into roughly two categories: supermassive and solar mass. Weighing in at millions or even billions of times the mass of our sun, supermassive black holes are the titans of the universe. Most galaxies, including our own [4], have a supermassive black hole at their centre. These monsters can drive some of the most energetic events in the universe. For example figure 2 shows the galaxy Centaurus A. The blue stuff you see is radiation being emitted by matter being launched away from the galaxy by its supermassive black hole at a huge fraction of the speed of light.

Solar mass black holes, on the other hand, are tiny in comparison. In the past, we found solar-mass black holes by looking for the light emitted by stuff falling into them [5]. Most of the black holes we found this way were between five times the mass of the sun and ten times. Certainly the biggest we had ever found were about twenty times more massive than the sun. Since we hadn't found any "solar mass" black holes bigger than that, people questioned whether they even existed. Perhaps there was some mechanism preventing their formation.

Indeed there are good reasons to believe such a mechanism exists. A solar mass black hole is formed by the collapse of a massive star after it runs out of nuclear fuel. And the more massive the black hole, the more massive its progenitor star must have been. So there is a limit to the maximum mass of a solar-mass black hole; it's based on the mass and make-up of the star from which it formed.

Stellar Winds and Mass

Throughout their lives, stars don't just emit light. They constantly spit out charged particles like electrons and protons, which then move away from them at high speed. This rapid stream of charged particles is called a stellar wind [6]. Our own star is no exception. Figure 3 shows a comet, Comet Encke, in transit. The comet tail acts as a solar windsock; it is blown away from the sun by all of the charged particles the sun is spitting out.

Stellar winds can have a pretty big effect on the final mass of a star. The material in a stellar wind comes from the star itself; it's literally blowing itself away, losing mass over time. So a star with strong stellar winds will lose a lot of mass by the time it becomes a black hole. Strong solar winds in the progenitor star means low mass black holes.

There's another factor, too: what the star is made of.

The Life Cycle of Stars

Stars are mostly composed of hydrogen gas. Indeed, young stars exist by harnessing the energy released when hydrogen is converted into helium [7]. As a star ages, it runs out of hydrogen in its core and so converts helium into heavier elements like carbon and oxygen. And when it runs out of helium, it converts those elements into ever-heavier elements, all the way up to iron. But something goes wrong with iron. When a star fuses iron into, say, zirconium, it doesn't gain energy, it loses it!

So when the star runs out of elements lighter than iron, fusion stops. But without the heat from fusion, the star can no longer resist its own gravity and it undergoes core collapse [8]. The star may explode in a fantastic supernova or it might simply collapse inward. In either case, the end result can be a black hole or a neutron star [9]. The precise mechanisms of core-collapse are not adequately understood; this is one of the things we want to learn via gravitational wave astronomy. [10] A supernova is energetic enough to fuse even heavier elements and eject them into the universe. So over time, as stars form and fuse elements, the amount of heavy elements in the universe increases. This is called stellar nucleosynthesis [11].

(The story I just described applies only to stars of sufficient mass. Lower-mass stars burn less quickly and can move more of their light elements to their core to burn them. Moreover, they simply cannot produce the pressure required to fuse the heavier elements. So light stars burn for a long time and eventually fade into white dwarves [12], but they never undergo core collapse.)


As stars go through their life cycles, the number of heavy elements in the universe increases... and so does the number of heavy elements in stars. A star formed in the very early universe will have very few heavy elements. A star formed more recently will have more of them. Scientists quantify this with metallicity [13], which is defined as the fraction of the star that isn't either hydrogen or helium. Metallicity is always small, otherwise the star wouldn't be a star. But as a general rule, stars formed recently have a higher metallicity than stars that formed in the distant past [14].

Simulations tell us that if the star goes supernova, metallicity has a big effect on the mass of the resulting black hole. The relationship isn't obvious---it has to do with the chemical and nuclear reactions going on inside the star---but the result is (qualitatively at least) pretty clear. Stars with higher metallicity expel more of their material when they go supernova and thus result in smaller black holes.

LIGO's Black Holes

The gravitational waves LIGO detected came from the in-spiral and merger of two black holes about 1.3 billion years ago and as many light-years away [15]. By carefully analysing the waveform, the LIGO team determined that each black hole had a mass about thirty times that of the sun. And this is a bit of a surprise [16]. We didn't know that solar-mass black holes could get that big! But these black holes clearly were that big. So what does this say about the stars from which they formed?

(Well, to be more accurate, we didn't know that TWO solar mass black holes could get that big and then merge. The merger of two black holes, each fifteen times the mass of the sun would produce a black hole that's thirty times the mass of the sun. But it seems incredibly unlikely that such a black hole would end up in orbit around another black hole that formed in the same way.)

The stars that collapsed into LIGO's black holes must have been very large. This means that they cannot have had a very strong stellar wind, because if they did, they wouldn't have been massive enough by the time they went supernova. Similarly, they must have had very low metallicity---if the metallicity was too high, the supernova would have ejected too much material and the remnant black hole wouldn't be large enough. And this means that the stars that became LIGO's black holes might have been some of the first stars ever formed in the universe.

These facts are summarized in figure 4. The red and blue horizontal bars are LIGO's black holes. The left panel shows black hole mass as a function of metallicity for both strong and weak solar winds. The bottom-left corner is high-metallicity with low mass and the top-right corner is low-metallicity and high mass. If the solar wind is too high, the black hole will never be sufficiently massive, no matter the metallicity. The right panel shows the mass of the black hole as a function of the mass of the original star for a few different metallicities. This tells us that if the metallicity is too high, the supernova will jettison too much mass and a sufficiently heavy black hole will never form.

Forming the Binary

When LIGO's black holes merged, they were orbiting each other. There are two ways this probably happened. Either they began their lives together as a binary star system (most stars form this way) or they began their lives separately but eventually found each other. In the latter case the stars probably would have formed in a dense cluster of stars, gone supernova, then "sunk" into the centre of the cluster and joined together. It's not possible to figure out from which of these situations LIGO's black holes emerged.

We'll Learn More Soon

LIGO has only claimed one detection. And yet even this one measurement has provided us with a wealth of information about astrophysics and (as I'll discuss in a later post) general relativity. From this one detection, we've been able to tenuously extrapolate a lot about the stars that formed the black holes LIGO heard. But with more detections we'll know more. We'll learn, for example, whether these very massive black holes are the exception or the norm. And we'll learn more about their distribution in the sky. Through gravitational wave astronomy, LIGO has opened a whole new lens through which we can view the universe. And that effort is already bearing fruit.

Related Reading

If you enjoyed this post, you may like reading my other posts on LIGO and black holes.

1. In this post, I attempt to capture the science---and poetry---of LIGO's gravitational waves.

2. In this post, I describe how the merger of a neutron star and a black hole can produce a gamma ray burst.

3. In this post, I discuss Carlo Rovelli's speculative proposals that black holes can explode.

4. In this post, I describe why black holes glow.

Technical Resources

1. This is LIGO's paper on how they figured out the masses of the black holes.

2. This is LIGO's paper on the astrophysics of the black holes they measured.

3. This is one of the many papers that calculated black hole remnant mass as a function of metallicity.

4. This is NASA's press release for Comet Encke.



#Science #ScienceSunday #Physics #Space #LIGO #AstroPhysics #GravitationalWaves  
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The Black Hole that Generated LIGO's Gravitational Waves

So here's the Earth. Usual story. But see that black sphere up in Canada? That's roughly the size of the 60 solar mass black hole that resulted from the merger LIGO observed.

Think about that. Sixty times the mass of the sun. Fits handily in Colorado.

Image source:

#physics #ligo #science #gravitationalwaves  

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So Many Fantastic, Insightful Questions!

This has been a great week for science, with the detection of #gravitationalwaves. It's been a flurry of excitement and elation at the +Perimeter Institute for Theoretical Physics.

But I've also had a blast interacting with you all online. I've gotten a huge number of great questions from people on Google+, Twitter, Reddit, and the comments on my blog. Thanks to all of you. You all rock.

On Google+, great questions have come from (at least) the following people. There are probably more people who deserve to be on this list and I just missed you.
+Kurt Lercher
+Rhys Taylor
+Gary Matthews
+Ólafur Jens Sigurðsson
+Arbab Irfan
+Phoenix Williams (who I can't tag for some reason)
+James Carlson
+Paul O'Malley
+Wardet Masr
+Bruce Elliott
+Raj Panchal (who I also can't tag)
+Charles Filipponi
+Ólafur Jens Sigurðsson 

(Image credit:

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LIGO Detected Gravitational Waves!

Here is the real waveform, generated by two merging black holes, each about 30 times more massive than the sun.

The figure came from this paper, which I am still trying to read, because the journal's server has been hugged to death by eager scientists:

Stay tuned. I'll be live-tweeting the panel at the +Perimeter Institute for Theoretical Physics (streamed here: in about an hour. And I'll write up a blog post tonight.

My twitter handle is @thephysicsmill and I'll use the hashtags #PILIGO   and #gravitationalwaves  

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Chirp for LIGO

So the gravitational waves that LIGO can detect, if they exist, are about the same frequency as sound. This, and excitement for the Thursday announcement has inspired +Katie Mack​ to start the #chirpforLIGO hashtag on twitter where we all do our best to pretend we're gravitational waves. Here's mine.

Original hashtag is here:
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