# Advanced LIGO detects gravitational waves!

The first observing run (O1) of Advanced LIGO was scheduled to start 9 am GMT (10 am BST), 14 September 2015. Both gravitational-wave detectors were running fine, but there were few a extra things the calibration team wanted to do and not all the automated analysis had been set up, so it was decided to postpone the start of the run until 18 September. No-one told the Universe. At 9:50 am, 14 September there was an event. To those of us in the Collaboration, it is known as The Event.

The Event’s signal as measured by LIGO Hanford and LIGO Livingston. The shown signal has been filtered to make it more presentable. The Hanford signal is inverted because of the relative orientations of the two interferometers. You can clearly see that both observatories see that same signal, and even without fancy analysis, that there are definitely some wibbles there! Part of Fig. 1 from the Discovery Paper.

## Detection

The detectors were taking data and the coherent WaveBurst (cWB) detection pipeline was set up analysing this. It finds triggers in near real time, and so about 3 minutes after the gravitational wave reached Earth, cWB found it. I remember seeing the first few emails… and ignoring them—I was busy trying to finalise details for our default parameter-estimation runs for the start of O1. However, the emails kept on coming. And coming. Something exciting was happening. The detector scientists at the sites swung in to action and made sure that the instruments would run undisturbed so we could get lots of data about their behaviour; meanwhile, the remaining data analysis codes were set running with ruthless efficiency.

The cWB algorithm doesn’t search for a particular type of signal, instead it looks for the same thing in both detectors—it’s what we call a burst search. Burst searches could find supernova explosions, black hole mergers, or something unexpected (so long as the signal is short). Looking at the data, we saw that the frequency increased with time, there was the characteristic chirp of a binary black hole merger! This meant that the searches that specifically look for the coalescence of binaries (black hole or neutron stars) should find it too, if the signal was from a binary black hole. It also meant that we could analyse the data to measure the parameters.

A time–frequency plot that shows The Event’s signal power in the detectors. You can see the signal increase in frequency as time goes on: the characteristic chirp of a binary merger! The fact that you can spot the signal by eye shows how loud it is. Part of Fig. 1 from the Discovery Paper.

The signal was quite short, so it was quick for us to run parameter estimation on it—this makes a welcome change as runs on long, binary neutron-star signals can take months. We actually had the first runs done before all the detection pipelines had finished running. We kept the results secret: the detection people didn’t want to know the results before they looked at their own results (it reminded me of the episode of Whatever Happened to the Likely Lads where they try to avoid hearing the results of the football until they can watch the match). The results from each of the detection pipelines came in [bonus note]. There were the other burst searches: LALInferenceBurst found strong evidence for a signal, and BayesWave classified it clearly as a signal, not noise or a glitch; then the binary searches: both GstLAL and PyCBC found the signal (the same signal) at high significance. The parameter-estimation results were beautiful—we had seen the merger of two black holes!

At first, we couldn’t quite believe that we had actually made the detection. The signal seemed too perfect. Famously, LIGO conducts blind injections: fake signals are secretly put into the data to check that we do things properly. This happened during the run of initial LIGO (an event known as the Big Dog), and many people still remembered the disappointment. We weren’t set up for injections at the time (that was part of getting ready for O1), and the heads of the Collaboration said that there were no plans for blind injections, but people wanted to be sure. Only three or four people in the Collaboration can perform a blind injection; however, it’s a little publicised fact that you can tell if there was an injection. The data from the instruments is recorded at many stages, so there’s a channel which records the injected signal. During a blind-injection run, we’re not allowed to look at this, but this wasn’t a blind-injection run, so this was checked and rechecked. There was nothing. People considered other ways of injecting the signal that wouldn’t be recorded (perhaps splitting the signal up and putting small bits in lots of different systems), but no-one actually understands all the control systems well enough to get this to work. There were basically two ways you could fake the signal. The first is hack into the servers at both sites and CalTech simultaneously and modify the data before it got distributed. You would need to replace all the back-ups and make sure you didn’t leave any traces of tampering. You would also need to understand the control system well enough that all the auxiliary channels (the signal as recorded at over 30 different stages throughout the detectors’ systems) had the right data. The second is to place a device inside the interferometers that would inject the signal. As long as you had a detailed understanding of the instruments, this would be simple: you’d just need to break into both interferometers without being noticed. Since the interferometers are two of the most sensitive machines ever made, this is like that scene from Mission:Impossible, except on the actually impossible difficulty setting. You would need to break into the vacuum tube (by installing an airlock in the concrete tubes without disturbing the seismometers), not disturb the instrument while working on it, and not scatter any of the (invisible) infra-red laser light. You’d need to do this at both sites, and then break in again to remove the devices so they’re not found now that O1 is finished. The devices would also need to be perfectly synchronised. I would love to see a movie where they try to fake the signal, but I am convinced, absolutely, that the easiest way to inject the signal is to collide two black holes a billion years ago. (Also a good plot for a film?)

There is no doubt. We have detected gravitational waves. (I cannot articulate how happy I was to hit the button to update that page! [bonus note])

I still remember the exact moment this hit me. I was giving a public talk on black holes. It was a talk similar to ones I have given many times before. I start with introducing general relativity and the curving of spacetime, then I talk about the idea of a black hole. Next I move on to evidence for astrophysical black holes, and I showed the video zooming into the centre of the Milky Way, ending with the stars orbiting around Sagittarius A*, the massive black hole in the centre of our galaxy (shown below). I said that the motion of the stars was our best evidence for the existence of black holes, then I realised that this was no longer the case. Now, we have a whole new insight into the properties of black holes.

## Gravitational-wave astronomy

Having caught a gravitational wave, what do you do with it? It turns out that there’s rather a lot of science you can do. The last few months have been exhausting. I think we’ve done a good job as a Collaboration of assembling all the results we wanted to go with the detection—especially since lots of things were being done for the first time! I’m sure we’ll update our analysis with better techniques and find new ways of using the data, but for now I hope everyone can enjoy what we have discovered so far.

I will write up a more technical post on the results, here we’ll run through some of the highlights. For more details of anything, check out the data release.

### The source

The results of our parameter-estimation runs tell us about the nature of the source. We have a binary with objects of masses $36^{+5}_{-4} M_\odot$ and $29^{+4}_{-4} M_\odot$, where $M_\odot$ indicates the mass of our Sun (about $2 \times 10^{30}$ kilograms). If you’re curious what’s going with these numbers and the pluses and minuses, check out this bonus note.

Estimated masses for the two black holes in the binary. $m_1^\mathrm{source}$ is the mass of the heavier black hole and $m_2^\mathrm{source}$ is the mass of the lighter black hole. The dotted lines mark the edge of our 90% probability intervals. The different coloured curves show different models: they agree which made me incredibly happy! Fig. 1 from the Parameter Estimation Paper.

We know that we’re dealing with compact objects (regular stars could never get close enough together to orbit fast enough to emit gravitational waves at the right frequency), and the only compact objects that can be as massive as these object are black holes. This means we’re discovered the first stellar-mass black hole binary! We’ve also never seen stellar-mass black holes (as opposed to the supermassive flavour that live in the centres of galaxies) this heavy, but don’t get too attached to that record.

Black holes have at most three properties. This makes them much simpler than a Starbucks Coffee (they also stay black regardless of how much milk you add). Black holes are described by their mass, their spin (how much they rotate), and their electric charge. We don’t expect black holes out in the Universe to have much electric charge because (i) its very hard to separate lots of positive and negative charge in the first place, and (ii) even if you succeed at (i), it’s difficult to keep positive and negative charge apart. This is kind of like separating small children and sticky things that are likely to stain. Since the electric charge can be ignored, we just need mass and spin. We’ve measured masses, can we measure spins?

Black hole spins are defined to be between 0 (no spin) and 1 (the maximum amount you can have). Our best estimates are that the bigger black hole has spin $0.3_{-0.3}^{+0.5}$, and the small one has spin $0.5_{-0.4}^{+0.5}$ (these numbers have been rounded). These aren’t great measurements. For the smaller black hole, its spin is almost equally probable to take any allowed value; this isn’t quite the case, but we haven’t learnt much about its size. For the bigger black hole, we do slightly better, and it seems that the spin is on the smaller side. This is interesting, as measurements of spins for black holes in X-ray binaries tend to be on the higher side: perhaps there are different types of black holes?

We can’t measure the spins precisely for a few reasons. The signal is short, so we don’t see lots of wibbling while the binaries are orbiting each other (the tell-tale sign of spin). Results for the orientation of the binary also suggest that we’re looking at it either face on or face off, which makes any wobbles in the orbit that are there less visible. However, there is one particular combination of the spins, which we call the effective spin, that we can measure. The effective spin controls how the black holes spiral together. It has a value of 1 if both black holes have max spin values, and are rotating the same way as the binary is orbiting. It has a value of −1 if the black holes have max spin values and are both rotating exactly the opposite way to the binary’s orbit. We find that the effective spin is small, $-0.06_{-0.18}^{+0.17}$. This could mean that both black holes have small spins, or that they have larger spins that aren’t aligned with the orbit (or each other). We have learnt something about the spins, it’s just not too easy to tease that apart to give values for each of the black holes.

As the two black holes orbit each other, they (obviously, given what we’ve seen) emit gravitational waves. These carry away energy and angular momentum, so the orbit shrinks and the black holes inspiral together. Eventually they merge and settle down into a single bigger black hole. All this happens while we’re watching (we have great seats). A simulation of this happening is below. You can see that the frequency of the gravitational waves is twice that of the orbit, and the video freezes around the merger so you can see two become one.

What are the properties of the final black hole? The mass of the remnant black holes is $62^{+4}_{-4} M_\odot$. It is the new record holder for the largest observed stellar-mass black hole!

If you do some quick sums, you’ll notice that the final black hole is lighter than the sum of the two initial black holes. This is because of that energy that was carried away by the gravitational waves. Over the entire evolution of the system, $3.0^{+0.5}_{-0.4} M_\odot c^2 \simeq 5.3_{-0.8}^{+0.9} \times 10^{47}~\mathrm{J}$ of energy was radiated away as gravitational waves (where $c$ is the speed of light as in Einstein’s famous equation). This is a colossal amount of energy. You’d need to eat over eight billion times the mass of the Sun in butter to get the equivalent amount of calories. (Do not attempt the wafer-thin mint afterwards). The majority of that energy is radiated within the final second. For a brief moment, this one black hole merger outshines the whole visible Universe if you compare its gravitational-wave luminosity, to everything else’s visible-light luminosity!

We’ve measured mass, what about spin? The final black hole’s spin in $0.67^{+0.05}_{-0.07}$, which is in the middling-to-high range. You’ll notice that we can deduce this to a much higher precisely than the spins of the two initial black holes. This is because it is largely fixed by the orbital angular momentum of the binary, and so its value is set by orbital dynamics and gravitational physics. I think its incredibly satisfying that we we can such a clean measurement of the spin.

We have measured both of the properties of the final black hole, and we have done this using spacetime itself. This is astounding!

Estimated mass $M_\mathrm{f}^\mathrm{source}$ and spin $a_\mathrm{f}^\mathrm{source}$ for the final black hole. The dotted lines mark the edge of our 90% probability intervals. The different coloured curves show different models: they agree which still makes me incredibly happy! Fig. 3 from the Parameter Estimation Paper.

How big is the final black hole? My colleague Nathan Johnson-McDaniel has done some calculations and finds that the total distance around the equator of the black hole’s event horizon is about $1100~\mathrm{km}$ (about six times the length of the M25). Since the black hole is spinning, its event horizon is not a perfect sphere, but it bulges out around the equator. The circumference going over the black hole’s poles is about $1000~\mathrm{km}$ (about five and a half M25s, so maybe this would be the better route for your morning commute). The total area of the event horizon is about $37000~\mathrm{km}^2$. If you flattened this out, it would cover an area about the size of Montana. Neil Cornish (of Montana State University) said that he’s not sure which we know more accurately: the area of the event horizon or the area of Montana!

OK, we’ve covered the properties of the black holes, perhaps it’s time for a celebratory biscuit and a sit down? But we’re not finished yet, where is the source?

We infer that the source is at a luminosity distance of $410^{+160}_{-180}~\mathrm{Mpc}$, a megaparsec is a unit of length (regardless of what Han Solo thinks) equal to about 3 million light-years. The luminosity distance isn’t quite the same as the distance you would record using a tape measure because it takes into account the effects of the expansion of the Universe. But it’s pretty close. Using our 90% probability range, the merger would have happened sometime between 700 million years and 1.6 billion years ago. This coincides with the Proterozoic Eon on Earth, the time when the first oxygen-dependent animals appeared. Gasp!

With only the two LIGO detectors in operation, it is difficult to localise where on the sky source came from. To have a 90% chance of finding the source, you’d need to cover $600~\mathrm{deg^2}$ of the sky. For comparison, the full Moon is about $0.2~\mathrm{deg^2}$. This is a large area to cover with a telescope, and we don’t expect there to be anything to see for a black hole merger, but that hasn’t stopped our intrepid partners from trying. For a lovely visualisation of where we think the source could be, marvel at the Gravoscope.

### Astrophysics

The detection of this black hole merger tells us:

• Black holes 30 times the mass of our Sun do form These must be the remains of really massive stars. Stars lose mass throughout their lifetime through stellar winds. How much they lose depends on what they are made from. Astronomers have a simple periodic table: hydrogen, helium and metals. (Everything that is not hydrogen or helium is a metal regardless of what it actually is). More metals means more mass loss, so to end up with our black holes, we expect that they must have started out as stars with less than half the fraction of metals found in our Sun. This may mean the parent stars were some of the first stars to be born in the Universe.
• Binary black holes exist There are two ways to make a black hole binary. You can start with two stars in a binary (stars love company, so most have at least one companion), and have them live their entire lives together, leaving behind the two black holes. Alternatively, you could have somewhere where there are lots of stars and black holes, like a globular cluster, and the two black holes could wander close enough together to form the binary. People have suggested that either (or both) could happen. You might be able to tell the two apart using spin measurements. The spins of the black holes are more likely to be aligned (with each other and the way that the binary orbits) if they came from stars formed in a binary. The spins would be randomly orientated if two black holes came together to form a binary by chance. We can’t tell the two apart now, but perhaps when we have more observations!
• Binary black holes merge Since we’ve seen a signal from two black holes inspiralling together and merging, we know that this happens. We can also estimate how often this happens, given how many signals we’ve seen in our observations. Somewhere in the observable Universe, a similar binary could be merging about every 15 minutes. For LIGO, this should mean that we’ll be seeing more. As the detectors’ sensitivity improves (especially at lower frequencies), we’ll be able to detect more and more systems [bonus note].  We’re still uncertain in our predictions of exactly how many we’ll see. We’ll understand things better after observing for longer: were we just lucky, or were we unlucky not to have seen more? Given these early results, we estimate that the end of the third observing run (O3), we could have over 30. It looks like I will be kept busy over the next few years…

### Gravitational physics

Black holes are the parts of the Universe with the strongest possible gravity. They are the ideal place to test Einstein’s theory of general relativity. The gravitational waves from a black hole merger let us probe right down to the event horizon, using ripples in spacetime itself. This makes gravitational waves a perfect way of testing our understanding of gravity.

We have run some tests on the signal to see how well it matches our expectations. We find no reason to doubt that Einstein was right.

The first check is that if we try to reconstruct the signal, without putting in information about what gravitational waves from a binary merger look like, we find something that agrees wonderfully with our predictions. We can reverse engineer what the gravitational waves from a black hole merger look like from the data!

Recovered gravitational waveforms from our analysis of The Event. The dark band shows our estimate for the waveform without assuming a particular source (it is build from wavelets, which sound adorable to me). The light bands show results if we assume it is a binary black hole (BBH) as predicted by general relativity. They match really well! Fig. 6 from the Parameter Estimation Paper.

As a consistency test, we checked what would happen if you split the signal in two, and analysed each half independently with our parameter-estimation codes. If there’s something weird, we would expect to get different results. We cut the data into a high frequency piece and a low frequency piece at roughly where we think the merger starts. The lower frequency (mostly) inspiral part is more similar to the physics we’ve tested before, while the higher frequency (mostly) merger and ringdown is new and hence more uncertain. Looking at estimates for the mass and spin of the final black hole, we find that the two pieces are consistent as expected.

In general relativity, gravitational waves travel at the speed of light. (The speed of light is misnamed, it’s really a property of spacetime, rather than of light). If gravitons, the theoretical particle that carries the gravitational force, have a mass, then gravitational waves can’t travel at the speed of light, but would travel slightly slower. Because our signals match general relativity so well, we can put a limit on the maximum allowed mass. The mass of the graviton is less than $1.2 \times 10^{-22}~\mathrm{eV\,c^{-2}}$ (in units that the particle physicists like). This is tiny! It is about as many times lighter than an electron as an electron is lighter than a teaspoon of water (well, $4~\mathrm{g}$, which is just under a full teaspoon), or as many times lighter than the almost teaspoon of water is than three Earths.

Bounds on the Compton wavelength $\lambda_g$ of the graviton from The Event (GW150914). The Compton wavelength is a length defined by the mass of a particle: smaller masses mean large wavelengths. We place much better limits than existing tests from the Solar System or the double pulsar. There are some cosmological tests which are stronger still (but they make assumptions about dark matter). Fig. 8 from the Testing General Relativity Paper.

Overall things look good for general relativity, it has passed a tough new test. However, it will be extremely exciting to get more observations. Then we can combine all our results to get the best insights into gravity ever. Perhaps we’ll find a hint of something new, or perhaps we’ll discover that general relativity is perfect? We’ll have to wait and see.

## Conclusion

100 years after Einstein predicted gravitational waves and Schwarzschild found the equations describing a black hole, LIGO has detected gravitational waves from two black holes orbiting each other. This is the culmination of over forty years of effort. The black holes inspiral together and merge to form a bigger black hole. This is the signal I would have wished for. From the signal we can infer the properties of the source (some better than others), which makes me exceedingly happy. We’re starting to learn about the properties of black holes, and to test Einstein’s theory. As we continue to look for gravitational waves (with Advanced Virgo hopefully joining next year), we’ll learn more and perhaps make other detections too. The era of gravitational-wave astronomy has begun!

After all that, I am in need of a good nap! (I was too excited to sleep last night, it was like a cross between Christmas Eve and the night before final exams). For more on the story from scientists inside the LIGO–Virgo Collaboration, check out posts by:

• Matt Pitkin (the tireless reviewer of our parameter-estimation work)
• Brynley Pearlstone (who’s just arrived at the LIGO Hanford site)
• Amber Stuver (who  blogged through LIGO’s initial runs too)
• Rebecca Douglas (a good person to ask about what build a detector out of)
• Daniel Williams (someone fresh to the Collaboration)
• Sean Leavey (a PhD student working on on interferometry)
• Andrew Williamson (who likes to look for gravitational waves that coincide with gamma-ray bursts)
• Shane Larson (another fan of space-based gravitational-wave detectors)
• Roy Williams (who helps to make all the wonderful open data releases for LIGO)
• Chris North (creator of the Gravoscope amongst other things)

There’s also this video from my the heads of my group in Birmingham on their reactions to the discovery (the credits at the end show how large an effort the detection is).

Discovery paper: Observation of Gravitational Waves from a Binary Black Hole Merger
Date release:
LIGO Open Science Center

### Bonus notes

#### Search pipelines

At the Large Hadron Collider, there are separate experiments that independently analyse data, and this is an excellent cross-check of any big discoveries (like the Higgs). We’re not in a position to do this for gravitational waves. However, the different search pipelines are mostly independent of each other. They use different criteria to rank potential candidates, and the burst and binary searches even look for different types of signals. Therefore, the different searches act as a check of each other. The teams can get competitive at times, so they do check each other’s results thoroughly.

#### The announcement

Updating Have we detected gravitational waves yet? was doubly exciting as I had to successfully connect to the University’s wi-fi. I managed this with about a minute to spare. Then I hovered with my finger on the button until David Reitze said “We. Have detected. Gravitational waves!” The exact moment is captured in the video below, I’m just off to the left.

#### Parameters and uncertainty

We don’t get a single definite number from our analysis, we have some uncertainty too. Therefore, our results are usually written  as the median value (which means we think that the true value is equally probable to be above or below this number), plus the range needed to safely enclose 90% of the probability (so there’s a 10% chance the true value is outside this range. For the mass of the bigger black hole, the median estimate is $36 M_\odot$, we think there’s a 5% chance that the mass is below $32 M_\odot =(36 - 4) M_\odot$, and a 5% chance it’s above $41 M_\odot =(36 + 5) M_\odot$, so we write our result as $36^{+5}_{-4} M_\odot$.

#### Sensitivity and ranges

Gravitational-wave detectors measure the amplitude of the wave (the amount of stretch and squash). The measured amplitude is smaller for sources that are further away: if you double the luminosity distance of a source, you halve its amplitude. Therefore, if you improve your detectors’ sensitivity by a factor of two, you can see things twice as far away. This means that we observe a volume of space (2 × 2 × 2) = 8 times as big. (This isn’t exactly the case because of pesky factors from the expansion of the Universe, but is approximately right). Even a small improvement in sensitivity can have a considerable impact on the number of signals detected!

# General relativity at 100

General relativity, our best theory of gravitation, turns 100 this week!

Happy birthday general relativity! Einstein presented his field equations to the Prussian Academy of Science on 25 November 1915.

Gravity is the force which pulls us down towards the ground and keeps the Earth in orbit around the Sun. It is the most important force in astrophysics, causing gas clouds to collapse down to become stars; binding gas, stars and dark matter to become galaxies, and governing the overall evolution of the Universe.

Our understanding of gravity dates back to Isaac Newton. Newton realised that the same force that makes apples fall from trees also controls the motion of the planets. Realising that we could use physics to explain the everyday and the entire cosmos was a big leap! Newton’s theory was hugely successful, but he was never quite satisfied with it. In his theory gravity acted between distant objects (the Earth and an apple or the Earth and the Sun) instantaneously, without any explanation of what was linking them. The solution to this would come over 200 years later from Albert Einstein.

Einstein’s first big idea didn’t come from thinking about gravity, but thinking about electromagnetism. Electromagnetism is the force that is responsible for fridge magnets sticking, atoms binding to form molecules and the inner workings of whatever device you are currently reading this on. According to the rules of electromagnetism, ripples in electromagnetic fields (better known as light) always travel at a particular speed. This tweaked Einstein’s curiosity, as the rules didn’t say what this speed was relative to: you should measure the same speed if standing still, travelling at 100 miles per hour in a train or at a million miles per hour in a spacecraft. Speed is the distance travelled divided by the time taken, so Einstein realised that if the speed is always the same, then distances and times must appear different depending upon how you are moving! Moving clocks tick slower; at everyday speeds this effect is tiny, but we have confirmed that this is indeed the case. These ideas about space and time became known as Einstein’s theory of special relativity. Special relativity has a couple of important consequences, one is the infamous equation, the other is that the speed of light becomes a universal speed limit.

Special relativity says that no information can travel faster than the speed of light; this is a problem for Newton’s theory of gravitation, where the effects of gravity are transmitted instantaneously. Einstein knew that he would have to extend his theory to include gravity and freely falling objects, and he spend almost 11 years pondering on the problem. The result was general relativity.

In special relativity, space and time become linked, merging into one another depending upon how you are moving relative to what you are measuring. General relativity takes this further and has space–time distorted by the energy and matter. This idea can be a little tricky to explain.

In Newtonian mechanics, things (apples, light, billiard balls, etc.) like to travel in straight lines. They keep going at a constant speed in the same direction unless there is a force acting on them. Gravity is a force which pulls things away from their straight line, pulling the Earth into its circular orbit around the Sun, and accelerating an apple towards the ground. In general relativity, we take a different view. Things still travel in a straight line, but the effect of gravity is to bend space–time! A straight line in a curved space is a curve. If we don’t know about the curvature, it looks like the object is pulled off its straight line and there must be a force doing this, which we call gravity. Alternatively, we can say that gravity curves the space–time, and that the object follows its straight line in this. In general relativity, space–time tells matter how to move; matter tells space–time how to curve.

The shortest way to travel from London Heathrow airport to JFK International airport. On a long-distance flight, you may have noticed that it appears that you are moving along a curved line, but that is because the shortest distance across the Earth’s curved surface is a curve. We call this a geodesic, and the same idea applies to curved space–time in general relativity. Credit: Mr Reid.

General relativity solves Newton’s original worries. Objects are connected by space–time. This is not the rigid background of Newtonian physics, but a dynamic object, that is shaped by its contents. Space–time is curved by mass, and when the mass moves or reshapes itself, it takes time for the curvature everywhere else to readjust. When you drop a pebble into a pond, you disturb the surface, but it takes a while for the water further away to know about the splash; there’s a ripple that travels outwards, carrying the information about the disturbance. A similar thing happens for changes in gravity, there are ripples in space–time. Ripples in electromagnetic fields are electromagnetic waves, and these ripples in the gravitational fields are gravitational waves: both travel at the speed of light, in agreement with special relativity.

General relativity is not only a beautiful theory, it has so far passed every experimental test. Right from the start Einstein looked for checks of his theory. One of the calculations he did while formulating his theory was how the orbit of Mercury would change. Mercury is the planet closest to the Sun and so experiences the strongest gravity. Its orbit isn’t a perfect circle, but an ellipse so that Mercury is sometimes a little closer to the Sun, and is sometimes a little further. In Newtonian gravity, each orbit should trace out exactly the same path, but in general relativity there is some extra rotation. Each orbit is slightly shifted with respect to the last, so if you traced out many orbits, you’d end up with a Spirograph-like pattern. This is known as precession of the orbit, and is a consequence of there being slightly greater curvature closer to the Sun. This evolution of Mercury’s orbit had already been measured. Some thought it indicated there was a new planet inside Mercury’s orbit (which was called Vulcan but isn’t Spock’s home) that was giving it a little pull. However, Einstein calculated the general relativity predicted exactly the right amount of extra rotation!

The next test came in 1919. General relativity predicts that the path of light is bent by massive objects. This is gravitational lensing. At the time, the only object that could cause measurable bending was the Sun. If we could measure a change in the position of background stars when the Sun was in front of them, we could check if the amount of bending was as expected. There’s an obvious problem here: the Sun’s so bright that you can’t see stars around it. Arthur Eddington had the idea of making the measurement during an eclipse. He mounted an expedition and confirmed the prediction. This was big news and made Einstein a superstar.

Now, 100 years after Einstein proposed his theory, we are poised to make the most precise tests. There is currently a global effort to directly detect gravitational waves. Measuring the gravitational waves will tell us if ripples in space–time behave as Einstein predicted. The waves will also tell us about the systems that created them, this will give us an up-close glimpse of black holes. Black holes are the regions of strongest gravity; they are where the curvature of space–time becomes so immense that all straight lines lead inwards. Checking that the black holes of Nature match what we expect from general relativity, will test the theory in the most extreme conditions possible.

The Advanced LIGO detectors are currently listening for gravitational-wave signals from merging neutron stars or black holes, and next year Advanced Virgo plans join the hunt too. We don’t (yet) know how often such signals occur, so we can’t say when the first detection will be made. Perhaps this will be soon and we will learn something more about gravitation…

Merging black holes create ripples in space time. These can be detected with a laser interferometer. Credit: Gravitational Wave Group.

# Advanced LIGO: O1 is here!

Aerial views of LIGO Hanford (left) and LIGO Livingston (right). Both have 4 km long arms (arranged in an L shape) which house the interferometer beams. Credit: LIGO/Caltech/MIT.

The first observing run (O1) of Advanced LIGO began just over a week ago. We officially started at 4 pm British Summer Time, Friday 18 September. It was a little low key: you don’t want lots of fireworks and popping champagne corks next to instruments incredibly sensitive to vibrations. It was a smooth transition from our last engineering run (ER8), so I don’t even think there were any giant switches to throw. Of course, I’m not an instrumentalist, so I’m not qualified to say. In any case, it is an exciting time, and it is good to see some media attention for the Collaboration (with stories from Nature, the BBC and Science).

I would love to keep everyone up to date with the latest happenings from LIGO. However, like everyone in the Collaboration, I am bound by a confidentiality agreement. (You don’t want to cross people with giant lasers). We can’t have someone saying that we have detected a binary black hole (or that we haven’t) before we’ve properly analysed all the data, finalised calibration, reviewed all the code, double checked our results, and agreed amongst ourselves that we know what’s going on. When we are ready, announcements will come from the LIGO Spokespreson Gabriela González and the Virgo Spokesperson Fulvio Ricci. Event rates are uncertain and we’re not yet at final sensitivity, so don’t expect too much of O1.

There are a couple of things that I can share about our status. Whereas normally everything I write is completely unofficial, these are suggested replies to likely questions.

Have you started taking data?
We began collecting science quality data at the beginning of September, in preparation of the first Observing Run that started on Friday, September 18, and are planning on collecting data for about 4 months

We certainly do have data, but there’s nothing new about that (other than the improved sensitivity). Data from the fifth and sixth science runs of initial LIGO are now publicly available from the LIGO Open Science Center. You can go through it and try to find anything we missed (which is pretty cool).

Have you seen anything in the data yet?
We analyse the data “online” in an effort to provide fast information to astronomers for possible follow up of triggers using a relatively low statistical significance (a false alarm rate of ~1/month). We have been tuning the details of the communication procedures, and we have not yet automated all the steps that can be, but we will send alerts to astronomers above the threshold agreed as soon as we can after those triggers are identified. Since analysis to validate and candidate in gravitational-wave data can take months, we will not be able to say anything about results in the data on short time scales. We will share any and all results when ready, though probably not before the end of the Observing Run.

Analysing the data is tricky, and requires lots of computing time, as well as carefully calibration of the instruments (including how many glitches they produce which could look like a gravitational-wave trigger). It takes a while to get everything done.

We heard that you sent a gravitational-wave trigger to astronomers already—is that true?
During O1, we will send alerts to astronomers above a relatively low significance threshold; we have been practising communication with astronomers in ER8. We are following this policy with partners who have signed agreement with us and have observational capabilities ready to follow up triggers. Because we cannot validate gravitational-wave events until we have enough statistics and diagnostics, we have confidentiality agreements about any triggers that hare shared, and we hope all involved abide by those rules.

I expect this is a pre-emptive question and answer. It would be amazing if we could see an electromagnetic (optical, gamma-ray, radio, etc.) counterpart to a gravitational wave. (I’ve done some work on how well we can localise gravitational-wave sources on the sky). It’s likely that any explosion or afterglow that is visible will fade quickly, so we want astronomers to be able to start looking straight-away. This means candidate events are sent out before they’re fully vetted: they could just be noise, they could be real, or they could be a blind injection. A blind injection is when a fake signal is introduced to the data secretly; this is done to keep us honest and check that our analysis does work as expected (since we know what results we should get for the signal that was injected). There was a famous blind injection during the run of initial LIGO called Big Dog. (We take gravitational-wave detection seriously). We’ve learnt a lot from injections, even if they are disappointing. Alerts will be sent out for events with false alarm rates of about one per month, so we expect a few across O1 just because of random noise.

While I can’t write more about the science from O1, I will still be posting about astrophysics, theory and how we analyse data. Those who are impatient can be reassured that gravitational waves have been detected, just indirectly, from observations of binary pulsars.

The orbital decay of the Hulse-Taylor binary pulsar (PSR B1913+16). The points are measured values, while the curve is the theoretical prediction for gravitational waves. I love this plot. Credit: Weisberg & Taylor (2005).

# LIGO Magazine: Issue 7

It is an exciting time time in LIGO. The start of the first observing run (O1) is imminent. I think they just need to sort out a button that is big enough and red enough (or maybe gather a little more calibration data… ), and then it’s all systems go. Making the first direct detection of gravitational waves with LIGO would be an enormous accomplishment, but that’s not all we can hope to achieve: what I’m really interested in is what we can learn from these gravitational waves.

The LIGO Magazine gives a glimpse inside the workings of the LIGO Scientific Collaboration, covering everything from the science of the detector to what collaboration members like to get up to in their spare time. The most recent issue was themed around how gravitational-wave science links in with the rest of astronomy. I enjoyed it, as I’ve been recently working on how to help astronomers look for electromagnetic counterparts to gravitational-wave signals. It also features a great interview with Joseph Taylor Jr., one of the discoverers of the famous Hulse–Taylor binary pulsar. The back cover features an article I wrote about parameter estimation: an expanded version is below.

### How does parameter estimation work?

Detecting gravitational waves is one of the great challenges in experimental physics. A detection would be hugely exciting, but it is not the end of the story. Having observed a signal, we need to work out where it came from. This is a job for parameter estimation!

How we analyse the data depends upon the type of signal and what information we want to extract. I’ll use the example of a compact binary coalescence, that is the inspiral (and merger) of two compact objects—neutron stars or black holes (not marshmallows). Parameters that we are interested in measuring are things like the mass and spin of the binary’s components, its orientation, and its position.

For a particular set of parameters, we can calculate what the waveform should look like. This is actually rather tricky; including all the relevant physics, like precession of the binary, can make for some complicated and expensive-to-calculate waveforms. The first part of the video below shows a simulation of the coalescence of a black-hole binary, you can see the gravitational waveform (with characteristic chirp) at the bottom.

We can compare our calculated waveform with what we measured to work out how well they fit together. If we take away the wave from what we measured with the interferometer, we should be left with just noise. We understand how our detectors work, so we can model how the noise should behave; this allows us to work out how likely it would be to get the precise noise we need to make everything match up.

To work out the probability that the system has a given parameter, we take the likelihood for our left-over noise and fold in what we already knew about the values of the parameters—for example, that any location on the sky is equally possible, that neutron-star masses are around 1.4 solar masses, or that the total mass must be larger than that of a marshmallow. For those who like details, this is done using Bayes’ theorem.

We now want to map out this probability distribution, to find the peaks of the distribution corresponding to the most probable parameter values and also chart how broad these peaks are (to indicate our uncertainty). Since we can have many parameters, the space is too big to cover with a grid: we can’t just systematically chart parameter space. Instead, we randomly sample the space and construct a map of its valleys, ridges and peaks. Doing this efficiently requires cunning tricks for picking how to jump between spots: exploring the landscape can take some time, we may need to calculate millions of different waveforms!

Having computed the probability distribution for our parameters, we can now tell an astronomer how much of the sky they need to observe to have a 90% chance of looking at the source, give the best estimate for the mass (plus uncertainty), or even figure something out about what neutron stars are made of (probably not marshmallow). This is the beginning of gravitational-wave astronomy!

Monty, Carla and the other samplers explore the probability landscape. Nutsinee Kijbunchoo drew the version for the LIGO Magazine.

# Parameter estimation for binary neutron-star coalescences with realistic noise during the Advanced LIGO era

The first observing run (O1) of Advanced LIGO is nearly here, and with it the prospect of the first direct detection of gravitational waves. That’s all wonderful and exciting (far more exciting than a custard cream or even a chocolate digestive), but there’s a lot to be done to get everything ready. Aside from remembering to vacuum the interferometer tubes and polish the mirrors, we need to see how the data analysis will work out. After all, having put so much effort into the detector, it would be shame if we couldn’t do any science with it!

### Parameter estimation

Since joining the University of Birmingham team, I’ve been busy working on trying to figure out how well we can measure things using gravitational waves. I’ve been looking at binary neutron star systems. We expect binary neutron star mergers to be the main source of signals for Advanced LIGO. We’d like to estimate how massive the neutron stars are, how fast they’re spinning, how far away they are, and where in the sky they are. Just published is my first paper on how well we should be able to measure things. This took a lot of hard work from a lot of people, so I’m pleased it’s all done. I think I’ve earnt a celebratory biscuit. Or two.

When we see something that looks like it could be a gravitational wave, we run code to analyse the data and try to work out the properties of the signal. Working out some properties is a bit trickier than others. Sadly, we don’t have an infinite number of computers, so it means it can take a while to get results. Much longer than the time to eat a packet of Jaffa Cakes…

The fastest algorithm we have for binary neutron stars is BAYESTAR. This takes the same time as maybe eating one chocolate finger. Perhaps two, if you’re not worried about the possibility of choking. BAYESTAR is fast as it only estimates where the source is coming from. It doesn’t try to calculate a gravitational-wave signal and match it to the detector measurements, instead it just looks at numbers produced by the detection pipeline—the code that monitors the detectors and automatically flags whenever something interesting appears. As far as I can tell, you give BAYESTAR this information and a fresh cup of really hot tea, and it uses Bayes’ theorem to work out how likely it is that the signal came from each patch of the sky.

To work out further details, we need to know what a gravitational-wave signal looks like and then match this to the data. This is done using a different algorithm, which I’ll refer to as LALInference. (As names go, this isn’t as cool as SKYNET). This explores parameter space (hopping between different masses, distances, orientations, etc.), calculating waveforms and then working out how well they match the data, or rather how likely it is that we’d get just the right noise in the detector to make the waveform fit what we observed. We then use another liberal helping of Bayes’ theorem to work out how probable those particular parameter values are.

It’s rather difficult to work out the waveforms, but some our easier than others. One of the things that makes things trickier is adding in the spins of the neutron stars. If you made a batch of biscuits at the same time you started a LALInference run, they’d still be good by the time a non-spinning run finished. With a spinning run, the biscuits might not be quite so appetising—I generally prefer more chocolate than penicillin on my biscuits. We’re working on speeding things up (if only to prevent increased antibiotic resistance).

In this paper, we were interested in what you could work out quickly, while there’s still chance to catch any explosion that might accompany the merging of the neutron stars. We think that short gamma-ray bursts and kilonovae might be caused when neutron stars merge and collapse down to a black hole. (I find it mildly worrying that we don’t know what causes these massive explosions). To follow-up on a gravitational-wave detection, you need to be able to tell telescopes where to point to see something and manage this while there’s still something that’s worth seeing. This means that using spinning waveforms in LALInference is right out, we just use BAYESTAR and the non-spinning LALInference analysis.

### What we did

To figure out what we could learn from binary neutron stars, we generated a large catalogue of fakes signals, and then ran the detection and parameter-estimation codes on this to see how they worked. This has been done before in The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo which has a rather delicious astrobites write-up. Our paper is the sequel to this (and features most of the same cast). One of the differences is that The First Two Years assumed that the detectors were perfectly behaved and had lovely Gaussian noise. In this paper, we added in some glitches. We took some real data™ from initial LIGO’s sixth science run and stretched this so that it matches the sensitivity Advanced LIGO is expected to have in O1. This process is called recolouring [bonus note]. We now have fake signals hidden inside noise with realistic imperfections, and can treat it exactly as we would real data. We ran it through the detection pipeline, and anything which was flagged as probably being a signal (we used a false alarm rate of once per century), was analysed with the parameter-estimation codes. We looked at how well we could measure the sky location and distance of the source, and the masses of the neutron stars. It’s all good practice for O1, when we’ll be running this analysis on any detections.

### What we found

1. The flavour of noise (recoloured or Gaussian) makes no difference to how well we can measure things on average.
2. Sky-localization in O1 isn’t great, typically hundreds of square degrees (the median 90% credible region is 632 deg2), for comparison, the Moon is about a fifth of a square degree. This’ll make things interesting for the people with telescopes.

Probability that of a gravitational-wave signal coming from different points on the sky. The darker the red, the higher the probability. The star indicates the true location. This is one of the worst localized events from our study for O1. You can find more maps in the data release (including 3D versions), this is Figure 6 of Berry et al. (2015).

3. BAYESTAR does just as well as LALInference, despite being about 2000 times faster.

Sky localization (the size of the patch of the sky that we’re 90% sure contains the source location) varies with the signal-to-noise ratio (how loud the signal is). The approximate best fit is $\log_{10}(\mathrm{CR}_{0.9}/\mathrm{deg^2}) \approx -2 \log_{10}(\varrho) +5.06$, where $\mathrm{CR}_{0.9}$ is the 90% sky area and $\varrho$ is the signal-to-noise ratio. The results for BAYESTAR and LALInference agree, as do the results with Gaussian and recoloured noise. This is Figure 9 of Berry et al. (2015).

4. We can’t measure the distance too well: the median 90% credible interval divided by the true distance (which gives something like twice the fractional error) is 0.85.
5. Because we don’t include the spins of the neutron stars, we introduce some error into our mass measurements. The chirp mass, a combination of the individual masses that we’re most sensitive to [bonus note], is still reliably measured (the median offset is 0.0026 of the mass of the Sun, which is tiny), but we’ll have to wait for the full spinning analysis for individual masses.

Fraction of events with difference between the mean estimated and true chirp mass smaller than a given value. There is an error because we are not including the effects of spin, but this is small. Again, the type of noise makes little difference. This is Figure 15 of Berry et al. (2015).

There’s still some work to be done before O1, as we need to finish up the analysis with waveforms that include spin. In the mean time, our results are all available online for anyone to play with.

arXiv: 1411.6934 [astro-ph.HE]
Journal: Astrophysical Journal; 904(2):114(24); 2015
Data release: The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo
Favourite colour: Blue. No, yellow…

### Notes

The colour of noise: Noise is called white if it doesn’t have any frequency dependence. We made ours by taking some noise with initial LIGO’s frequency dependence (coloured noise), removing the frequency dependence (making it white), and then adding in the frequency dependence of Advanced LIGO (recolouring it).

The chirp mass: Gravitational waves from a binary system depend upon the masses of the components, we’ll call these $m_1$ and $m_2$. The chirp mass is a combination these that we can measure really well, as it determines the most significant parts of the shape of the gravitational wave. It’s given by

$\displaystyle \mathcal{M} = \frac{m_1^{3/5} m_2^{3/5}}{(m_1 + m_2)^{1/5}}$.

We get lots of good information on the chirp mass, unfortunately, this isn’t too useful for turning back into the individual masses. For that we next extra information, for example the mass ratio $m_2/m_1$. We can get this from less dominant parts of the waveform, but it’s not typically measured as precisely as the chirp mass, so we’re often left with big uncertainties.

# Advanced LIGO (the paper)

Continuing with my New Year’s resolution to write a post on every published paper, the start of March see another full author list LIGO publication. Appearing in Classical & Quantum Gravity, the minimalistically titled Advanced LIGO is an instrumental paper. It appears a part of a special focus issue on advanced gravitational-wave detectors, and is happily free to read (good work there). This is The Paper™ for describing how the advanced detectors operate. I think it’s fair to say that my contribution to this paper is 0%.

LIGO stands for Laser Interferometer Gravitational-wave Observatory. As you might imagine, LIGO tries to observe gravitational waves by measuring them with a laser interferometer. (It won’t protect your fencing). Gravitational waves are tiny, tiny stretches and squeezes of space. To detect them we need to measure changes in length extremely accurately. I had assumed that Advanced LIGO will achieve this supreme sensitivity through some dark magic invoked by sacrificing the blood, sweat, tears and even coffee of many hundreds of PhD students upon the altar of science. However, this paper actually shows it’s just really, really, REALLY careful engineering. And giant frickin’ laser beams.

The paper goes through each aspect of the design of the LIGO detectors. It starts with details of the interferometer. LIGO uses giant lasers to measure distances extremely accurately. Lasers are bounced along two 3994.5 m arms and interfered to measure a change in length between the two. In spirit, it is a giant Michelson interferometer, but it has some cunning extra features. Each arm is a Fabry–Pérot etalon, which means that the laser is bounced up and down the arms many times to build up extra sensitivity to any change in length. There are various extra components to make sure that the laser beam is as stable as possible, all in all, there are rather a lot of mirrors, each of which is specially tweaked to make sure that some acronym is absolutely perfect.

Fig. 1 from Aasi et al. (2015), the Advanced LIGO optical configuration. All the acronyms have to be carefully placed in order for things to work. The laser beam starts from the left, passing through subsystems to make sure it’s stable. It is split in two to pass into the interferometer arms at the top and right of the diagram. The laser is bounced many times between the mirrors to build up sensitivity. The interference pattern is read out at the bottom. Normally, the light should interfere destructively, so the output is dark. A change to this indicates a change in length between the arms. That could be because of a passing gravitational wave.

The next section deals with all the various types of noise that affect the detector. It’s this noise that makes it such fun to look for the signals. To be honest, pretty much everything I know about the different types of noise I learnt from Space-Time Quest. This is a lovely educational game developed by people here at the University of Birmingham. In the game, you have to design the best gravitational-wave detector that you can for a given budget. There’s a lot of science that goes into working out how sensitive the detector is. It takes a bit of practice to get into it (remember to switch on the laser first), but it’s very easy to get competitive. We often use the game as part of outreach workshops, and we’ve had some school groups get quite invested in the high-score tables. My tip is that going underground doesn’t seem to be worth the money. Of course, if you happen to be reviewing the proposal to build the Einstein Telescope, you should completely ignore that, and just concentrate how cool the digging machine looks. Space-Time Quest shows how difficult it can be optimising sensitivity. There are trade-offs between different types of noise, and these have been carefully studied. What Space-Time Quest doesn’t show, is just how much work it takes to engineer a detector.

The fourth section is a massive shopping list of components needed to build Advanced LIGO. There are rather more options than in Space-Time Quest, but many are familiar, even if given less friendly names. If this section were the list of contents for some Ikea furniture, you would know that you’ve made a terrible life-choice; there’s no way you’re going to assemble this before Monday. Highlights include the 40 kg mirrors. I’m sure breaking one of those would incur more than seven years bad luck. For those of you playing along with Space-Time Quest at home, the mirrors are fused silica. Section 4.8.4 describes how to get the arms to lock, one of the key steps in commissioning the detectors. The section concludes with details of how to control such a complicated instrument, the key seems to be to have so many acronyms that there’s no space for any component to move in an unwanted way.

The paper closes with on outlook for the detector sensitivity. With such a complicated instrument it is impossible to be certain how things will go. However, things seem to have been going smoothly so far, so let’s hope that this continues. The current plan is:

• 2015 3 months observing at a binary neutron star (BNS) range of 40–80 Mpc.
• 2016–2017 6 months observing at a BNS range of 80–120 Mpc.
• 2017–2018 9 months observing at a BNS range of 120–170 Mpc.
• 2019 Achieve full sensitivity of a BNS range of 200 Mpc.

The BNS range is the distance at which a typical binary made up of two 1.4 solar mass neutrons stars could be detected when averaging over all orientations. If you have a perfectly aligned binary, you can detect it out to a further distance, the BNS horizon, which is about 2.26 times the BNS range. There are a couple of things to note from the plan. First, the initial observing run (O1 to the cool kids) is this year! The second is how much the range will extend before hitting design sensitivity. This should significantly increase the number of possible detections, as each doubling of the range corresponds to a volume change of a factor of eight. Coupling this with the increasing length of the observing runs should mean that the chance of a detection increases every year. It will be an exciting few years for Advanced LIGO.

arXiv: 1411.4547 [gr-qc]
Journal: Classical & Quantum Gravity; 32(7):074001(41); 2015
Science summary: Introduction to LIGO & Gravitational Waves
Space-Time Quest high score: 34.859 Mpc

# 12 Astronomy Highlights of Christmas

I regularly help out with Astronomy in the City here at the University. Our most recent event was a Christmas special, and we gave a talk on 12 festive highlights covering events past, present and future, somewhat biased towards our research interests. Here is our count-down again.

## A Newton under an apple tree

Isaac Newton, arguably the greatest physicist of all time, was born on 25 December 1642. I expect he may have got many joint birthday–Christmas presents. Newton is most famous for his theory of gravity, which he allegedly thought up after being hit on the head by a falling apple. Realising that the same force could be responsible for mundane things like falling as for keeping celestial bodies such as the planets in their orbits, was a big leap (or fall?). Netwon’s theory of gravity is highly successful, it’s accurate enough to get us to the Moon (more on that later) and only breaks down for particularly strong gravitational fields. That’s when you need Einstein’s theory of general relativity.

Newton may have been a Pink Floyd fan, we may never know.

Newton also did much work on optics. He nearly blinded himself while prodding his eye to see how that would affect his sight. Even smart people do stupid things. Newton designed the first practical reflecting telescope. Modern astronomical telescopes are reflecting (using a mirror to focus light) rather than refracting (using a lens). The first telescope installed at the University’s Observatory was a Newtonian reflector.

Newton’s reflecting telescope, one of the treasures of the Royal Society. Newton was President of the Royal Society, as well as Master of the Royal Mint, Member of Parliament for University of Cambridge and Lucasian Professor of Mathematics. It’s surprising he had any time for alchemy.

## 2 clear nights

At Astronomy in the City, we have talks on the night sky and topics in astrophysics, a question and answer session, plus some fun activities after to accompany tea and biscuits. There’s also the chance to visit the Observatory and (if it’s clear) use the Astronomical Society’s telescopes. Since the British weather is so cooperative, we only had two clear observing nights from this year’s events (prior to the December one, which was clear).

If you had made one of the clear nights, you could have viewed the nebulae M78 and M42, or Neptune and its moons. Neptune, being one of the ice giants, is a good wintry subject for a Christmas talk. It’s pretty chilly, with the top of its atmosphere being −218 °C. You don’t have a white Christmas on Neptune though. It’s blue colouring is due to methane, which with ammonia (and good old water) makes up what astronomers call ices (I guess you should be suspicious of cocktails made by astronomers).

One of the most exciting views of the year was supernova 2014J, back in January. This was first spotted by students at University College London (it was cloudy here at the time). It’s located in nearby galaxy M82, and we got some pretty good views of it. You can see it out-shine its entire host galaxy. Supernovae are pretty bright!

Supernova 2014J in M82. Image from the University of Birmingham Observatory.

## 3 components of a cluster

Galaxy clusters are big. They are the largest gravitationally-bound objects in the Universe. They are one of astrophysical objects that we’re particularly interested in here at Birmingham, so they’ll pop up a few times in this post.

Galaxy clusters have three main components. Like trifles. Obviously there are the galaxies, which we can see because they are composed of stars. Around the galaxies there is lots of hot gas. This is tens of millions of degrees and we can spot it because it emits X-rays. Don’t put this in your trifles at home. The final component is dark matter, the mysterious custard of our trifle. We cannot directly see the dark matter (that’s why it’s dark), but we know its there because of the effects of its gravity. We can map out its location using gravitational lensing: the bending of light by gravity, one of the predictions of general relativity.

Different views of cluster Abell 209. The bottom right is a familiar optical image. Above that is a smoothed map of infra-red luminosity (from old stars). The top left is a map of the total mass (mostly due to dark matter) as measured with gravitational lensing. The bottom left is a X-ray map of the hot intergalactic gas. Credit: Subaru/UKIRT/Chandra/University of Birmingham/Nordic Optical Telescope/University of Hawaii.

Measuring the dark matter is tricky, but some of the work done in Birmingham this year shows that is closely follows the infra-red emission. You can use the distribution of jelly in your trifle to estimate how much custard there should be. In the picture above of galaxy cluster Abell 209, you can see how similar the top two images are. Using the infra-red could be a handy way of estimating the amount of dark matter when you don’t have access to gravitational-lensing measurements.

## 4 km long laser arms

A highlight for next year: the first observing run of Advanced LIGO. Advanced LIGO is trying to make the first direct detection of gravitational waves. Gravitational waves are tiny stretches and squeezes in spacetime, to detect them you need to very carefully measure the distance between two points. This is where the 4 km arms come in: the Advanced LIGO detectors bounce lasers up and down their arms to measure the distance between the mirrors at the ends. The arms need to be as long as possible to make measuring the change in length as easy as possible. A typical change in length may be one part in 1021 (that is 1,000,000,000,000,000,000,000 or one sextillion… ). For comparison, that’s the same as measuring the distance between the Earth and the Sun to the diameter of a hydrogen atom or the distance from here to Alpha Centuri to the width of a human hair.

Aerial shot of LIGO Livingston, Louisiana. Two arms come out from the central building, one goes up the middle of the picture, the other goes off to the left out of shot. I think this gives a fair indication of the scale of the detectors. In addition to the instruments in Livingston, there is another LIGO in Hanford, Washington.

Making such an precise instrument is tricky. At least twice as tricky as remembering the names of all seven of the dwarfs. We shouldn’t be Bashful about saying how difficult it is. We need to keep the mirrors extremely still, any little wibbles from earth tremors, nearby traffic, or passing clouds need to be filtered out. Lots of clever Docs have been working on cunning means of keeping the mirrors still and then precisely measuring their position with the lasers. Some of that work was done here in Birmingham, in particular some of the mirror suspension systems. We’ll be rather Grumpy if those don’t work. However, things seem to be going rather well. Getting the mirrors working isn’t as simple as pushing a big red button, so it takes a while. On the 3 December, which is when we gave this talk at Astronomy in the City, the second detector achieved its first full lock: lock is when the mirrors are correctly held stably in position. This made me Happy. Also rather Sleepy, as it was a late night.

Team inspecting the optical systems at LIGO Livingston back at the start of 2014. (It’s a bit harder to detect the systems now, since they’re in a vacuum). You need to wear masks in case you are Sneezy, you’d feel rather Dopey if you ruined the mirrors by sneezing all over them. Credit: Michael Fyffe

## 5 (or more) planet-forming rings!

ALMA image of the young star HL Tau and its protoplanetary disc. The gaps in the disc indicate the formation of planets that sweep their orbits clear of dust and gas. Credit: ALMA, C. Brogan & B. Saxton

One of the most exciting discoveries of 2014 is this remarkable image of a planet-forming disc.There may be more than five planets, but it seemed like a shame not to fit this into our countdown here. The image is of the star HL Tauri. This is a young star, only a million years old (our Sun is about 4.6 billion years old). Remarkably, even at this young age, there seems to be indication of the formation of planets. The gaps are where planets have sucked up the dust, gas and loose change of the disc. This is the first time we’ve seen planet-formation in such detail, and matches predictions extremely well.

## 6 Frontier Fields

The six Frontier Fields are a group of six galaxy clusters that are being studied in unprecedented detail. They are being observing with three of NASA’s great observatories, the Hubble Space Telescope, the Spitzer Space Telescope (which observes in the infra-red) and the Chandra X-ray Observatory. These should allow us to measure all three components of the clusters (even the custard of the trifle). The clusters are all selected because the show strong gravitational lensing. This should give us excellent measurements of the mass of the clusters, and hence the distribution of dark matter.

Gravitational lensing by a galaxy cluster. The mass of the galaxy cluster bends spacetime. Light travelling through this curved spacetime is bent, just like passing through a lens. The amount of bending depends upon the mass, so we can weigh galaxy clusters by measuring the lensing. Credit: NASA, ESA & L. Calcada.

## 7 months until New Horizons reaches Pluto

New Horizons is a planetary mission to Pluto (and beyond). Launched in January 2006, New Horizons has been travelling through the Solar System ever since. In 2007 it made a fly-by of Jupiter, taking some amazing pictures. It is now just 7 months from reaching Pluto. This will give us the first ever detailed look at Pluto and its moons. You’ll need to wrap up warm if you wanted to head there yourself. I hope that New Horizons packed some mittens. New Horizons will tell us about Pluto and other icy (yes, that’s astronomers’ definition of ice again) items in the Kuiper belt.

Full trajectory of New Horizons, it’s come a long way! Credit: John Hopkins

New Horizons has been in hibernation for much of its flight. Who doesn’t like a good nap? New Horizons was woken up ahead of arriving at Pluto on 7 December. It got a special wake-up call from Russell Watson. I don’t think it has access to coffee though.

## 800 TB of data

This year’s Interstellar featured the most detailed simulations of the appearance of black holes. This involved a truly astounding amount of data. I’ve previously written about some of the science in Interstellar. I think it’s done a good at getting people interested in the topic of gravity. It’s scientific accuracy can be traced to the involvement of Kip Thorne, who has written a book on the film’s science (which might be a good Christmas present). Kip has done many things during his career, including being one of the pioneers of LIGO. After an exciting 2014 with the release of Interstellar, I’m sure he’s looking forward to 2015 and the first observations of Advanced LIGO too.

Light-bending around the black hole Gargantua in Interstellar. This shows the accretion disc about the black hole, the disc seen above and below the hole are actually the top and bottom of the disc behind the black hole. This extreme light-bending is a consequence of the extremely curved spacetime close to the black hole. This light-bending is exactly the same as the gravitational-lensing done by galaxy clusters, except much stronger!

## 999 Kepler exoplanets

When we gave the talk on 3 December, Kepler had discovered 998 exoplanets. It’s now 999, which I think means we get all the bonus points! Kepler is still doing good science, despite some technical difficulties. Kepler has been hugely successful. We now know that planets (as well as forming in quite short times) are common, that they are pretty much everywhere. Possibly even down the back of the sofa. Some of the work done here in Birmingham has been to estimate just how common planets are. On average, stars similar to the Sun have around 4 planets with periods shorter than 3 years (and radii bigger than 20% of Earth’s). That’s quite a few planets! But, if Christopher Nolan wants to direct another reasonably accurate sci-fi, we need to know how many of those are Earth-like. We don’t have enough data to work out details of atmospheres, but just looking at how many planets have a radius and period about the same as Earth’s, it seems that about 4% of these stars have Earth-like planets.

Kepler-186, the first system discovered with an Earth-sized planet on the edge of the habitable zone (where liquid water could exist), was discovered in 2014.

## 10 lunar orbits

A Christmas highlight from 1968. On December 21, Apollo 8 launched. This was the first manned mission to ever leave Earth orbit. On Christmas Eve, it entered into orbit about the Moon. It’s three-man crew of Frank Borman, James Lovell and William Anders were the first people ever to orbit a body other than the Earth. To date, only 24 men have ever done so. Of course, even fewer have actually walked on the Moon, perhaps we should go back? Jim Lovell was also on the ill-fated Apollo 13 mission (you may have seen the film), making him the only person to orbit the Moon on two separate occasions and never land. Apollo 8 was successful, it orbited the Moon 10 times, giving us the first ever peek at the dark side of the moon (not the Pink Floyd album). This was also the first viewing of an Earthrise. Their Christmas Eve broadcast was most watched TV broadcast at the time. After orbiting, Apollo 8 returned home, splashing down December 27. I’m guessing they had a good New Year’s celebration!

Earthrise taken by the crew of Apollo 8, Christmas Eve 1968. Credit: NASA

## 11 (10 ¾) years for Rosetta

This year we landed on a comet. Rosetta has received fair amount of press. It is an amazing feat, Rosetta was in space for almost 11 years before making its comet rendezvous. It’ll be doing lots of science form orbit, such as determining that comets are unlikely to have delivered water to Earth. Most of the excitement surrounded the landing of Philae on the surface of the comet. That didn’t go quite as planned, but still taught us quite a bit. Rosetta has been heralded as one of the science breakthroughs of 2014. We’ll have to see what 2015 brings.

Colour image (yes, it’s grey) of 67P/Churyumov-Gerasimenko from Rosetta. Credit: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

## 12 (or more) galaxies in a cluster

To finish up, back to galaxy clusters. Galaxy clusters grow by merging. We throw two trifles together to get a bigger one. As you might imagine, if you throw two triffles together, you don’t get a nice, neat trifle. The layers do tend to mix. For galaxy clusters, you can get layers separating out: dark matter passes freely through everything, so it isn’t affected by a collision. The gas, however, does feel the shock and ends up a turbulent mess. It has been suggested that turbulence caused by mergers could trigger star formation: you squeeze the gas and some of it collapses down into stars. However, recent observational work at Birmingham can’t find any evidence for this. We’ll have to see if this riddle gets unravelled in 2015.

The merging bullet cluster. A composite of an optical image (showing galaxies), an X-ray image (in red, showing the hot gas), and a map of the total mass (in blue, from gravitational lensing). Dark matter, making up most of the mass, has past straight through the collision without interacting. Credit: NASA/CXC/CfA/STScI/ESO/U.Arizona/M. Markevitch/D. Clowe