Gravitational-Wave Astronomy

Gravitational-wave astronomy

Professor John Barrow

One of the most striking ways in which astronomy advanced and became a more spectacular subject during the 20th Century was by extending the look that it gave us at the universe from just the optical band of light into other parts of the electromagnetic spectrum, so suddenly we had the capability to detect radio waves, infrared radiation, ultraviolet.  In this way, all sorts of different astronomies grew up – x-ray astronomy, infrared astronomy and so forth.  What I am going to talk about today is a further extension of astronomy that we believe is just beginning, which allows us to look at the universe in a new way, not in ordinary electromagnetic radiation, but through another form of radiation that is created by the force of gravity itself.  This is now known as gravitational wave astronomy.  We are going to see what gravitational waves are, how we believe that there is already evidence that they exist and we can see their effects, and some of the prospects for detecting them directly in the future.

Like many exotic features of Einstein’s General Theory of Relativity, there is a more straightforward Newtonian counterpart which it is best to understand first before you start grappling with Einstein’s conception on its own.  Gravitational waves have their counterpart in a familiar aspect of gravity.  Ordinary gravity has two manifestations that we are familiar with.  On the one hand, there is what I call direct gravity, so if you are a large mass and you put another mass up above it in space, the two masses will attract one another with a gravitational force which is inversely proportional to the square of their separation.

This is what I call direct gravity, and it is rather familiar, like Newton’s famous law of gravitation which we met at school, but there is another manifestation of the force of gravity that is different, although very familiar, and it is what we call tidal gravity or the effects of tidal forces.  Imagine that mass is just a point, that it has no finite size.  Whereas suppose we think of an object that has a finite size, so suppose it is a rod whose length is H, then the top of the rod will be attracted towards the mass with a slightly different gravitational pull to the bottom, because the top is further away, and so the top and the bottom are feeling different gravitational attractions, so you can imagine that there would be some stretching of the rod because there is a stronger gravitational force in some places than others.  This is known as the tidal gravitational force.  If you just use a little formula to work out the force on the bottom, at a distance R, and you use it again to work out the force when you are a distance R plus H away, subtract one from the other and you will have the tidal force, which is the difference in the force pulling the two points.  That force does not vary like an inverse square but as an inverse cube of the distance away.  This is the Newtonian tidal force, and it is very real.  We see evidence of it on Earth in a rather periodic fashion, and we refer to forces that have this differential character as tidal forces.  In the case of the Earth, the surface of the Earth is a rigid solid body, and two-thirds of its surface are covered by oceans, which are not rigid and are incompressible, and so the Moon exerts a gravitational pull on the Earth, the Earth’s body moves as a whole, there is not a significant differential which can move the Earth, but the oceans of course are shifted in a tidal fashion.  So the oceans are pulled toward the Moon, and what is happening is rather interesting.  The total volume of the ocean is conserved, and so if you pull it in one direction, you will necessarily have a push in the other direction. This is something that is characteristic of tidal forces: the overall volume, as it were, is conserved but the shape changes, so spheres are changed into ellipsoids, circles are changed into ovals.  So a large tide is rising, even though it looks as though there is no force acting on the point.

The Moon is not the only object that exerts tides on the Earth.  The Sun also has a tidal effect.  Very roughly speaking, the relative effects of tides on the Earth from things that you can see in the sky is proportional to their apparent size on the sky.  So Jupiter or Mars, which look absolutely tiny, have a completely negligible tidal effect on the Earth compared with the Moon.  But as you know, because we see complete eclipses of the Sun, the Moon and the Sun have almost the same apparent size on the sky.  It is one of the great coincidences of nature.  As a result, if we think of the Earth and the Sun, and possible positions of the Moon, the situation where you are going to get the biggest net tidal force on the Earth is going to be where you have an alignment between the Sun, the Moon and the Earth.  The Sun’s tides are about 42% of the Moon’s, so they are rather similar, although not exactly the same.  When things are aligned in this way, we say there is a spring tide.  Then you are getting a total effect which is about 1.42 times the tidal effect of the Moon alone, and that is no doubt when you want to put up the Thames Barrier and things like that.  At 90 degrees, when the Moon is in one of these positions, then we have what is called a neap tide - neap is just an old English word meaning weak or feeble – and in those situations, the tidal effect is a minimum and it will be about 56% of the effect of the Moon alone.

These are simple manifestations of tidal forces.  What is curious about these tidal forces is that they are what mathematicians call transverse.  This is like the effect of changing the sphere into the ellipsoids, the Earth’s tides, so they produce accelerations and effects perpendicular to the direction in which they are acting.  Remember, the direct gravity pulls the two points together along their line of centres, but the tidal force produces that distortion at right angles to it.  So that is the idea of a transverse acceleration or a transverse force.

Now, in general relativity, we see exactly the same phenomena acting in rather more exotic ways. Einstein teaches us that we should think of space as not being an untouched cosmic stage on which all the heavenly bodies’ motions are played out, but something which is affected by the motion of matter and energy upon it and which in turn can affect the way in which matter and motion take place.  So instead of thinking as if it is a stage, we think of it rather like a rubber sheet, a trampoline; as a large mass moves around on it, it deforms the shape of the trampoline, and the larger the mass, the greater the deformation. 

If I was to introduce another object and to fire it from A to B, if it moved in such a way so as to minimise the time that it took to get from the first point to the second, then because the geometry is distorted by this mass, the shortest path is to take a slightly bent route that makes it look as though you are being attracted towards the central mass.  So if you were a Newton, you would say there is a force acting which is attracting you towards that large mass, but Einstein’s picture is not to talk about forces at all, but just to have a view that this mass distorts the geometry and everything moves so as to take the shortest path that it can on whatever geometry it discovers.  And so if you want to take a path, then you have to take a very bent path, and Newton would say you were feeling a very large force.

Once you have taken up this picture of the curved space, distortion of space and distortion of time as well, created by mass and energy, you have two other things that could happen.  On the one hand, if you spun an object, if you twisted it around, then in the Newtonian picture, nothing would happen.  So if we spin a top in one place, it does not affect somebody standing elsewhere.  But if you had the picture of a rubber sheet distortion of space time, then if you twist the rubber sheet in one place, it makes it move around and fire away, you get carried around in the same direction.  So spinning objects have an effect on things which are far away.  This is not an effect that you would see in Newton’s picture of the world.  There is a satellite project at the moment which is flying gyroscopes around the world to watch how their direction of rotation, of the gyroscope, gets dragged around in the same direction that the Earth is rotating. It is a tiny effect, but it should be unambiguously observable.

But today we are more interested in the second effect of having this rubber sheet picture.  Suppose I grab hold of the edge of the sheet and start waving it around, producing waves, ripples in the geometry, then these will spread across the sheet.  They will behave like waves.  If you are sitting at one place when one of these ripples passes you, you will move up and down and in other ways you will respond to this movement of the curvature passing through space.  As they get further and further away, they should get smaller and smaller and smaller, and gradually damp out.  So if you are a long way away from the source of these ripples, violent events perhaps, you will see much bigger effects than if you are far, far away.  This effect of the rippling through space time, is the relativistic Einstein version of the tidal forces of Newton that we have just been looking at, and so we expect that it is going to have the same type of effect.  These ripples move at the speed of light and they also have an effect just like tidal forces.  So if there is a ring of particles, in front of me, and one of these gravitational waves comes in from the ceiling and goes downwards, it expands the ring in one direction and compresses it in the other direction, so it turns the circle of particles into an ellipse –just like the tidal force.  This is the reason why we think of this rather like a Newtonian tidal force.  More graphically, this is the effect on you.  There are two sorts of effect: you could find yourself being stretched in one direction and being squeezed in one direction; or, just like the hall of mirrors on the pier at the seaside, you could find yourself being squeezed in one direction and stretched in one direction.  This is the effect of a gravitational wave which is coming through the projector from above, or coming up from below.

More technically, it is interesting to look at that effect in comparison with other sorts of waves that we meet in physics, like those of electromagnetism.  Electromagnetic waves, when they pass through a ring of particles, cause every particle just to move backwards and forwards in the same way.  So when light hits your eye, it causes a movement, which creates little electric and magnetic fields, which then send a signal to your brain.  They hit a photographic plate; those movements call little chemical signals to record light having fallen on the emulsion.  In the case of gravitational waves, each particle behaves differently, and we have an effect where some of them move out and some of them move in.  So gravitational waves are not like ordinary electromagnetic waves.

If we look at the same idea again, reinforce this idea, there are two types of action, two modes of distortion that a gravitational wave would produce.  You start with a ring of particles, and as the wave comes in, as time goes on, you first create an ellipse of particles, and then it oscillates back to the circle, back to an ellipse of the other orientation, and then back to where it started.  This other sort produces an inclined ellipse, back to a circle, back to an inclined ellipse, back to where you began.  So as time goes on, this is the signal that you would expect to see in your particles that you might be suspending in space.  You can watch them expand and contract in one direction and then in the other.  So the challenge is to exploit this feature in some way in building a detector to try and tell when this sort of wave energy has passed through it.

One way that you might set about trying to gauge this is to say, well, let’s measure the magnitude of the effect by looking at the little change in distance, so let us look at the change that happens to the particles that move up there, the little shift in their position, divided by the radius of the circle of particles. This would be the relative shift produced by the gravitational wave.  Here, things get a bit alarming.  So you define a famous parameter in this subject which, for reasons of history, it is just twice the shift – it is the shift across the diameter divided by the radius of the circle of particles – and you know a few things about this quantity, that if you try to throw in a gravitational wave that was too strong, fantastically strong, you would bring in particles in one direction so dramatically that you would create a black hole.  So there is a sort of ultimate no-go for this type of phenomenon, that if you have the parameter “H” trying to be bigger than this quantity, where this is the mass of the object that you are hitting, “R” is its radius and “C” is the speed of light, then it would be torn apart by the gravitational waves that are coming through.

Let us look at a simple example that is realistic.  Suppose we had a neutron star, 1.4 times the mass of the Sun – that is the smallest it could be – and we put it 50 million light years away, then if we put 50 million light years in, put the mass in, and “G” and “C”, and work out the number, it is 6 times 10 to the minus 21.  So this is fantastic, fantastically small.

To give you an idea, suppose you were looking for a relative shift in a detector that was a couple of meters long, so the radius of the circle would be a meter or so, then you are looking at a shift that is about 10 to the minus 21 of a meter, 10 to the minus 19 of a centimetre.  That is one millionth of the size of a single proton.

So your first guesstimate is that the effects of these waves are fantastically small, so you have got to either have some stupendously accurate type of detector, or you have got to look at something that is closer and much more violent than a simple neutron star.

When one looks more carefully at what this source of this perturbation might be, you realise that you can do rather better than this formula, that what is creating the gravitational waves is not all of the energy involved, it is just the energy that is producing non-spherical pulsing and oscillations, that is changing the shape in that non-spherical way.  So it is even harder to do, if you had a very strong gravitational field created by a perfectly spherical object, and the spherical object was just changing its radius, but not its shape, going backwards and forwards like a balloon being inflated and then deflated, but always perfectly spherical.  There would be no gravitational radiation at all.  So the gravitational radiation is produced by the asymmetrical, non-spherical movements of an object.  You can regard “H” as being a bit like the “G” and the speed of light squared, the distance away times the energy, the kinetic energy, in the elliptical and non-spherical motions, divided by the speed of light squared.  It is these speeds of light squared that sit in at the bottom here which are very large numbers – so C squared is 10 to the 21 centimetres squared per square second.  This is why this effect is so small.

Let us first look at the sorts of places where you could go searching for effects of this sort, and then think about how you might detect them.  There is a little list of prime candidates.  Anywhere in the universe where you see something rather violent and dramatic going on is likely to be a good source of gravitational radiation.  Exploding stars, like supernovae, are good candidates. 

A few years ago, I think it was back in 1987, there was a supernova in the nearby dwarf galaxy to ourselves called the Large Magellanic Cloud.  An astronomer in Australia was looking at a plate in real time, they had just taken a photograph of a bit of the sky; he looked again a few minutes later, and suddenly the whole of the image was burnt out on the plate.  A star had exploded in that other galaxy, which he had caught virtually in real time.  In fact, after that explosion, people realised that had gravitational wave detectors been turned on in places where they existed, they might well have seen some gravitational wave signal from this explosion.

So supernovae are one candidate.  It turns out another candidate, really the best of all, is a situation where you have a pair of neutron stars or a pair of black holes, which orbit around one another, rather like the Earth and the Moon do, but after a long, long period of history of doing that, they gradually run out of energy, they get closer and closer to one another, and eventually they merge.  That merger event, which could be quite a common occurrence because there are so many of these pairs around in our galaxy and beyond, gives the most ‘seeable’ burst of gravitational radiation.

Another possibility is something that is periodic, like a pulsar.  It is just orbiting around another object, in a very asymmetrical orbit, and would give a signal of gravitational waves that had a periodic pattern representing its orbit.  That is another possibility.

The others, that astronomers are very interested in, are gravitational waves which are just produced by all sorts of things, all over the place, some exotic, some not so exotic, perhaps the early formation of the first galaxies, and all these would just get added together, rather like background noise in a radio signal.  You might hope that one day you could discover this random background of gravitational waves being added together from all the sources in the past.

The last one, which I will not say anything about today because my next lecture will say quite a bit about this in another context, is that we expect that there should be very particular types of gravitational wave left over from the beginnings of the universe, and it is a great challenge to try and detect them and to check whether they have the particular properties that are predicted, the particular pattern of energies.

We will now have a look at one of the most interesting situations.  It is one of these binary stars, and it is one we have met before in another context in these lectures, and it is the so-called binary pulsar.  This was discovered in the early 1970s by Hulse and Taylor and they received the Nobel Prize for this discovery some years later.  What they discovered were two objects orbiting around a common centre.  These objects seemed to be neutron stars, so they had a density equal to a single atomic nucleus, 10 to the 14 times the density of ordinary material around us now, and yet their size is just about 3 kilometres.  So they are incredibly dense.  If they were just twice as heavy as they are, they would be black holes.  These are both of mass of about 1.4 or so solar masses and one of them has the remarkable feature that it is a pulsar, so no doubt it is spinning fantastically rapidly and, rather like a lighthouse, when it spins and faces in our direction, we see a pulse, and we see a pulse then in a period of time equal to the spin time.  So this pulsar is like a clock.  It is an object moving around with its own clock attached, and the pulsing period responds to the gravitational field that it is in and enables us to make fabulously accurate observations of what is going on in this system.

These objects in this system, so dense are they and so close together, that these orbiting stars are moving at one per cent of the speed of light, so they are objects a little more massive than the Sun, about the size of a small part of London, moving around at one per cent of the speed of light.  That is about two miles per second or something like that.  What you can focus on in this system, as they go around, one is going around the common centre, to a first approximation it is orbiting in an ellipse, but the ellipse never quite closes up, and if you follow it from one orbit to another, the ellipse is slightly displaced, by a little more than 4 degrees each time it goes around many, many orbits.  You could measure what is going on by, for example, working out what this angle is, how much the orbits get displaced, and the displacement amounts to about 4-and-a-third degrees every year.  In the case of our solar system, you see an analogous phenomenon for the planet Mercury.  It advances by 43 seconds of arc every century, so this is fantastically bigger.  This system has very, very strong gravitational fields.  It has non-circular motions.  It is a prime site for searching for the effects of gravitational radiation.

Here are some of the statistics about it.  The nice thing is that each one of these orbits takes less than 8 hours to complete, so you can watch, in real time, what is going on in this system and observe it in enormous detail.  The pulsar period is very slowly changing, and the rate at which it is changing are a few parts in 10 to the 12 seconds per second, so if the orbital period is in seconds, you are interested in how much did it change per second.  This is an incredibly small number.  It is a reflection of how accurately you can measure the period of the orbit of this system. 

But why is this interesting and what has it got to do with gravitational waves?  Well, if you use the formula that tells you how much of the energy is involved in produces distortions in the shape as it orbits around.  In this system, as the 2 objects move around their common centre, they should gradually lose a small amount of their energy by gravitational radiation going away from the system.  As they lose energy, their orbit gets a little bit smaller, and they will get closer together.  What you expect is, as time goes on, the system will lose energy by gravitational radiation, the objects will get closer together, so the period of their orbit will get smaller.  We can predict, from the formula for the amount of the rate of gravitational wave production, exactly how much we expect the orbit to shrink by as time goes by.  You can use this prediction then as a test of whether gravitational radiation is really leaving this system, and leaving it at exactly the rate that general relativity predicts.  Over 25 to 30 years, the results of this experiment are very remarkable.

When you reach a particular point on the orbit, so it is giving you a measure of the shrinkage of the orbit, and time, in years, from the discovery – 1974 – up to the present year, or last year.  This is the prediction from general relativity of how the orbit should decay if it is losing energy by radiating gravitational waves, and there is a beautiful agreement to this 12 decimal place accuracy in effect of how the orbital period should change.  Most astronomers would regard this as a very, very powerful indirect discovery, that gravitational radiation does exist and it is being radiated by this system at exactly the rate that Einstein’s theory predicts that it should be.

The challenge resulting from this is to try and find ways to detect radiation like this directly, so when it reaches the Earth, can you see its effects directly?  Well, the prime candidates are systems a bit like the binary pulsar.  Its motion is causing ripples in the geometry of space time around it.  Those ripples are moving away.  They eventually reach us.  But when the orbit decays enough, it will start to speed up dramatically, and eventually the objects will coalesce and collide.  So we are looking for objects which are like the binary pulsar, but in the final stages of their lifetime, when they have produced an incredibly strong nearby gravitational field and they are both about to go bang.  That is the most ‘seeable’ event, and we see lots of binary pulsars around in different stages of maturity.  So it is not that the binary pulsar was a very special, unique event that we do not have any reason to find anywhere else.  They seem quite common phenomena.  Most stars are in binary pair systems, and there will be other ones which are heavier still, where the two objects are not neutron stars but they are black holes, and they will produce even more gravitational radiation.  So in many ways, these are the most interesting prime candidates for gravitational waves.

Astronomers produce simulations, by computer, of what would happen in detail when one of these coalescences occurs. They can produce a picture, colour coded by radiation intensity, being squeezing out in one direction, coming in in another direction, as these 2 objects coalesce.  The reason for doing this is that you want to predict in enormous detail what should be the profile, what should be the pattern, of the gravitational wave energy that comes out of one of these objects.  So if you detect something in your experimental detector, can you identify it, can you say “oh, that’s a binary star system that’s coalescing,” or is it a supernova, or is it something else?  Can you really do astronomy one day with gravitational waves?

I have 3 pretty pictures, just to remind you of these scenarios.  The colliding, orbiting neutron stars, eventually their collision to form gravitational waves in the merger event.  They might eventually themselves settle down to form a black hole, or the formation of a black hole might be a completely different violent gravitational event.

The most interesting thing of all to try to predict and understand is the magnitude of the signals that we should get from events like this.  So that parameter “H” that we mentioned before, so if you had a ring of particles, as it were, and a gravitational wave is going to hit it, it stretches and squeezes, this is the amount of stretching divided by the size of the detector.  There are very, very small numbers – 10 to the minus 18 to 10 minus 24 – and the frequency of the radiation.  This will depend on the size of the source and how quickly it is varying, and you want to build your detectors so that they are most sensitive in places where you expect there to be most signals or the most visible signals. You have what are called compact binaries: these are very close pairs of stars, rather like the binary pulsar.  You have got an example of 2 black holes in a binary system.  They could be much, much bigger, 100,000 solar masses each. 

There is a model for an event for forming a black hole of about that size - 100,000 solar masses – so the burst of radiation you get from that.  Then there is what happens if that black hole binary pair eventually spiral in and coalesce and merge, and that is really the biggest of all.  You have got supernova formation, exploding stars, and so on.  We are dealing with numbers of order 10 minus 20.  In the case of the smallest things, we are identifying smaller black holes, going down to about 10 minus 23.  Supernova collapse, depending on how close it is, how asymmetrical and non-spherical it is, you have got a wide range of possibilities, and the frequency range spans a factor of about 10 to the 7, 10 to the 8.

The other curves are marked LIGO and LISA.  What they are showing us are the expected sensitivities of the detectors. Obviously those detectors were designed and planned with the express intention of covering these crucial areas where we expect the signals to lie.

What are the detectors like?  When the subject first began, long, long ago, the ’60s and the ’70s, the original detectors that people had in mind were enormous metal bars that would weigh many, many tons: a great cylinder of metal, perhaps a metre in diameter and several metres long.  What you wanted to do was to try to detect what happens when a gravitational wave passes through your bar - it will stretch in one direction and contract in the other - and you try and tune the mechanical properties of the bar so that you get a resonance between the natural vibration frequencies of your bar and those of the gravitational wave.  As always in this subject, the trick is not being able to detect these tiny effects, but making sure you do not detect anything else.  So you have to suspend the bar in as good a vacuum as you can possibly make, at low temperature; you have to isolate it from all seismic disturbances, like football teams running past next door or people driving cars around, or even physicists walking around next to it.  This is a fantastically challenging problem.  Bars were the first generation of detectors.  There are still some gravitational wave bar detectors that exist.  They have a sensitivity, at best, 10 minus 18, so they are severely limited by their internal mechanics and the extent to which you can remove noise. 

One of the other things that you wanted to do in that type of detecting work, if you had one bar and it suddenly deflected in some way and you claimed to see a signal, people might not believe you.  They might say it is the football team running past.  So what Joe Weber, who was one of the pioneers of this, wanted to do was to have 2 of these detectors in very different places.  In his case, it was in different states in the United States – Illinois and in Maryland – and you would monitor the signals in each one, and of course, if you found a signal in one which you did not see in the other, it is probably the football team, but if you see the same signal in detectors on other sides of the country, it is very likely to be a real signal.

The problem historically was that when Weber first set out to do this, he claimed after a while that he did see signals for a long period.  Nobody else believed him at the time, and I think even now, no one believes that he really saw gravitational waves – he could not possibly have done at that time, unless there was some sudden outburst that just happened then and disappeared ever after.  Weber died some years ago, so we cannot ask him any more what he was really doing, but Weber was a great pioneer in the building of detectors.

But if you want to really see gravitational waves, enormous bars are not the way to go, so there is another technology which enables you to get down to these fantastically small numbers, and what that technology is is interferometry.  What you want to do here is you imagine that we have got a crossover, gravitational waves coming in from above, and so what it is going to do is it is going to stretch things in this direction, and it is going to squeeze them in the direction at right angles to them.  How can we exploit this in a detector?  Well, interferometry has the following type of set-up.  Suppose you have a laser beam, and you fire it into a beam splitter, so this is something that allows, say, half of the light to go on through, but reflects half of it at right angles.  Half of the light goes on through and eventually meets a mirror at the end, a suspended mirror, and so is reflected back; the light that has gone at right angles has the same fate, gets reflected back from a mirror, and so the 2 beams meet again at the centre. 

This is the secret of fabulously accurate measurement in physics, so that you can measure a mismatch between the oscillations of those light beams when they come back together in the middle to fantastic accuracy.  You can keep on making the accuracy almost as good as you like by simply making these arms longer and longer, so the longer you make the arms, the more time there is for the light to feel the effects of the gravitational wave, as it goes out, hits the mirror and comes back.  If you want to make the effect twice as big, you make the arm twice as long.  If you want to make it a thousand times more sensitive, you make the arms a thousand times as big. 

This is the essence of laser interferometry, and there are all sorts of cunning tricks that you can now employ to make the sensitivity ever greater.  The laser beams are all confined inside a low temperature environment, so that everything is kept as cold as possible, so that jittering due to thermal agitation is absolutely minimised.

The next thing you are interested in is generating lots of laser power, and that is a technological challenge.  When you send your beam back, you need not just send it once before you check whether the interference occurs with the orthogonal beam; you could put silvered mirrors and send the beam back and forth millions and millions of times.  This would have the same effect as making the arm fantastically longer, but as a constraint, the silvering of the mirrors had better be extraordinarily good, otherwise you get a degradation of the signal.  This is one of the great technical advances of this gravitational wave experimental development - I think it probably counts as one of the highest technology areas of science - so this type of astronomy has pioneered the most accurate detectors anywhere in science anywhere on Earth.

I can remember being involved in the European appraisal panel that had to decide whether to fund the big European project of this sort many years ago, and there was a remarkable development during the appraisal process that there had been people around the world who had tried to estimate how good you could make a detector like this, and that they had produced an argument that there was a fundamental limit to how good you could produce a silvered mirror to reflect the laser beam back, and this placed a limit on how well you could do the experiment.  Then, rather unannounced and completely unexpectedly, British Aerospace declassified some of their work on high silvering coatings, so presumably this was all something to do with Star Wars and bouncing laser beams around, but it turned out that they had fully functioning, working mirrors, which had reflectivities 10,000 times better than the so-called absolute maximum possible!  So overnight, they made some of these super-high-tech surfaces available for this sort of experiment, and you had a massive increase in expected capability.

These are the key ingredients.  You have also got to suspend these mirrors.  They are very heavy masses – they are the things that the gravitational waves when they come through are shifting and wobbling in different directions, and you are trying to detect that tiny wobble by its effect on the reflected laser beams.  By making the arms extremely long, you can get the sensitivity that you require.  By long, I really mean long.  The existing project, which is known as LIGO, so the Laser Interferometer Gravitational-Wave Observatory – one of the political things you soon learned about this area of the subject, that suddenly gravitational wave detectors started to be called gravitational wave observatories, so that means they can make bids for astronomical funding rather than just for physics funding!  So if you call it an observatory, it is astronomy, and if you call it detector, it is physics!

For example, in the USA, there are 2 stations like this, so again, you want to have more than one so you can play this game of saying, “If we see a signal and you see a signal on the other continent, it’s likely to be a real signal, but if we see a signal in only detector, people won’t believe you.”  So in these 2 places, in Louisiana and in Washington state at Hanford, there are huge L-shaped interferometers, and by huge, I mean these arms are 2, 3, 4 kilometres in size, and they are also bouncing light back over a long period of time.  The timer period is determined by how good your reflectivity is.  So you have surfaces with a reflectivity good to a part in a million, and so that enables you to use many more bounces of the light, effectively increasing the length of your arm.

I have a couple of photographs of those American stations, to give you the idea of the scale.  Of course, it’s in the middle of nowhere so that you are not bothered by the football team.  So where there is one arm, there will be another one perpendicular to it, and another one going through the desert.

There is also, as I mentioned, a European, in fact a UK, presence in this project.  The UK, through the group at Glasgow, has played a key role in developing the technology that can actually make this detection.  The European group does not have a site which enables you to fit 3 kilometre arms in undisturbed in some desert, so the European project is based in Germany, in Lower Saxony, and it has a 600 metre arm, and it is known as GEO600.  That is very much used for developing the next stage of the technology – better suspensions for the mirrors, better silverings, better laser technology, and so forth.  The key is to have 2 detectors, on opposite sides of the American continent, one in Europe as well, and in the future, there will be operating detectors in the Far East and the Southern hemisphere as well.

Has anything been seen by these detectors?  Well, for many years, it was constantly a game of improving your sensitivity, making sure the lasers as stable over long periods of time but, a couple of years ago, the first engineering runs started to be operating in this experiment.  This was very exciting.

No one is claiming to have detected gravitational waves yet.  What they are trying to show is how sensitive the detectors are.  There have been relentless and impressive progress. The sensitivity is down around 10 minus 21, approaching 10 minus 22. One can see things in 10 minus 21, 10 minus 22, if you are lucky.  You could see something, if you took to pieces all the signals, analysed them in detail, you would be capable of seeing some of these events, but people are really expecting that the most probable events are going to be really down near 10 minus 22 and below.

There is no doubt noise.  It is different sources of randomness and noise in the detector, fluctuations in the lasers.  You have a procedure for cleaning this and removing all those things, and you want to then look at what’s left.  The next stage in the game will be, when you have improved your sensitivity a bit more, to start doing that cleaning much more seriously, and to start arguing whether or not there are residual signals.

What would you do with them?  How do you go about saying whether signals are real or if they are just some form of noise?  There are many research groups around the world who spend their time calculating in enormous detail what you would see if your detector was hit by a real gravitational wave signal.  Unfortunately, in many cases, the pattern of the signal is relatively straightforward – the real signal – and you can predict in enormous detail what you would see as time went on, and produce a series of templates.  This is the magnitude of the fluctuations in “H” against time, and it is the binary pulsar in effect, so what would happen the binary pulsar when it came to the end of its life – 2 neutron stars spiralling in until they eventually hit one another.  The frequency of the radiation is going up, so it is like a chirp, birdsong, change of frequency, in this case going up, rather steadily going up, and then finally, when the merger occurs, there is a rather sudden burst.  This would be what you would call a template.  You could make a template of this sort for all sorts of different types of merger, adding all sorts of complications, which are not present here, and a computer will overlay your data stream with these templates, and it is looking for a match, looking for a suspicious situation.  It is rather like a fingerprint analysis: you are looking for the fingerprint, some matching features, of the gravitational wave burst in time, and then you focus in on that part of the signal in enormous detail.

So that is the state of play with LIGO, and we all hope that over the next few years there might begin to emerge some evidence for a real signal.  It is rather amusing that when this began, I think in 2004, that Ladbrokes were offering odds of 500 to 1 against a gravitational wave being detected by LIGO before 2012.  So all the people involved in this experiment immediately went out and took those odds, and apparently, 4 weeks later, the odds were down to 2 to 1!  This is very gratifying, that the odds are now actually only 2 to 1 that we will detect a gravitational wave by 2012.

But the last thing I want to show you is something yet more ambitious, regarding where we might hope to get to with a detector. LIGO is looking for the coalescences.  There is another detector range, which is called LISA.  LISA is a laser interferometer, as before; not on the Earth’s surface, but in space.  This is a planned project in which one will have orbiting in the solar system a trio of satellites, and they will send laser beams to one another and around the triangle, using their highly reflective surfaces, and of course, being in space, we don’t have problems of temperature fluctuations or football teams running nearby.  You have some analogous problems.  The interesting thing is that instead of having the arms of your interferometer a few kilometres in size, you can have them as half the radius of the solar system.  This space project will be monitoring laser beams moving around this triangle, looking to see if you get little interference patterns created by a gravitational wave that comes through the centre of the triangle, as it were, causing some arms to expand in this direction and these to contract.  This is a spectacular future space project that is more than on the drawing board, it is planned in enormous detail, and the hope is that in combination with LIGO on the ground, we will by this means finally detect gravitational waves directly. 

As we will see in my next lecture, in a couple of weeks’ time, that will not only confirm that these objects like black holes and neutron stars really are shaking the structure of space and time, they will allow us to look back to the first instance after the beginning of the expansion of the universe commenced, far, far further back than the background radiation of photons allows us to see.  Gravitational waves allow you, as it were, to surf the universe in a new way, and in years to come, we expect that this will be a new type of astronomy.  It is the astronomy that doesn’t just look at visible light or other parts of the electromagnetic spectrum, but you can view it as looking at tidal gravitational forces directly.  It is a probe of the places where the most violent things are happening in the universe, and look at the force of gravity very directly.

© Professor John Barrow, Gresham College, 30 November 2007