So today we're going to start talking about uh one of the more recent uh major advances in relativistic astrophysics namely the detection of gravitational waves uh and we'll talk about it first from a conceptual point of view and then after intermission uh we'll talk about the specific instrument uh with which this has now been done the objects we've been talking about so far in this part of the course the pulsars the X-ray binaries the quazars all followed a kind of very similar historical pattern uh in the 1960s some new phenomenon was discovered uh uh and the reason it was able to be discovered is because new windows of electromagnetic radiation were opened up radio astronomy x-ray astronomy and so forth uh and then uh within 10 years a basic hypothesis of what these objects actually were had been uh put forward and more or less established uh and over the ensuing decades uh more detailed observations were made more refined ideas were created uh and uh by the turn of the century in all three of these cases you had a pretty densely woven web of ideas and observations and theories and a whole set of stories that encompassed and connected all of these different kinds of objects and so that was the big achievement in this area in the latter part of the 20th century and now what we're going to do uh is go on to the 21st century uh all of these objects the pulsars the X-ray binaries the quazars the Stellar Mass black holes the super massive black holes these all continue to be studied um and uh and the observations refined and so forth uh but uh we're now going to talk about a phenomenon uh the first evidence of which was only discovered about five years ago and that is the direct detection of gravitational waves now this is very important from the point of view of understanding relativity uh gravitational waves were one of the very first predictions that Einstein made uh over a century ago when he developed the theory and so to have them verified observationally is is a great Triumph but it's also very important from the point of view of observational astronomy uh because at the end of the 20th century we had pretty much gone through the entire spectrum of electromagnetic radiation from low frequency radio waves to radio microwave infrared Optical ultraviolet X rays and high energy gamma rays top to bottom we pretty much uh explored the whole of the electromagnetic uh radiation spectrum and now we get a new kind of radiation and the expectation is that whenever you start looking at a new kind of radiation new and exciting objects come to the four and so I would say that with respect to studying the gravitational radiation gravitational w we are right now at a comparable point to where we were in the 1960s in terms of radio astronomy and x-ray astronomy and so there is the Hope indeed the expectation uh that uh many exciting things uh will come that we've only just started uh this new kind of astronomy so uh let me remind you about gravitational uh wave radiation we talked a little bit about this in the context of the binary Pulsar uh what happens is uh you have some Mass that's being accelerated uh for example it's an orbit going around in circles uh and this generates waves what's waving what's waving is the space type curvature the amount of curvature is changing periodically in both space and time and that gives you a wave of space-time curvature and these waves propagate outward into space uh at the speed of light as do electromagnetic waves uh and uh they have the an the effect of changing the sizes and the shapes of objects slightly that is to say if all of a sudden uh the space-time Continuum that you're in is curved more than it was a second ago uh then all of the distances all of the triangles add up to slightly you know different numbers of degrees and all the distances are all slightly changed uh and then when the wave passes or you get back into the trough of the wave you go back to normal and then a second later the curvature changes again and so objects kind of move uh back and forth uh and we've seen the effect of gravitational waves although we haven't seen the waves themselves uh but we have seen the effect of gravitational waves on the orbit of the binary pulsar and you again remember how this works two neutron stars are in orbit around each other the orbit super short uh and that orbit is observed to decrease here's the observational data from 1975 to 2005 why is the orbit decreasing because gravitational wave radiation is being emitted by this system and that energy that goes into the gravitational waves is being pulled out of the orbit and therefore the orbit is marching inward uh so that that the source of the energy is basically the gravitational potential energy of this orbit and there's an equation uh and you can figure out how long it will take uh these things to merge with each other and the answer is some number of tens of millions of years uh and that's actually quite short in this context because the universe is billions of years old and so we have an example of something uh in which first of all you can observe the uh effect of the gravitational wave the shortening of the orbit uh and it works out perfectly according to the theory and according to that very same theory if it continues to uh the orbit continues to shrink at this rate uh these two neutron stars will run into each other uh some number of millions of years in the future so the question then arises what happens at the end what happens when these two objects spiral closer and closer together and eventually murder so as they get closer one of the things that happens is that the amount of GRA gravitational wave radiation that's emitted increases you get more and more radiation that's because they're getting closer to each other's schield radius and so any relativistic effect is going to increase uh and that fact the fact that there's more and more gravitational wave radiation emitted makes the period decrease even faster because that's where the energy is coming from to supply these W and so uh as you get closer and closer this whole process uh takes off uh it's uh an exponentially increasing thing so gradually moving together and then faster and faster and faster until it merges the frequency of the Waves increases uh what that means is there's one wave given off every orbit and so if the orbit gets shorter and faster more waves are being given off faster and so the frequency of the Waves increases uh that's another way of saying that the wavelength of these waves decreases one wave is emitted per orbit the Orbit's getting shorter so the waves are coming faster and faster uh and because the amount of gravitational wave radiation is increasing uh the amplitude of the waves that is to say the size of the waves is also increasing and you can see it on this little diagram here out here uh when it begins uh you have these waves going up and down and as the two objects approach each other what happens is uh the waves come more and more frequently and the amplitude of the Waves increases uh in an exponentially increasing manner uh this is referred to as a chirp because if you were to have sound waves in which the frequency and the amplitude is increasing that is to say the pitch is getting higher and the sound is getting louder uh so high pitch things have high frequencies uh High amplitude things are loud uh then you would get a sound that sort of sounds like [Music] this uh and uh that's referred to as a chirp it's kind of like uh noises that uh some birds make so uh you get this chirp uh and that brings the objects ever closer together ever faster and eventually these two objects whatever they are will touch and merge and if it's two neutron stars then they're going around really fast and so there's a lot of centrifugal force and so as they uh touch each other merge they throw some material off into space but the rest of it combines to make a rapidly Ro rotating much more massive star and one of the things about neutron stars is you can't get much more massive without becoming a black hole uh and so in many cases it is likely for example with the binary Pulsar it is likely that when they merge they will end up being a rapidly rotating black hole if you've got two objects that are black holes already uh then the event arizons eventually touch each other and you end up with uh uh a sort of nonspherical schwar radius radius is the wrong word but you end up with an event horizon that has sub weird shape with two singularities inside it the singularities are driven together and the result is a rapidly rotating black hole this is described not by the schwar show metric but by the so-called Curve Metric which I think I showed you in passing at some point along the way uh you can figure out the masses of the two objects uh if you see these waves uh by the size of the orbit immediately pre merger that is to say they're going at close to the speed of light uh they're traveling a distance 2 pi times the schwar radius the more massive it is the bigger the Schwarz Shield radius but the speed of light doesn't change uh and so the frequency right before the merger tells you how much mass there is but you can also determine how much mass there is afterwards uh by watching the things settle back down what's called the ringdown phase and so this is a little plot again we're dealing with a tiny fraction of a second here uh uh and when you're doing the ins spiral for example what the uh binary puls is doing now gradually getting closer and closer together uh you can basically use the post neonian Theory when you get close enough so that you're not really traveling in circles anymore uh but you're starting to merge and you're starting to perturb the shape of the event horizon or the neutrons star uh then you have to use the full Theory and in order to use the full Theory it's too complicated to to to actually do the algebra and so you have to do this by computer simulations uh and so in the merger phase as these things are really getting close to each other and touching uh the way you do it is you construct a computer simulation of what ought to happen but then after they actually merge and there and this ringdown is in progress there's another kind of approximate Theory uh black hole perturbation Theory so you've got a black hole but it's a little lopsided uh that's again something you can do algebraically so there's one approximation that works out here there's an approximation that works out here but in between when all of the features of Relativity are in play uh you probably have to deal with it as a computer simulation one last piece of theoretical work uh which is there is this very curious number which is C to the 5th / G C and G have their usual meanings in this little equation that's the speed of light that's the gravitational constant we've been using these constants all along and it turns out you know each of these constants has units associated with it the units of the speed of light are meters per second uh there's some more complicated set of units for the gravitational constant but it turns out this particular combination C the 5 / G has units of a Luminosity units of luminosity and if you ask okay let's do the multiplication C5 C the 5th power over G these are constants of nature so this is somehow some kind of very special um luminosity in the same way that c is a very special speed and it turns out this Luminosity is equal to something like 3.7 10 52 Watts lot of wattage uh in fact it's 10 the 25 almost 10 26 times brighter than the sun uh and this is greater than all of the electromagnetic radiation in the universe put together so this is would be a greater Luminosity than the whole universe put together at least as observed uh in ordinary electromagnetic radiation the reason this is interesting is it turns out that this is the maximum is a maximum luminosity in the same way that the speed of light is a maximum velocity and in particular it's the maximum Luminosity emitted in gravitational waves of a emerging binary black hole so at the very moment when the two event Horizons touch each other uh you just for that instant achieve this Luminosity remember the brightness of this thing in gravitational wavs has been increasing all along uh it's been getting brighter and brighter and brighter and brighter and it gets brighter right up to the point where it hits this number and that's the moment that it merges so the reason this is interesting is that this is so bright that there's so much gravitational radiation being emitted at the point of merger that it outshines the whole rest of the universe for that one tiny second and it's because there's so much gravitational radiation emitted uh that it turns out it's possible to actually detect it uh if you have sophisticated enough instruments and that's what we'll talk about uh after

intermission okay so the question then is how would you go about observing these gravitational waves uh the first thing is that there is as we've said before a plausible source of these waves uh that's really uh expected to be very powerful we know that there are double neutron stars that's what the binary Pulsar is we know there are double neutron stars that will emerge in a relatively short amount of cosmic time we also know that there are systems that contain a black hole some of which have a large enough companion star a massive enough comp companion star uh that you expect the companion star itself to turn into a black hole after it undergos a supernova explosion an example of this is the CIS famous system signis X1 and so you know that these will evolve into double black hole systems so we observe double neutron star systems we observe things that are likely to end up as double black hole systems we know that if you merge these kinds of things you get very large amounts of of gravitational wave radiation so there's some expectation that there are sources of this radiation uh which will produce large amounts of it that you want to be able to see so uh this is what's said down here given the huge amplitude of these waves such systems should be observable not just in our own Galaxy uh but in any Galaxy anywhere in the universe and that's important because while we do know about these objects they're only a dozen of them in our in our galaxy uh we only expect double black hole systems uh to be produced I don't know uh once in a long while uh these things will merge in a few million years and so the expectation is that there'll be an event of this kind a merger of neutron stars on black holes um once every million years or so in this galaxy so if you're going to be able to see these things you'd better be looking at millions of galaxies so that you have a hope of seeing such an event once a year or so because we can't be waiting around for a million years uh to see these things in our own galaxies fortunately the amount of gravitational waves emitted is very large and so you do expect to be able to see these mergers at very great distances uh and so uh there are millions and millions perhaps billions of galaxies uh in which such an event could be observed and you do expect expect to see at least one per year and perhaps more depending on the sensitivity of the instrument so what happens when a gravitational wave rolls over you so we're sitting around on Earth in the distant Universe somewhere two black holes collide with each other uh the black holes emit all of this gravitational wave radiation some tiny fraction of which reaches us uh because it's a one over R squ process just like life so when you're very far away you only see a small fraction of what was emitted but there was a lot emitted we're a long way away but there's still some so this wave Rolls by us and what happens as that happens is that the curvature of SpaceTime changes and the sizes and shapes of objects uh are changed periodically and and this is represented down here here's the wave uh o over the course of one wavelength basically and you can imagine this wave is moving from left to right uh and as it does so it passes over some object uh and what happens is uh that as it passes over the object gets squeezed first in One Direction then in the other direction then in One Direction then in the other direction uh as the wave passes over it as is indicated here So the plan is that you want to be able to measure the length of something to incredibly High accur Because by the time this gravitational wave this curvature reaches the Earth uh it's uh although it started out very powerful it's it's a pretty it's a pretty small effect uh and so this is this down here is greatly exaggerated uh the uh effect is is small even compared to a single atom so you better be able to measure the length of something to super high accuracy but if you can do that you'll see it uh going back and forth as the wave passes over the exact effect depends on the orientation of the length you're measuring compared to the direction of the gravitational wave if it's coming sideways you'll see something like this if it's coming from uh out of the plane into the into the uh paper there uh you'll see it move you'll see it stretch and and decrease in the other direction so uh it depends exactly on the direction that the wave is coming from uh and something that's important to keep in mind is that you're not looking for a one-time effect you're not looking for this thing to suddenly get bigger or suddenly get smaller what you're looking for is a very specific and well-known pattern of changes it's G to do this and the thissing uh will get higher in frequency and larger in size as time goes on uh because you're looking for a chirp uh and that's important because you know any instrument that is likely to be able to detect this will also be sensitive to uh earthquakes uh to a truck going down the road 30 miles away and things like that and the way that you uh uh prevent yourself from being fooled by terrestrial events uh is basically to look for this particular pattern the chirp rather than uh simply a a a slight change in size so how do you do this we know how to do measurements high accuracy measurements of lengths of things they knew how to do this in the late 19th century Michaelson and Morley did it uh you do this with an interferometer uh and remember the setup for the Michael soring experiment uh they figured this ether wind was coming down here and so they wanted to compare uh the distance from from uh the beam splitter here to one mirror as opposed to the distance between the beam splitter and a different mirror uh and you do that by sending the light in these two directions recombining it and seeing if it recombines as constructive interference where the Peaks line up with the Peaks or destructive interference where the Peaks line up with the troughs and you cancel uh you cancel the light out so if you were to do this in such a way that rather than just sending it up once and bouncing it back you send it up and bounce it back thousands of times if you do it that way then a change of one 1,000th of the wavelength changes you from a peak to a trough uh and so if this distance were to change by one part in a thousand uh you'd be able to see a change from destructive to constructive interference if you bounce the thing back and forth enough it turns out you can also detect very small changes you don't have to go all the way from purely constructive to purely destructive interference uh you can change just a tiny little bit make it just a fraction more destructive and the light will diminish very slightly in intensity but we've gotten really good at measuring how bright light is that's what cameras do is they measure how bright light is we have very high-powered uh Optical detection uh uh uh equipment and so uh by combining bouncing the light up and down a large number of times with a situation in which you can detect a very tiny change in the interference pattern uh you can have a situation in which you can measure changes in the length between the beam splitter and the mirror to incredibly high accuracy and in particular you can compare it to the length in the other

direction uh and so uh for uh they figured it out for a merging Stellar Mass black hole in a distant Galaxy you better be able to observe changes of one part in 10 to the 21 of the length so if you have a kilometer long path if the distance between the beam splitter and the mirror is a kilometer uh then that's about 10 Theus 18 M which is a small fraction of an atomic nucleus now you would think that measuring something to 1 1000 the size of an atomic nucleus would be very difficult and you would be correct that it's very difficult but it turns out that with this kind of a laser driven interferometer uh that uh the technology was developed over the past few decades good enough to actually measure a change in the length that small that was a tremendous technical achievement uh but it has indeed been achieved uh and so here's what this laser interferometry gravitational wave Observatory looks like it's basically two long tubes four kilometers as it happens uh they're set up at right angles to each other uh and it works just like Michaelson and Morley had it only uh with an additional C worth of technology so you send in laser light you pass it through a beam splitter some of it goes this way some of it goes that way it bounces back and forth for a while uh then you recombine it you have a detector out this end which measures to very very high Precision how bright that light is we've constructed two of these things actually by now there's there's a a third and a fourth coming online the the first two one was in Louisiana the other in Washington state so couple thousand miles apart from each other uh the point of having more than one of these things is that um it helps you filter out uh local events little local earthquakes or uh uh trucks and other other kinds of local events uh because you are looking for chirps and you're looking for identical chirps in two systems 2,000 miles away because if there's going to be a gravitational wave passing through the Earth it'll pass through both Louisiana and Washington and indeed everywhere else on the planet there'll be a little bit of a time offset by a couple of milliseconds why because it takes light a couple of milliseconds to make it from one place on the earth to another and this wave is propagating at the speed of light so you there may be a time offset of a few milliseconds but other than that you're looking for identical chirps in two places by now as I said there's a third online in Italy uh three of them is good because the time delays between them allows you to triangulate the position that the gravitational wave was coming from uh there are more in construction there's one that's going to come online in Japan there's one that's going to come online in India uh and uh all of them are being constantly upgraded so that they're increasingly sensitive as time goes on so uh here's what it looks like these things actually EX this amazingly enough here's the one in Louisiana and Livingston here's the one in Hanford Washington you can see uh the difference in the uh vegetation of those two uh of those two places and uh they have been in operation now uh for some number of years and in early 2016 so just under five years ago uh they announced that they had indeed discovered a gravitational wave cave presumably coming from a merger of two black holes that had passed through the Earth the observation was made on September 14 2015 and then they spent a number of months making sure that they hadn't screwed up in some way and here's the data notice down here this is time in seconds this is two10 of a second from the start of this plot to the end of this plot so this is the two10 of a second where we are observing the merger of two black holes so uh and this is strain uh that's basically how much the um the length has changed uh as a fraction of the length you're observing so you're observing four 4 kilometer thing uh and so the change in the in the in the length of the thing between zero and one is 10us 21 Time 4 kilometers so this is some kind of Delta Factor and it gets bigger and it gets smaller so uh this is how it is ordinarily and it gets bigger and smaller here's what they saw at Hanford and this uh orange spiky thing is a what they actually observe and the yellow line drawn through it is a prediction of uh one of these computer simulations of black holes merging together so similarly here in Livingston Louisiana uh the D the the fat blue line here is the observations and the thinner blue line is the prediction made by one of these computer simulations uh and if that wasn't can uh and and notice what's happening uh it's uh the uh waves are getting closer and closer together and bigger and bigger just like they're supposed to that just like a CH and if the comparison between Theory and data wasn't enough what you can do is take the um Washington data shift it by a couple of milliseconds and put it on top of uh the uh Livingston data the data from Louisiana and they lie right on top of each other and so they had this fabulous press conference uh in on February 11th 2016 and I have to say I saw this data and you know the hair went up on the back of my neck because this is just like it looks in the textbooks it's unbelievable uh I know I wrote Such a textbook and it's this this is figure 9.3 you know in in every textbook on relativistic astrophysics that's ever been uh that's ever been made and here it was come to life uh and uh the implications of this and the subsequent observations that have been made since then there are now dozens of these kinds of objects observed uh that's what we're going to talk about uh uh in the next lecture