Afternoon, everybody, and welcome to this Friday's physics colloquium or physics kilowatt hour special, of course, by definition. But this one is particularly special because it is being given by Jocelyn Bell. Burnell Well, it's a great pleasure to introduce to you this afternoon. 50 years ago, of course, Jocelyn was the first person ever to see the signal from a pulsar, and she will tell us more about that this afternoon.
But before she does so, I'd just like to tell you a little bit about her subsequent career. So she she was an undergraduate in Glasgow. She graduated with a doctorate from Cambridge in 1969. About which one minute I'm sure she worked and she's worked as a number of universities. She worked at Southampton University College, London, the Royal Observatory, Edinburgh. She was a professor of physics in the Open University for a long time.
She also is was as many years visiting professor at Princeton University, which, of course, is an honour not accorded to all that many. And she also served a period as dean of science at the University of Bath. She's been president of the Royal Astronomical Society. She's been president of the Institute of Physics when she retired as president of the Institute of Physics. Her successor, unfortunately, died a few months later.
And it's absolutely typical of Jocelyn that she immediately stepped into the breach and took the job over again, having just got out the other side. And she did that until about Choo Choo successor was elected in due course. Jocelyn's commitment to the physics community has always been absolute, and her service to the physics community has been fantastic.
So we were very lucky in the end to persuade her to come to to Oxford, where she's now been a visiting professor and a fellow of Mansfield College for many years. Subsequent to that, she became president of the Royal Society of Edinburgh, which she currently holds, and she was elected pro-chancellor of the University of Dublin in 2013.
So this has been a career full of events, full of great service to the community, and it's a great pleasure to welcome you today to talk to us about what started 50 years ago. Jocelyn Belbin. Thank you very much, John, for that generous introduction. And thank you all for turning out on a Friday afternoon. What I thought I would talk about is a bit about the discovery of pulsars.
This is pitched primarily as other grad students. A synopsis of the properties of pulsars and then some of the heavier physics that pulsars are giving us information or lack of information on to do with gravity. Our understanding of gravity to do with very condensed matter and to do with the prince. The equivalence principle. Einstein or not.
But I'm going to start. In 1965 when I turned up in Cambridge, roar from the northern fringe of the country and got presented with a set of tubes, as did every incoming grad student to radio astronomy, except a few peculiar people called theoreticians. And they're not microelectronics tubes. This is heavy duty stuff, and they've been very heavily used and it was very nice to get given the set.
I partly chose, partly was assigned to a project working with Tony Hewish to use a new technique called interplanetary scintillation to find more quasars. And the first thing we had to do was build an enormous radio telescope. Tony had got a grant of about £12,000 from. What on earth was it called than a saucy movie? Something like that. That sum of money then would have bought starter houses for three young married couples.
Just to give you an idea of the scale. It wasn't a big grant as grants go, but we don't advertise that too loudly. With its half a dozen of us worked for a couple of years building a telescope. And this slide I tried to convince grad students is the typical working conditions for a student. It was certainly fairly typical of my working conditions. Here you see the ends of some low loss air space cable.
The other end is down by the other hut. It's so precious, you can't coil it up and take it indoors. And if, like me, you're putting the connectors on either end. You work through the winter in these little hubs. And now we're testing the importance of these cables. We have a slotted waveguide here and some electronics. And what you can't see is about 400 yards of cable back to the nearest mains plug. Working in the field literally is quite difficult.
For example, the wind cools the smouldering ion and it won't sodapoppin it. It's it's annoying. This is Don Rolfe, who was assigned to me as technical assistant rather reluctantly on his point part as he'd never worked with a woman before and wasn't sure he wanted to. And quite a lot of my effort went into trying to convince him that what we needed to do next was his idea, not my idea. And sometimes it worked, but it didn't always.
This is the finished product. It looks homemade because it is homemade. Wooden posts are the most striking things. They're merely to keep the antennae and open cave, open wiring out of the wet grass, which would be an electrical shock. The next most noticeable thing are perhaps these slanting bars. They carry a reflecting screen strands of wire that run along here, and they're tilted because the sun is up there. And we're using a solar based technique, which I'll explain in a minute.
These nice bluey stuff is copper. Very valuable, has subsequently been pinched, but you're still there at this time. And there's a whole row of antennae there, half wave antennae, 81.5 megahertz. So that's 3.7 metres wavelength, distinctly low frequency. And there's 248 of these antennae. There's over a thousand wooden posts. There's 120 miles of wire and cable. But more importantly, let me tell you how it works. Young slits, too. Slits. You get an interference pattern, dark and light fringes.
If the slips are coast close together, the fringes of current spacing is small. If the slit is large, if the slits are far apart. The fringe spacing is fine. This is operating a bit like young slips because although it's physically in one unit electrically, it's in two halves. It's an interferometer. Back to the slips. If the slips are fine, then there's good spread of the fringes. If the slips are broad, then this fringe pattern is governed by the diffraction pattern of the wide slit.
Here we have two things right adjacent to each other. So the fringe pattern is one faint fringe, one bright fringe, one faint fringe. And that's it. Which is quite good if you've got lots of things happening. As an undergraduate in Glasgow, at least for a project I had used transistors. But when I came to Cambridge, it had transistors. Noisy, unreliable. We use valves and they did for quite a bit longer. I think they could have used transistors, but they were sticking with what they knew.
So this telescope took us two years to build, and when it was built, the rest of the team melted away. And as a grad student, I was left to run it or actually to get it operating and run it. But thanks to Don, the technicians tenacity, it worked the first time it was switched on, which is very unusual for a radio telescope. No. What was all this about? Well, we were using a technique called interplanetary scintillation. Let's work off the bigger diagram. The sun is somewhere over here.
Earth is done here. Here's a radio telescope and there's a quasar somewhere away. Way up there. And coming off the sun is a solar wind travelling a few hundred kilometres per second. And it's not uniform. It contains density irregularities, which I have drawn as clouds. Small fluctuations in electron density. It's a plasma, so there are free electrons. And the size of these clouds, blobs expands as they get further away from the sun.
Now, if you have a radio galaxy somewhere up here, it's broad on this scale and you're viewing it through this kind of cloudy medium. Doesn't have a big effect. But if you have a very, very compact object, then as this cloudy medium blows past, you see the thing dimly bright, dimly bright. It fluctuates. And here's a typical signal that you get from this sort of situation. There's a time scale of one second. Up till then, radio astronomers had rarely used timescales this short.
But Tony had got a hint of this fluctuation, and we decided we would run with a much shorter time constant. And that's key to the whole story. At that stage, we were only about 20 quasars. And one of the reasons Tony got this grant was it's a brilliant way of picking up quasars. He also pitched that we could measure the angular diameter. That really didn't work, to be honest. And these days, there are better ways of measuring angular diameters.
But then it was the only one to tackle angular diameters, you know, a few seconds of arc. So it's quite easy. You just observe the sky and anything that twinkles simulates this equation and anything that doesn't is a radio galaxy. Except that you've got four acres of collecting area and the faintest whistle of radio interference anywhere within a hundred miles will swamp your cosmic source. Equally, if the sun misbehaves and produces radio waves, you get a lot of interference.
So you get used to identifying interference along with identifying quasars. But in six months observing with this telescope, I find about 100 further quasars. So it certainly worked as a project and I got my thesis on that. At that time, Cambridge University had one computer is occupied, a room not quite as big as this, but a big room. And it had less memory than your laptop. And very few people had time on it.
Martin Ryle, who was the head of the radio astronomy group, did because they were doing aperture synthesis, they were doing Fourier inversions, and the computer was a big help. You're doing four weird inversions. Every other academic had grad students. Maybe still true. So our output came out on chart paper and most of the time chart paper ran relatively slowly. So in a day we only got three metres, 30 metres. It took four days to scan the sky totally. So one scan sky was about 120 metres.
But having operated the telescope for six months, I had over three miles or five kilometres of this stuff. And I can assure you, I have looked at every fraction of an inch of that, sometimes twice over. So this is a sample of it. Just occasionally in this vicious fix of stuff, there was half a centimetre of signal that I couldn't properly classify. It didn't look exactly like a quasar, and it didn't look exactly like interference.
And the first few times I loved it with a question mark and passed on. Now, I guess most people in this room are physicists. So I wonder if you share this ceiling with me. Most acute when I was an undergraduate. You're revising for an exam. There's something you still don't understand and you've got to learn it. Parrot fashion and it really bugs you. Things you understand, you know, you can reconstruct if you go to question on it, that's fine.
But the things that you didn't understand, or at least in my case, lodged at the back of my brain. For attention later. And clearly this thing lodged at the back of my mind because it was something I didn't understand. And after seeing it a few times, my brain said, You've seen something like this before, haven't you? You've seen something like this before from this bit of the sky, haven't you?
And then it's easy. Because this radio telescope relies on the Earth's rotation to do the coverage in this direction and. Right ascension. But we can control the beam in elevation in declination by phasing between the different rows. And I have the charts filed in shoeboxes by Declination Strip. So you get out the shoe box for that strip of the sky, you get out the records. This would be a great place because you need lots of long floor and you spread them out and you line them up.
Well, yep, I saw that one. That's one I logged. It's not. They're not. They're not. They're. Might be there. I didn't notice that. Yes. And I logged that. And here's this one. And they're all lined up in. Right. Ascension. They're coming from the same bit of the sky, the same spot amongst the stars. Now before I pass on, this is an example of this very, very weak signal. The the truly interference fringes have been smoothed out.
It's been high, passed, filtered, and we're left with the scintillation. Only this isn't scintillation because the spikes only go up and scintillation goes up and down. This is some very low level interference and it looks different. People at the front may be able to see that. You can see the chart paper between the spikes and the spikes go up and down, whereas here's a block where you can't see anything between the spikes. You're doing thorough analysis when you say that kind of thing.
You're looking at the frequencies present in the signals and you're looking at the amplitudes and signs of the coefficients for each frequency. That was actually the first time we saw it, but I didn't recognise it. It was. A month or two later before it began to click. At this time of year. This bit of sky is in the night sky. It's about as far away from the sun as you can get. And yet I'm doing a solar based technique.
Usually you twinkling caused by the solar wind. There ain't much solar wind in the night sky. So what's making this intimate? It's clearly a very peculiar thing. I discussed it with Tony and we decided that what we needed was to get an amplification. Basically to spread this out a bit. And the way you do that with charts is easy. You just run the chart paper faster. The high speed works, except the pen recorder gets through the rule of paper in 20 minutes.
And if you just switch to high speed, the grad student lives at the telescope, putting a fresh roll of paper in every 20 minutes, day and night. So that's not such a good idea. Instead, what clearly we had to do was the grad student to go out to the observatory about here, switch to high speed, let it run to about here and switch it back to normal. It's been over the month of November and during the whole of the first 28 days of 27 days of November, I go out to the observatory.
The dedication switched to the high speed recorder and make high speed recordings of receiver noise. The thing has disappeared. Tony's livid. It's a flare star. And you've been gone and missed it. Most of you will know some of the younger people may not know. Grad students are like the cat they're for kicking. So I got kicked out. One day I skipped. I thought after 27 or 28 days of this stuff, this thing is now transiting at lunch time. And there's a very interesting lecture on ageing in.
In the university, and I decided to go to it. And next morning I come out and the thing is reappeared. And that's the one day I've skipped in the whole of several months. So I don't leave the observatory. I stay there till the transit and. This is what happens. These are artificial time pips broadcast every 1 seconds and this ignore the top one into the percent of a pulse. No pulse pulse pulse, no pulse post, post, post, pulse, pulse post. Several missing. And then back in face on beat.
And you can see, even as the pen charts rolling, that those pulses are equally spaced. But as soon as that transit was over, I got it out. Spread it on the floor, moved along with bits of paper with ticks on it, and established that it was constant and it had a period of one in the 30 seconds. And at that point, I dared to phone my supervisor, Tony.
He was in Cambridge, in the university, in an undergraduate physics laboratory, probably dealing with some twits of a physics undergraduate who thought that his diffraction grating had two lines per inch or something like that. And then his Twitter for grad students opens up and says, Hey, Tony, you know that funny, scruffy signal? It's a string of pulses, one in the 30 seconds apart. Oh, well, that settles it. It's man made. I'm not good at marshalling arguments quickly.
I knew it wasn't man made. I knew it. Kept sidereal time, not human time. But I couldn't marshal the argument quickly enough. Anyway, Tony was interested enough to come out to the observatory the next day and stand looking over my shoulder as we switched to the high speed recorder. And that's really scary. This thing's been absent for a month. It's appeared the day I wasn't there. It's appeared the day I got it. Is it going to appear on the third day? And it did.
And he saw it with his own eyes. And he established that the spirit hadn't changed since yesterday. And then we started wondering what on earth it was. Tony finally became convinced that it kept sidereal time, so the idea that it was manmade interference really doesn't work. And we had to come up with some other explanation. So it's not local radio interference.
We got a colleague, Paul Scott and his graduate students who also had a radio telescope on site with its own receiver, which also worked at 81.5 megahertz for the mega cycle for a second at that time, but in their mind, same frequency. And they turned their telescope on and we sat and waited. And nothing happened. It had already appeared in my telescope beam and we knew it was there and posting.
What had happened was Robin had miscalculated by 5 minutes when it would appear in his telescope beam. And it did, but not after until after an agonising 5 minutes. If he'd made a mistake at 25 minutes, we'd have all packed up and gone home. The story might be very different.
It became clear because I kept observing this thing that the posters were short, which implied the object was small, but the posters were maintaining period, which implied that it was big because it had large reserves of energy. It wasn't getting tired. So it's small and it's big. Yeah. A good example of what you have to do in physics. Be really precise about the question you're asking. It's small in the sense of angular diameter.
It's big in the sense of mass. What you might think meant big angular diameter. But let's just be strict. It's big in terms of mass, and we now know that neutron stars fit that bill perfectly. But at the time it was a little puzzling. John Pilkington managed to get a dispersion measurement, not for the benefit of any students present. You would have seen dispersion with light. Every time you see a rainbow or shine, light through a prison.
There's also dispersion of radio frequencies, because when a radio wave passes through a space with some free electrons, the high frequencies travel faster than the low frequencies. Radio hams have known about this for a long time. Unidentified Vertical Whistlers. Coming from a lightning strike on the far side of the earth, radio wave travels round, high frequencies arrive before the low frequencies. So we thought, we wonder, is there any dispersion on these pulses?
And by setting up two receivers at slightly different frequencies don't. Pilkington showed that the high frequencies arrive first. And by making a guess that the number of free electrons in space. We came up with a distance of 200 light years, which puts it beyond the solar system, but well within our own galaxy. I go back a side or two? This, I regret to say, was my original terminology.
It was a joke which has never gone away, and Tony was still hung up on the idea that this was man made artificial. So he thought we ought to test and see if it his little green men. If it's little green men, they probably live on a planet and their planet goes round their sun and there will be Doppler shifts. Therefore, on the pulse period, closer spacing as it approaches, larger spacing as it retreats.
So the grad student continues going to the observatory and switching to the high speed recorder and so on. And we studied this post period and we found a doctor shift. But it's the Doppler shift due to the motion of the earth around the sun because moving observer also gives the Doppler shift. We saw no sign of any further Doppler shift. We know Christmas time almost. Actually, I know the dates. It's the 21st of December. And I go down to Tony's office to talk about something with them.
And the door's normally open, but this occasion, the door shut. So I knock and Tony has come in and put my head around the door. Jocelyn, come in and shut the door. So I went in and shut the door and there was a discussion going on that I think I should have been part of right from the beginning. There was Tony, there was Martin Ryle, the head of the group.
It was John Shakeshaft, who is one of the editors of monthly notices, and they were having a discussion about how the [INAUDIBLE] we published this. We've only got one. We have no real intelligence about what it is. There are some ideas floating around, but there's only one. And we didn't resolve the issue. And I went home for supper.
Really very cross. Why do some lot of literary men have to pick my telescope on my frequency to signal to us just when I'm trying to get a Ph.D. and I've only got six months of money left. The main program was still going on, and there were still stacks and stacks of paper charts coming in. And my logbook says No. A thousand foot behind with a chart analysis. No. 2000 foot behind with the chart analysis.
And I came back in after supper to do some more chart analysis and I was looking at a patch of the sky which is around. Right, Ascension 11 hours 33. There's a very, very strong radio source called Cassiopeia A. That's 12 hours difference from that. Cassiopeia, A in Britain does not set north, is there? So Cassiopeia A is high in the south. It goes down in the west. It grazes the horizon and it comes up again. And it's so flipping strong, you can see it through the back of the radio telescope.
But you're also seeing it through a great thickness of ionosphere and they on a sphere can also cause scintillation. So there's immense sort of turbulence. And because of CAS, a lower culmination, there was six or eight inches of chart recording that I just couldn't use and I usually just passed over it. But this night the turbulence was slightly less and I suddenly noticed. It's 5 to 10. The Cavendish is locked at ten and you can be locked in or locked out.
I'm going to Ireland tomorrow with my boyfriend for Christmas to announce our engagement. I need to be there. And this thing's transiting at about 3:00 in the morning. So I have all the charts of that strip of sky out on the floor lined up and. Yes, no, no, no. We have maybe on this one. Right. I need to go out to the observatory. So bundle, charge out as the janitor locks the doors behind you and go to the observatory, 2:00, 3:00 in the morning and December and very cold.
And in those circumstances, something I think something in the receivers didn't always work and it was only at kind of half or a third power. When I got out there, it was at half or a third power. So I flicked switches and I breathed on it and I swore at it and I got it to work for 5 minutes at full strength, and it was the right 5 minutes on the right setting. And then came pulse, pulse, pulse, pulse, pulse, one and a quarter seconds apart.
No. Your guess by the amount of time I spent describing that, that for me is the sweet moment. It's not little green men. There are two lots of little green men on opposite sides of the universe singing to earth at 81.5 megahertz y. Y. Signalling to Earth. And why, apparently using an amplitude modulated technique. Now. This has to be something stellar. So I left a message for Tony, went off to Ireland.
Tony kindly kept the survey running while I was away, which meant putting in the inquest and paper in the chart recorder and piled the charts on my desk. Amanda and I came back sporting an engagement ring, which I was incredibly proud of, but I wore it to the lab, which was a very, very bad mistake. Because back in the 1960s, married women didn't work. It was shameful if a married woman had to work. It meant that he couldn't earn enough money to keep them both.
And mother certainly didn't work because it was absolutely proven that if mother worked, the kids were delinquent. Beware of proof. Anyway, I reappeared. Big pile of charts. Okay. What I had to do. Busy analysing some more. Pretty routine. Oh, yeah. Which ones? That. Any. It's not either. Wow. Okay, I'll just finish this chart and then we'll get out the other ones for this. What? Oh 833 and oh 954.
The posts are people. This one actually was quite strong and I had missed it because I thought it was a quasar. It was so strong, the pen was hitting the end stops top and bottom. But at this point, Tony appears and I say, look, happy New Year, Tony, look at this. How many more of you missed? Go back through all your old records. So I did, but we didn't find any more. And those two were ultimately confirmed. So we had four. Wrote up paper on the first one.
A super intelligent journalist asked, Have we ever considered extraterrestrial life from being truthful characters? We said yes. And for a couple of weeks, we got no work done, you know, just take a taxi to the observatory. CBC wants you. And so on. And I find that very, very difficult, because what would typically happen was they would ask Tony about the astrophysical significance of the discovery.
And they turned to me for the human interest, which means they wanted to know my vital statistics, whether I was brunette or blonde and how many boyfriends I had. And I found this very difficult. I felt like a bit of meat. And I would have loved to have been rude. But you're a grad student who hasn't finished a thesis. You haven't got a job to go to. You're going to need references from the lab. The lab could do with the publicity. I'd better be not rude.
But it wasn't. It wasn't a totally comfortable experience. So when I get onto some proper physics 35 minutes later. Yeah, sorry about that. So. What type of stars are these? Stars. Most stars that you see in the night sky are shining because they're fusing hydrogen to helium or maybe helium to carbon. And most stars and their life after that. But more massive stars like the Pleiades. They're currently probably fusing hydrogen to helium.
They're doing it very fast. The process goes as temperature to the power 17. And these are massive stars. So the temperature in the middle because of the pressure is high. So they're very, very luminous and they have a relatively short life. They will go beyond fusing helium to carbon. They do fusion reactions right up to where they've got an iron nickel core. And as you probably know, the binding energy of the iron and nickel bits of the.
Periodic table mean that you can't fission hydrogen and get energy efficient iron and get energy out or fuse iron and get energy out. So these stars end up with an iron nickel core and are unable to generate any more energy. And the net result is a collapse followed by a massive explosion.
This is a very famous example of these large Magellanic Clouds in the Southern Hemisphere sky, lots of lovely hydrogen gas, H alpha emission, all this pink stuff, millions of little stars, one picked out with an arrow, and for the benefit of the non astronomers, the arrows added after the photographs taken. And this is the star we had to identify with an arrow. It turns out it was one of these massive stars and it exploded.
And in the explosion, 90 or 95% of the stellar material is thrown out and the other 5% collapses, at least in some of these explosions, to form a neutron star. The most famous example these days is the Crab Nebula, which is the remains of the star that exploded about a thousand years ago. It was a considerable problem. It's radiating by synchrotron radiation, this nebula. But it doesn't seem to be getting tired. The electrons. Are somehow being replenished.
And it was Jeffrey Burbage who said in the 1960s, there's two kinds of astrophysics, the study of the Crab Nebula and the study of everything else. It turns out that the exploding star left a pulsar about there, and the energy of the pulsar is what energises the nebula. A cartoon of what I'm talking about. The ones I always catch is the movie. So let's start with its very compact star spin axis vertical magnetic axis inclined. And coming out to the magnetic axis is a radial beam.
When it shines on your radio telescope, you see a pulse. Slightly more detail in this one. Again, spin axis, vertical, magnetic axis inclined. It's the magnetic field lines over the pole which form a kind of funnel shape which was quite a lot of hand-waving, I think still means that you get a beam of radio waves which comes out here and then sweeps around the sky. And it also means that there'll be a lot of pulsars that we don't see because the beam doesn't shine on our face, maybe 20%.
I think it's fair to say that the emission mechanism is still a bit of an issue. There are a few people who think they have cracked it. We don't know. The rest of us understand what they're talking about. Well, we're dealing, therefore, with the course of some of these massive stars, things that weigh typically a few times 10 to 27 tons, a little bit heavier than our sun. They have a radius of ten kilometres and I don't mean tens or something.
I mean ten kilometres. And so you have a [INAUDIBLE] of a lot of mass in a very small ball. And the average density is the average density is like the density of the nucleus of the atom. So there are strong surface gravity effects, tidal effects and lots of other things too.
Because of the strong gravitational force, light gets bent and you can get bent over the surface, around the surface of one of these stars, not quite as dramatically as it does around a black hole, but nonetheless on from one spot on the surface of a neutron star pulsar, you'd see 20 or 30 degrees over. So you can see most of the stars standing in one place. Gravity also redshifts light. So if there were little green men to us, they look like little red men.
But there aren't. And it also affects the rate at which clocks goes go roughly a factor of two. So a clock on the surface of a neutron star would. Tick every 2 seconds rather than every second. There is enormous gravitational force. I've worked out that the work you do climbing a mountain that's one micron high on one of these stars is comparable to the work you do climbing Everest here on Earth. And because of the strong gravity, the atmosphere is compressed.
In the absence of electrical forces, the atmosphere is about this thick. So if there were little green men, they'd need to get their nostrum stone at foot, and they'd be a different shape. But actually there are electromagnetic forces, and that inflates the atmosphere to be about the height of this bench. But again, you'd have to get your nostrils down there. There's a very strong gradient of gravity. And it will stretch anything that comes close.
So suppose you're. Suppose you're going to visit one of these and you're going to land feet first. So they do lightweight land on the pole so that as you go in, your body gets stretched. But actually the difference in force between your head and your feet is such that it would pull the body apart. And your body will land. Plop, plop, plop. The stretching is apparently called spaghetti ification.
So don't go visit a poster. There's a huge magnetic field, probably about ten to the eight Tesla, where there's an assumption in there and that is that their radio radiation is magnetic dipole or the energy losses. Magnetic dipole radiation. And if you spin that kind of magnetic field of the typical pulsar period, you get 10 billion volts, a centimetre, something like that. So the electromagnetic effects are extreme and quite hard to analyse, therefore.
And all that magnetic field included rotates as a solid body. The we believe the pulse period that we see is the rotation period. And we see rotation periods between one point 4 milliseconds. That's 700 hertz down to periods of 10 seconds. This is an interesting interestingly fast pulsar because there are some theories that say if a pulsar tries to spin faster than that, it will be braked. I don't mean broken.
I mean brakes will apply because the theory says in the very centre of the star you get rossby instabilities set up. They will produce gravitational radiation and that will carry away energy which effectively prevents the star from spinning any faster. So, of course, the hunt designed to find an even faster one to prove that theory wrong. But as far as I know, that's where we still stand.
And so we've got relativistic speeds in with all the other lovely gubbins to make some really difficult physics. Today. We know of about about two and a half thousand of these. Most of them are in the radial. The visible has proved a bit disappointing. There are some, but not many. X-rays produce a few. The really surprising thing is the number that have turned up in gamma rays.
There are now a number of gamma ray astronomy satellites, and I think the current tally is around 200 known in gamma rays, some of which are very, very hard to see in the radio. So. Mission mechanism must be from a different place in some of the gamma ray ones. Most of the 2500 are isolated single pulsars. But there's a number in binaries. There's one binary where both companions are pulsars. And there's one triple system. And there are, I think, about three or four with planets.
You can do this quite easily. Pulsar planet is the planet that roamed the pulsar moves just a little bit. You can't see the planet, but you're into the Doppler shift on the pulsar. So. A few with planets and we can explain some of them, but not all of them. Some of them are really, really hard to explain, but they clearly are planets and planets, plural. In that particular case. And the received wisdom is that there's about 100,000 pulsars in the galaxy.
But since I'm in Oxford, I think the figure is whereas I was 20,000. Could be. Could be? Yep. Numbers open for debate, which is good. When you get ten to the power, 27 tons spinning. It keeps spinning and it's the devil's own job to make it change its spin. So these pulses come round very, very accurately. And the period derivatives are between ten to the -12. That's a pretty grotty pulsar, 210 to the -21.
They're comparable with the best terrestrial clocks. And at one point we thought they might become the new time standard. But the US list is on the case and they're going to get a better clock. But they're still pretty good and they're dotted throughout the galaxy. So now we have clocks that we can use for some experimental relativity tests on an astronomical scale.
This is, strictly speaking, the spin down rate. There is, of course, inevitably a bit of noise or jitter or whatever you want to call it. But for the most stable pulsars, we can measure post arrival times to tens of nanoseconds. And through the Doppler effect that I've already described. We can measure the radius of a binary, a pulsar in a binary system to a few microns. And the orbit of the radius of that orbit might be half a million kilometres.
So an accuracy of a few microns in half a million kilometres. These are fantastic clocks. Some of the most interesting physics that I'm going to talk about in the next 10 minutes are from pulsars in binary systems, where pulsars are twinned with something else. Most often they're twinned with an ordinary star. Sometimes they're twinned with another neutron star, which is not a pulsar. In one case, it's twinned with another pulsar, and in one case, we have a pulsar in a triple system.
We would love a pulsar twin with a black hole. Yet. So this is the first pulsar ever found in a binary system, 1974. And it turns out to be a very close binary system. And it turns out to be relativistic. And because of relativistic effects, the orbit changes. This is the work by Hudson Taylor, for which they got a Nobel Prize. This graph has date along the bottom. 1974 goes up beyond this. This is one of the orbital parameters. These are the data points.
You can't see the error bars because they're about 20% the size of the dot. And the line is Einstein's prediction. For the change in that orbital parameter due to the emission of gravitational radiation. And it's a brilliant fit. So to say they got the Nobel Prize because this was the first and very good evidence for the emission of gravitational radiation.
The fit is good to the predictions of general relativity within 0.3%, but they continued to observe it because they'd like to beat that number down. The double pulsar where we've got two pulsars in a binary system are fairly recently discovered. It's a very tight binary system. The orbital period is about two and a half hours, which means the pair would fit inside the sun, actually twice over.
It fit within the radius of the sun. And because they're so close and the orbital period so short, the speeds are fast and it's relativistic. Oh, I think we skip the rest of that. So we've had to learn a bit about relativistic orbits. Kepler told us about the five parameters we need to define a classical orbit. Okay, if it's relativistic, you need another five parameters. The advance of the periosteum. The way the ovals turned around.
The gravitational redshift. I've mentioned that earlier. The change in the orbital period due to emission of gravitational radiation. And two quantities that we call the SHAPIRO DeLay, which is a bit which is the temporal equivalent of the way a light ray gets bent as it passes a massive object. And for the double pulsar. They have been studying it carefully for ever since it was found. They have got all these parameters, all five of them. In fact, they've got a few extra as well.
In fact, they've got five extra parameters. So we've got five independent tests of R with this system. And the way they have done it is they make a mass mass plot, the mass of the two pulsars, and then they put on top of this all of the other parameters. So there's the advance superior strong omega dot. That's this one which has a small error bar. There's the gravitational redshift, which is gamma, which is this curvy one, and so on.
And if general relativity is correct, all these lines intersect to the point. They're intersecting somewhere in. There will be some with quite big air of ours, but a blow up of X is like that. I think these error bars are 68% confidence, but. So. They're able to say already that the theory is okay to within 0.02% and they are seriously squeezing other theories of gravity other than Einstein's.
Not I don't think they have eliminated any yet, but they're really struggling to survive and the work is going on. It's being led by Michael Kramer in Bonn. This is for the solid state physicists, and this is going to have to be pretty fast. These objects are dense. They're very solid. And the solid state physics is huge fun. There's several hundred theories about what the structure would be. I'm going to pick out one or two features which are either curious or maybe instructional.
So we're going to start at the surface. We're going to take a ten or 11 kilometre journey into the centre, and in that ten kilometre journey, the density is going to go up ten orders of magnitude. So I'm going to deal with ten orders of magnitude of density in 5 minutes. One of the theories that I find really entertaining says that the surface of these objects is a thin iron polymer. You didn't know iron was a polymer, but where there's a strong magnetic field.
Atoms aren't spherical. They're slim, cylindrical. And in the strong magnetic field, it can come with a large lama radius or a small radius. So large, small, large, small, large, small. Make a polymer. A polymer strand, then the polymers will bind together beautifully or parallel to the magnetic field. Conductivity this way is like copper. Conductivity this way is like asbestos at the poles. It looks like a badly shaped hedgehog. And these stars start spending fast.
They're quite a blink. They have to adjust their shape as they cool and age. But this iron skin has a young's modulus. About half a million times that of iron of steam. Nice idea. Might not be true. Go inside. That'd get worse. Gets a bit more normal body centre, cubic lattice.
But if I go into just a tiny bit of quantum mechanics for the students shooting Schrodinger potential well energy levels two electrons in each two you run out of energy, you run out of electrons somewhere up here, which is called the Fermi Energy. Okay. Go a little bit further into the neutron star. The density is greater. The well shrinks. What happens to energy levels when the world shrinks? It's like squeezing a tube of toothpaste. So the Fermi Energy isn't here.
It's up at ceiling level. Over here is a radioactive nucleus that wants to do a bit of decay. The electron coming out can have a range of energies, but there is a maximum. And let's say it's at this level. And it's trying to get into this potential world where everything's full up to ceiling level. And it can't get in. So the decay is prevented. So you end up with nuclear neutron rich nuclei because beta decay is prevented. Go a bit further in the potential woes.
This width and the Fermi energy is way up at one point at 1.89 MTV covering the mass difference between a neutron and a proton. And a proton press. One of those electrons can make more neutrons and the nuclei get even more neutron fat. They get so fat that when you've got a density of about 10 to 14, neutrons drip out of the nucleus and you have free floating neutrons. They're probably super fluid. Standard BCS theory two. Spins net result zero. Superfluidity.
Not superconductivity, unless you've got electrons and protons, which you might have. But superfluidity is bad enough. Superfluid liquid can be quantised into what's called Feynman on Sagar Vortices. Tiny, tiny whirlpools. About a million of them per square centimetre. So you've got all these little whirlpools. You've got an inclined magnetic field and there are some theories that say the magnetic field can be in flux tubes.
So you've got two kinds of spaghetti at an angle inside a rapidly rotating body. Yippee. Closer in. This is work that has been done in Oxford. You get these pasta shapes, what's known as pasta shapes, the nuclear configuration. And then you hit the nuclear density at about two by 10 to 70 kilograms per cubic metre. And the very centre of the neutron star, we don't have a lot of data.
And I'm not sure we're going to get a lot of data because the accelerator data is not new tronic, it's hydraulic plutonic. It's perhaps the word I want and this might be different. And so the theories here, well, there's no constraints. So can you imagine? Oh, it's quite clues on plasma. It's mesons, it's quarks, it's Bose-Einstein condensate. Yeah, we don't know and I'm not sure how we will know. But anyway. Large Mars pulsars, it turns out, can constrain large mass pulsars.
If you can establish their mass can constrain the theorists. These curly lines are some of the hundreds of theories. Green ones involve quarks. Pink ones involve strange green, strange quarks, the pink, nuclear arms and other exotic stuff. And these are blue under nucleons. And this pulsar mass eliminates at least some of the models. And there is a second now really massive poster also up at the same sort of level. He's put more bottles on this diagram, but it's the same idea.
This one is in a very tight orbit with a white dwarf. And it's the first time we've got a massive pulsar in a very tight orbit. This particular post far post r is a good testbed for looking for scalar gravity fields. Always worth checking out that there are such things and also checking out where there is dipolar gravitational waves. So I would watch the work being done by Antoni artists. He's enormously impressive. Probably still a postdoc.
And this one will be very quick. I won't go on much longer. You know about the equivalent principle. You don't need to read that one equivalence principle, apparently first tested repeatedly by Galileo dropping things off the Tower of Pisa and resistance was a problem. It was repeated by the astronauts when they got to the moon. This is actually not the original one. The video there is too grainy, but there's a hammer and there's a feather and they're falling.
Simultaneously in the environment with a lack of air. But the gravity here is not very strong. So this is only testing the weak equivalence principle. To test the strong equivalence principle. Keep your fingers crossed, folks. We have not found a pulsar orbiting another star and the pair are orbiting a third star. And the gravity here is serious. So this is strong field stuff. So that's like the hammer and that's like the feather. And do they fall in the same way in the gravity of the star?
Or put differently, does this binary orbit change? Because the strong equivalence principle is violated. They're working on it. We don't know the answer yet. The rumours, I think, come and go is the fair thing to say. But I hope that very soon we'll have a test of the equivalence principle in a strong gravitational field. I think I've said all of that.
So police are astronomers are continuing to hammer various aspects of relativity theory because as you probably well know, there are some problems with general relativity. Singularities doesn't mesh to our quantum theory. And the force of gravity doesn't fit with the other forces. So maybe at some very fine level there's a problem. So they're continuing to chase it. I'm going to live with that and end with slides.
We've got postal work going on in Oxford. This was probably only about two thirds of the group could be present. Thank you for your attention.