Let us first start with Neutron Stars and Pulsars, which are a subset thereof. This is a picture of the crab nebula which doesn't look like a picture of crab nebula you know and love, because it's taken in X-rays. And the gas that's emitting X-rays or rather electrons has a different distribution. First, about the origin of Neutron stars, they always come from supernova explosions. And as you probably recall if the core of the collapsing star is more than the Chandrasekhar mass then even the generous pressure of electrons cannot sustain the gravity of the core, it has to collapse. But as it does that, temperature of course is at many billions of degrees. Gamma rays are overabundant. They dissociate any nuclei, helium or anything else, so essentially, what you get is a lot of protons and electrons. Now, that is such a density that actually electrons and protons combine, producing neutrons and emitting neutrinos, and what you end up with then is a whole lot of neutrons which are also fermions, following Pauli's exclusion principles. So now neutrons do what electrons did for white dwarfs. They create this new quantum mechanical pressure that sustains against gravity and stabilizes what's now a neutron star. And those neutrinos that fly away. Essentially, they're cooling off this collapsing core. Take away energy, they actually take most of the energy in the supernova. The stuff that you actually see is maybe 1% of the total energy. Most of it is neutrinos that are generated in this process. So then essentially what you have is almost like a gigantic atomic nucleus composed of neutrons and probably some other exotica. And the density is the density of atomic nucleus because it's an incompressible degenerate fluid. And so it doesn't matter whether it's a handful of nucleons or a whole lot of them, and when you divide mass, so 1.4 solar masses by the density, you find out that the radius of such a structure is about ten kilometers. So get nearly one and half masses, solar masses worth of stuff compressed into the size of, say less than inner Los Angeles. Well no wonder this is pretty dense, and that that there will be very strong gravity. We think we know what the actual structure of neutron stars is. These are from theoretical models but they're confronted with observations of pulsars all the time and interestingly enough most of this neutron fluid if you always super conducting or super fluid. Usually think of things that are really cold, like liquid helium, it can go into superfluid state. But for nuclear matter, it actually can be in millions of degrees. And because of that interior of neutron stars can be an excellent conductor and that's why they can retain the magnetic field so well. Now it's possible, I will say it's probably likely that in the central parts of a neutron star you have more exotic stuff. People then talk about quarkonium liquid but that's a whole other story. And the very surface of it may be composed of ordinary matter, large minerals would be the iron group elements. Remember, those were kind of the final product of nucleosynthesis. So whatever was retained within a collapsed core will tend to form this iron crust that encloses gigantic drop of nutrient superfluid. Of course there's things we can never do in the lab. So this is why neutron stars provide insight into extreme states of matter that we just cannot do any other way. Well how did this all come about? A neutron itself was discovered in a laboratory 1932 and already two years later, two of astrophysicists Walter Baade and Fritz Zwicky, who were studying supernovae which around that time they figured out they're not the ordinary novi but a completely different phenomenon. They speculated they come come collapse of a very massive star and at the core of a star could become a neutron star. Is a prediction way ahead of it's time, now that was pretty much untestable for a while and then with the birth of radio astronomy. A graduate student by name Jocelyn Bell was doing her thesis in Cambridge and she used the radio telescope that looks like this, it's a whole bunch of wires and sticks, but those are actually dipoles. And for some other reason they're probing the radio, celestial radio emission millisecond time scales looking for scintillation. And so she discovered there was a periodic signal coming from some directions of some tens or hundreds of milliseconds and it was rotating like a star, in sidereal rate. So this was completely unexpected, because it was rotating in sidereal rate, clearly had to be somewhere out there in the universe. There was nothing ever predicted like this, and all kinds of models of advanced, including that those could be signals of extraterrestrial civilizations. But then, her advisor, Anthony Hewish, figured it out. That these are actually rotating neutron stars. The key to this was that the pulses themselves are very narrow, a millisecond or less. And flight time for a millisecond carries only couple hundred kilometers, so the region from which those pulses are coming couldn't be more than a few hundred kilometers. Now white dwarfs are more like several thousand kilometers in radius. And they cannot be compressed any further, that's why they are the white dwarfs. And so this could only be something else and the only other thing that was anywhere in the literature would be neutron stars. So this is what pulsars really are. In addition to inheriting all this mass and achieving high density, they inherit two other things from the progenitor star. Angular momentum, which as you recall, cannot be radiated away, so it has to be retained. And because it collapsed by huge factor, than they'll start spinning really, really fast. And also the magnetic field was trapped in the plasma will be pulled down in that collapse highly concentrated, and the prevailing dipole magnetic field can serve as the particle accelerator. Now in general the magnetic poles and gravitational poles did not coincide. This is the case on planet Earth. Our magnetic pole is not a north geographic pole but it's a little off. And so that means that this magnetic dipole will keep rotating and if it accelerates particles along the magnetic lines of force radiation force. Then the beam of those particles in any synchrotron radiation, they emit will be sweeping around the sky in a current. And so if we happen to be in the beam, we're going to see pulses. So it's just like a lighthouse, although in radiar ways. But that also means there's many, many more pulsars out there than we see, because we only see those that happen to be pointing at us. But that all fits with our estimated rates of supernovae and what have you. So that's the basic model of how pulsars work. And they're all discovered in radio. The new preferred model of discovery is through gamma rays with Fermi's emission. And there are few that they're also seen as visible light pulsars. Crab Pulsar was the first one of them. They're two little stars in the middle of Crab and the south eastern. Sorry. Western one, is the pulsar itself. And so it pulses what's shown on here on the right is a series of videos frames and you can just see it come and go. And then it does the same thing in -rays and this measurements with Chandra satellite doesn't have the same angular resolution but you can see the points come and go at the exact right place. So Crab is probably the best study pulsar. It emits at all wavelengths. It's right, relatively speaking. It's one of the youngest we know. And it served as a milestone for many of the other studies. So this is what happens when you take the light curve enfolded by a period and a period is indicated there in the upper right corner, you can see from the number of significant digits that these things are measured with an exquisite precision. It's not that their calculator has ten decimal places so they just wrote them all down it actually is that precise. And because of that, those are really precise clocks. So now there's no period, you can fold the bit again and again and again and you get beautiful curve like that. You can see there's a big pulse and there is smaller pulse between and as the beam goes around. The Pulsar Timing, then, became a very useful tool, because pulsars have humongous moments of inertia. You guys can compute those on Friday. Then they'll be very stable in their spin. They're as good or better than the atomic clocks we have here on planet earth. So actually at one point there was power interruption in a receiver and they tuned their atomic clock according to the pulsars they were monitoring. Well, all right, so they radiate. That radiation has to come out of somewhere, and the only or the main source of energy that's available is the rotational kinetic energy of the neutron star. So that's one half moment of inertia times the angular frequency squared, right? And that will be universally proportional to the square root of period. Now luminosity is the change of energy per unit time, because energy's going down, it's negative, so minus will have the. Composite with the minus from derivative, just a simple derivation, and luminosity will be directly proportional to the period derivative in time, which you can measure using pulsar timing. And shown here is somewhat schematic representation how people actually observe. Here is a pulsar's slowly grind. Now, occasionally there is a glitch. It drops down a bit and since the only way it can do this is by changing it's moment of inertia. Essentially, pulsar rearranges itself, little bit, it's the starquakes. So it's goes into slightly lower agitated state of rotational motion and then continues doing the same thing again. So these are probably starquakes that are with amplitudes of some millimeters. The biggest mountains of these neutral stars are probably millimeters high. But nevertheless, they can be observed very easily. You may also remember that this enabled people to discover planets around pulsars, because you have a very precise clock going around, and you can measure Doppler shift of your idle pulses, just like you do with radial velocity, and this is how the first extra solar planets were found. But the really cool thing happened when the first binary pulsar was found. Since a lot of stars are in binaries, sometimes you're going to get massive star binary. Both of them will explode and both of them will leave a neutron star. And those two neutron stars will orbit around common center of mass. So the first one of those was found by Joe Taylor and Russell Hulse. Russell was a summer undergraduate student. So, who know one of you doing research today might get the Nobel Prize sometime in the future. So they found this binary pulsar with period I think seven something hours. And they can time it very precisely. Now what happens when you have such massive binary at such close separation, relativistic effects start coming in play. One of them is that two masses rotating will start creating gravitational waste and those gravitational waves do come at the expense of something, they come at the expense of the orbital kinetic energy. Just like pulsar emission from eternal rotation. This is from relativistic binary and when they compared that with predictions of theory of relativity they saw this. You never see such fantastic field in science this is amazing. Because of this, this was essentially first detection of gravitational waves. They could've closed Lyger shop right then but they didn't. These guys got Nobel Prize for this stuff. And something else interesting did happen with pulsars. So there are these binaries. They can be accreting just like with white dwarf binaries you can have X-ray binary that contains a pulsar and those are seen in cold X-ray bursters. But in some cases, or maybe most cases, what happens is this material is being accreted onto the neutron star and it comes with some finite angular momentum so neutron star soaks up not just the mass but also the angular momentum and spins up. And turns out you can do this in some circumstances to speed them up to about millisecond period which is phenomenal so. That then became a whole new industry of precise all pulsar timing because it's even more precise clock with shorter period.
