1 00:00:00,000 --> 00:00:06,018 I can't say that we have a. Completely captured everything that could 2 00:00:06,018 --> 00:00:10,491 be said about core collapsed supernova, but that's all we're going to have time 3 00:00:10,491 --> 00:00:13,039 for. just as with planetary nebuli, you can 4 00:00:13,039 --> 00:00:15,701 talk about the light show, the planetary nebula. 5 00:00:15,701 --> 00:00:18,872 But then you want to know what happens to the star's core. 6 00:00:18,872 --> 00:00:21,760 We left our star's core collapsing. What happens 7 00:00:21,760 --> 00:00:26,750 In the somewhat more energetic high mass version of core collapse. 8 00:00:26,750 --> 00:00:31,901 We know that electron degeneracy is not going to rescue our collapsing iron core. 9 00:00:31,901 --> 00:00:36,672 Electrons are essentially gone, luckily neutrons, like electrons or fermions, 10 00:00:36,672 --> 00:00:40,043 they too are subject to the poly exclusion principal. 11 00:00:40,043 --> 00:00:45,194 They too exert a degeneracy pressure that is proportional to the 5/3rds power of 12 00:00:45,194 --> 00:00:48,756 their density. A little more careful analysis shows that 13 00:00:48,756 --> 00:00:53,272 because in the confines of a, the collapsing core, these neutrons are in 14 00:00:53,272 --> 00:00:58,042 fact relativistic than like electrons. There are corrections to this 5/3rds 15 00:00:58,042 --> 00:01:02,175 rule, it's more like 4/3rds. But there subject to the same kind of 16 00:01:02,175 --> 00:01:06,300 degeneracy pressure and it turns out that neutron degeneracy pressure. 17 00:01:06,300 --> 00:01:09,775 You can think of that partially as the repulsive core. 18 00:01:09,775 --> 00:01:14,281 It's essentially equivalent as the repulsive core of the strong force. 19 00:01:14,281 --> 00:01:19,366 Remember we saw that attraction down to an optimal distance of about one Fermi 20 00:01:19,366 --> 00:01:23,035 between nucleons. And then a repulsive force, when you try 21 00:01:23,035 --> 00:01:27,284 to force them too close. This is essentially the same because that 22 00:01:27,284 --> 00:01:30,888 was a quantum treatment as the poly exclusion principle. 23 00:01:30,888 --> 00:01:35,394 And the density of six to seven times ten^17 kilos/meter^3, neutrons become 24 00:01:35,394 --> 00:01:39,450 degenerate, and the core stops. If you imagine that the core had. 25 00:01:39,450 --> 00:01:43,461 Of a stellar mass, let's give it the mass of a heavy white dwarf. 26 00:01:43,461 --> 00:01:48,191 Then at this density, your white dwarf with a radius essentially that of the 27 00:01:48,191 --> 00:01:52,861 Earth, will have collapsed to something with the radius of a city, so now we're 28 00:01:52,861 --> 00:01:57,400 talking about. Essentially a great big nucleus very, 29 00:01:57,400 --> 00:02:03,993 very rich in neutrons made Of containing a solar mass in a ball of 30 00:02:03,993 --> 00:02:08,432 radius ten km, clearly the gravitational effects are humongous. 31 00:02:08,432 --> 00:02:12,800 The surface gravity if you compute it classically and ignore. 32 00:02:12,800 --> 00:02:17,525 And incorrectly relativistic effects will be on the order of ten to the eleven or 33 00:02:17,525 --> 00:02:21,213 ten to the twelve g. you certainly do not want to go stand on 34 00:02:21,213 --> 00:02:24,440 this object. the physics, as I said, is relativistic, 35 00:02:24,440 --> 00:02:28,820 but with our calculation of the Chandrasekharan degenerate matter. 36 00:02:28,820 --> 00:02:31,932 We can repeat the degeneracy calculation for neutrons. 37 00:02:31,932 --> 00:02:36,427 The Chandrasekharan and again the heavier neutron star is, the smaller its size. 38 00:02:36,427 --> 00:02:40,864 And the details of the calculation are slightly different, and not as well 39 00:02:40,864 --> 00:02:43,803 understood. Because we do not understand degenerate 40 00:02:43,803 --> 00:02:46,108 nuclear matter as well as we understand degenerate nuclear matter as well as we 41 00:02:46,108 --> 00:02:48,394 understand. The general electrons, but the 42 00:02:48,394 --> 00:02:51,830 Chandrasekhar mass, the maximum mass of the neutron star. 43 00:02:51,830 --> 00:02:55,095 Is. Not 1.4 solar masses, but 2.2 to 2.9 44 00:02:55,095 --> 00:02:58,798 solar masses. This depends a little bit on details of 45 00:02:58,798 --> 00:03:02,920 the model and more on the rate at which this thing rotates. 46 00:03:02,920 --> 00:03:09,837 As we will talk we expect these stellar remnants to be rotating very fast and 47 00:03:09,837 --> 00:03:16,464 with fast rotation you can support degenerate neutron star with a mass of up 48 00:03:16,464 --> 00:03:21,658 to almost three solar masses. What happens if the ca, collapsing core 49 00:03:21,658 --> 00:03:26,840 ends up being more massive than this is something that we'll leave for next week. 50 00:03:26,840 --> 00:03:31,766 So, some physics predictions follow from this, and I want to, pay attention to 51 00:03:31,766 --> 00:03:34,645 them. So I said we expect, the remnant of a 52 00:03:34,645 --> 00:03:38,356 star to be rotating very fast. This is reasonably clear, 53 00:03:38,356 --> 00:03:43,346 If there was any rotation at all in the core, then, you know, this is back to, to 54 00:03:43,346 --> 00:03:46,672 the fun experiment with me standing on the platform. 55 00:03:46,672 --> 00:03:50,145 When I pulled the weights in, my rotation sped up. 56 00:03:50,145 --> 00:03:55,104 In this case, remember something is contracting from the size of earth to ten 57 00:03:55,104 --> 00:03:58,327 kilometers. The rate of rotation would have to speed 58 00:03:58,327 --> 00:04:00,869 up. If you think of angular momentum as N 59 00:04:00,869 --> 00:04:04,092 times V times R. And angular momentum is essentially 60 00:04:04,092 --> 00:04:07,192 conserved. There is some angular momentum loss, but 61 00:04:07,192 --> 00:04:10,497 not. orders of magnitude and you remember that 62 00:04:10,497 --> 00:04:14,438 v is two, pi, r over p. The ignoring the constants, as we are 63 00:04:14,438 --> 00:04:18,312 doing all week. You find that angular momentum depends on 64 00:04:18,312 --> 00:04:22,253 the relevant quantities as n times r squared divided by p. 65 00:04:22,253 --> 00:04:26,884 And so we can solve for p. Write as m r squared and if you remember 66 00:04:26,884 --> 00:04:31,915 that, the mass of the neutron star is about the mass of the core that 67 00:04:31,915 --> 00:04:34,779 collapsed, but the radii are much smaller. 68 00:04:34,779 --> 00:04:40,369 The period of the rotation of the neutron star is related to the period with, of 69 00:04:40,369 --> 00:04:45,190 the rotation of the core by this, ratio. If you, so how fast was the. 70 00:04:45,190 --> 00:04:47,611 Stellar core rotating before it collapsed. 71 00:04:47,611 --> 00:04:52,108 While we can get a handle on this perhaps by looking at the rotation rates of 72 00:04:52,108 --> 00:04:56,605 typical white dwarfs which are, after all, the cores of smaller stars making 73 00:04:56,605 --> 00:05:00,675 some reasonable assumptions. Defined that estimate that the period 74 00:05:00,675 --> 00:05:05,391 with which a neutron star will be, might be as short as five milliseconds. 75 00:05:05,391 --> 00:05:09,978 This is fast rotations, indeed. This is something that rotates 200 times 76 00:05:09,978 --> 00:05:14,630 a second, an object with the mass of the sun rotating 200 times a second. 77 00:05:14,630 --> 00:05:18,765 similar considerations predict a very intense magnetic field. 78 00:05:18,765 --> 00:05:23,546 And the reason is that, of course, by the time you get to a stellar core, 79 00:05:23,546 --> 00:05:27,680 everything is ionized. And you remember that we discussed the 80 00:05:27,680 --> 00:05:31,954 fact that charged particles. interact with a magnetic field in this 81 00:05:31,954 --> 00:05:36,767 interesting hydrodynamic way the magnetic field effects the motion of the charged 82 00:05:36,767 --> 00:05:41,462 particles but the charged particles drag the magnetic field with them so if you 83 00:05:41,462 --> 00:05:46,334 have the magnetic field the of a core of a the core of a star as the star implodes 84 00:05:46,334 --> 00:05:50,391 it drags the star with it. What you have is the same magnetic field 85 00:05:50,391 --> 00:05:54,591 confined to a smaller area. The intensity of a magnetic field, if you 86 00:05:54,591 --> 00:05:59,840 think about it as some number of magnetic lines, the intensity of a magnetic field 87 00:05:59,840 --> 00:06:04,842 can be measured by the flux of magnetic lines per unit area, since the area is 88 00:06:04,842 --> 00:06:09,412 shrinking by a factor of R squared, you expect a huge magnetic field, again 89 00:06:09,412 --> 00:06:13,549 plugging in what we know about the magnetic fields of white dwarfs. 90 00:06:13,549 --> 00:06:17,440 you expect magnetic fields on the order of a trillion times. 91 00:06:17,440 --> 00:06:21,605 The magnetic field of the Sun, there will be strong magnetic effects associated to 92 00:06:21,605 --> 00:06:23,637 this. You can make some estimate for the 93 00:06:23,637 --> 00:06:26,126 temperature. Remember I said that at collapse the 94 00:06:26,126 --> 00:06:28,870 temperature was billions of kelvin. By the time we see. 95 00:06:28,870 --> 00:06:33,588 The, core exposed and the envelope is gone, temperatures are expected to be 96 00:06:33,588 --> 00:06:38,020 down to a million kelvin. This means that Deans law tells us that 97 00:06:38,020 --> 00:06:42,811 these neutron stars will at least initially be radiating x-rays at three 98 00:06:42,811 --> 00:06:46,846 nanometer wave lengths. And given the temperature and the radius 99 00:06:46,846 --> 00:06:51,764 of ten kilometers, you can compute that the luminosity is about a quarter of a 100 00:06:51,764 --> 00:06:56,430 solar luminosity not visible from Earth but visible from x-ray telescopes. 101 00:06:56,430 --> 00:07:02,777 Okay so these are all nice stories that theorists told there was a theorist 102 00:07:02,777 --> 00:07:06,570 called Francis Vicky who first predicted that 103 00:07:06,570 --> 00:07:12,810 the outcome of a supernova explosion would be this nuclear density, 104 00:07:12,810 --> 00:07:17,082 Collection of neutrons, this was a very theoretical prediction. 105 00:07:17,082 --> 00:07:21,824 It was not clear at all. That such things could or should exist 106 00:07:21,824 --> 00:07:27,168 the discovery was made by Jocelyn Bell in 1967 and Jocelyn Bell was a radio 107 00:07:27,168 --> 00:07:32,583 astronomer she was looking at interactions of magnetic field with with 108 00:07:32,583 --> 00:07:38,419 quesar radiation but what she found was a periodic radio signal with a period that 109 00:07:38,419 --> 00:07:44,044 was very precisely 1.337 seconds and so there was a blip in her radio signal at 110 00:07:44,044 --> 00:07:49,600 the wavelength she was looking at the frequency she was listening at every 1.3. 111 00:07:49,600 --> 00:07:53,600 In three, seven seconds and of course of the. 112 00:07:53,600 --> 00:07:59,263 Immediate interpretation was, well maybe some radio station from, some other 113 00:07:59,263 --> 00:08:03,944 country is broadcasting a time signal at some weird period. 114 00:08:03,944 --> 00:08:09,230 this was quickly excluded. The next idea was maybe these were 115 00:08:09,230 --> 00:08:13,338 Literally termed LGM signals. Lgm stood for little green men. 116 00:08:13,338 --> 00:08:18,267 This could be the long-awaited SETI signal of some intelligent being 117 00:08:18,267 --> 00:08:21,914 somewhere else Contacting us, maybe it was their version 118 00:08:21,914 --> 00:08:24,740 of the BBC. It turns out quickly they turn their 119 00:08:24,740 --> 00:08:29,098 telescopes another direction, they found other sources at exactly the same 120 00:08:29,098 --> 00:08:33,043 frequency, it was unlikely that civilizations many, many light years 121 00:08:33,043 --> 00:08:37,518 apart would all be addressing us on the same frequency, so this is a natural 122 00:08:37,518 --> 00:08:40,050 source. Soon many of what became, came to be 123 00:08:40,050 --> 00:08:44,408 called pulsars, these pulsing radio sources were found, their periods range 124 00:08:44,408 --> 00:08:46,999 between a tenth of a second and two seconds. 125 00:08:46,999 --> 00:08:49,590 So this is a little longer than the maximum. 126 00:08:49,590 --> 00:08:54,164 rotation period to be expected for neutron stars. 127 00:08:54,164 --> 00:08:58,441 But it's within the ballpark, and nothing else rotates that fast. 128 00:08:58,441 --> 00:09:01,381 And they're almost universally slowing down. 129 00:09:01,381 --> 00:09:04,789 So the rates of rotation were very, very precise. 130 00:09:04,789 --> 00:09:10,402 The repetition of a pulsar is such that you could it competes almost with atomic 131 00:09:10,402 --> 00:09:13,525 clocks. But, they very slowly and in a regular 132 00:09:13,525 --> 00:09:17,995 fashion are slowing down. if you estimate how long it'll be before 133 00:09:17,995 --> 00:09:22,918 a pulsar stops pulsing the rate of rotation is such that a lifetime of a 134 00:09:22,918 --> 00:09:26,545 pulsar would be predicted to be about ten million years. 135 00:09:26,545 --> 00:09:30,705 This is a musing view of the original LGM signal. 136 00:09:30,705 --> 00:09:34,290 It was recorded as was done in the sixties and. 137 00:09:34,290 --> 00:09:39,216 I can tell you in the late seventies, by an [xx] quarter moving on a rolling piece 138 00:09:39,216 --> 00:09:43,447 of paper and you see here the signals from the pulsar and a lot of radio 139 00:09:43,447 --> 00:09:46,403 interference from which it had to be distinguished. 140 00:09:46,403 --> 00:09:51,039 This is a clean done version of the same over here on the right and those blips 141 00:09:51,039 --> 00:09:55,676 are actually the regularly spaced but not very regularly shaped, this is in fact 142 00:09:55,676 --> 00:09:59,069 true, Pulses from the pulsar and so these are 143 00:09:59,069 --> 00:10:04,490 this is the discovery of a the first pulsar so what are these things well. 144 00:10:04,490 --> 00:10:10,012 I'm going to claim that there are neutron stars people try to invent all kinds of 145 00:10:10,012 --> 00:10:15,470 other models for what a pulsar might be, but you can imagine trying to invent the 146 00:10:15,470 --> 00:10:18,153 binary system. That rotates every.2 seconds. 147 00:10:18,153 --> 00:10:22,677 But a binary system orbiting every.2 seconds would have two white dwarves 148 00:10:22,677 --> 00:10:27,385 right on top of each other and inside each other and would very rapidly slow 149 00:10:27,385 --> 00:10:30,198 down. You can try to imagine maybe a star that 150 00:10:30,198 --> 00:10:33,683 is rotating, and has some hot spot that emits radio waves. 151 00:10:33,683 --> 00:10:37,596 And again an order of magnitude calculation tells you something. 152 00:10:37,596 --> 00:10:42,121 So how fast can a star rotate without centrifugal forces ripping it apart? 153 00:10:42,121 --> 00:10:46,340 Well we can do the calculation, because we know everything we need to. 154 00:10:46,340 --> 00:10:51,402 In order for a star to rotate its a objects on its surface must be 155 00:10:51,402 --> 00:10:57,673 accelerating towards the middle with the sintripital acceleration that we computed 156 00:10:57,673 --> 00:11:03,491 long ago v squared over r that's two pie r divided by p squared divided by r 157 00:11:03,491 --> 00:11:08,514 because v is two pie r divided by. The period and R in this case is just the 158 00:11:08,514 --> 00:11:12,021 radius of the star. That's the radius at which, with which, 159 00:11:12,021 --> 00:11:15,119 of the circle at the equator, along which things move. 160 00:11:15,119 --> 00:11:17,866 So plugging that into here, I get one R cancels. 161 00:11:17,866 --> 00:11:20,380 And I get four pi squared R over P squared. 162 00:11:20,380 --> 00:11:25,580 And, why would these objects be? accelerating towards the center of the 163 00:11:25,580 --> 00:11:30,133 star well of course because gravity is accelerating them, in the case of earth 164 00:11:30,133 --> 00:11:34,405 we too are accelerating towards the center of earth at least at the equator 165 00:11:34,405 --> 00:11:39,183 with this acceleration but that is a far smaller number that the force that earth 166 00:11:39,183 --> 00:11:43,342 applies to us the gravitational acceleration g and so that is why even at 167 00:11:43,342 --> 00:11:47,062 the equator we don't float. What I'm asking is how fast does a star 168 00:11:47,062 --> 00:11:51,632 need to spin before it's equator floats? And if it spins any faster it's equator 169 00:11:51,632 --> 00:11:54,660 will be blown apart. So that is obtained by setting the 170 00:11:54,660 --> 00:11:58,900 centrifugal acceleration equal to the gravitational acceleration of the star. 171 00:11:58,900 --> 00:12:02,810 You can solve this with a period. And here's the result you get and you. 172 00:12:02,810 --> 00:12:08,840 Sticking in a period of around a second, you real, you quickly realize that a 173 00:12:08,840 --> 00:12:12,692 white dwarf, the. Most massive object known to exist at the 174 00:12:12,692 --> 00:12:16,321 time, would blow itself apart if it tried to spin that fast. 175 00:12:16,321 --> 00:12:20,380 And remember we calculated it for the Earth about two hours is 176 00:12:20,380 --> 00:12:25,092 the Wrote the, the, the period with which it 177 00:12:25,092 --> 00:12:30,056 could spin before it blew itself apart. Remember lower satellites orbit every 178 00:12:30,056 --> 00:12:32,448 hour and a half. That's about the period. 179 00:12:32,448 --> 00:12:37,472 notice that this is determined completely by the ratio R cubed divided by M, or M 180 00:12:37,472 --> 00:12:41,480 over R cubed, which is the density. So we need something much denser. 181 00:12:41,480 --> 00:12:47,044 Barometrically denser than a white dwarf and only neutron stars turn out to be, an 182 00:12:47,044 --> 00:12:50,580 object that can exist that is dense enough to survive. 183 00:12:50,580 --> 00:12:56,220 Rotating this fast and then the mechanism is that the emission is somehow aligned 184 00:12:56,220 --> 00:13:01,655 to the star's magnetic access, axis, and that perhaps, remember, neutron stars are 185 00:13:01,655 --> 00:13:05,300 endowed we expect with very powerful magnetic fields. 186 00:13:05,300 --> 00:13:10,941 And like the Earth's magnetic field, the neutron star's magnetic field need not be 187 00:13:10,941 --> 00:13:15,481 aligned to its rotation axis. So if it is emitting light along the 188 00:13:15,481 --> 00:13:19,203 magnetic axis and. The magnetic axis and its axis of 189 00:13:19,203 --> 00:13:24,461 rotation, in this picture over here on the right, is vertical, then over a 190 00:13:24,461 --> 00:13:28,404 rotation the magnetic axis sweeps out a cone in space. 191 00:13:28,404 --> 00:13:34,174 And if Earth happens to lie somewhere along this cone, then the axis is pointed 192 00:13:34,174 --> 00:13:40,089 at us, we see a blip of radiation in this case radio radiation, the detection soon 193 00:13:40,089 --> 00:13:45,640 thereafter of the crab pulsar with both a period much shorter than a second. 194 00:13:45,640 --> 00:13:50,020 And its know relation with a super nova remnant nailed. 195 00:13:50,020 --> 00:13:57,800 Both the pulsars both neutron stars as the source pulsars and. 196 00:13:57,800 --> 00:14:02,350 Neutron stars as supernova remants and so how does this work. 197 00:14:02,350 --> 00:14:05,016 Now modeling a pulsar is a difficult exercise. 198 00:14:05,016 --> 00:14:09,712 It's not completely understood what goes on, and the physics that goes into it is 199 00:14:09,712 --> 00:14:14,002 a little bit beyond what we have. But the rough idea is that you have this 200 00:14:14,002 --> 00:14:18,350 star which is rotating very rapidly, it's got a very intense magnetic field. 201 00:14:18,350 --> 00:14:22,635 That means that at any point there's a rapidly changing and very intense 202 00:14:22,635 --> 00:14:25,454 magnetic field. The magnetic field, which changes, 203 00:14:25,454 --> 00:14:29,916 remember are friend Faraday, a changing magnetic field creates an intense 204 00:14:29,916 --> 00:14:33,673 magnetic field, this is intense enough to lift charged particles. 205 00:14:33,673 --> 00:14:38,664 A neutron stars mostly neutrons, but it does have certainly in its upper layers 206 00:14:38,664 --> 00:14:41,482 proton and heavy nuclei and certainly electrons. 207 00:14:41,482 --> 00:14:44,359 They are lifted. In fact the, electric field is so 208 00:14:44,359 --> 00:14:48,939 intense, that it can almost create, pairs of electrons and positrons out of the 209 00:14:48,939 --> 00:14:51,347 vacuum. And so it can pair create its own 210 00:14:51,347 --> 00:14:55,931 magnetic electrically charged particles. These have been accelerated by the 211 00:14:55,931 --> 00:14:59,281 changing magnetic field to vary relevantistic velocities. 212 00:14:59,281 --> 00:15:03,982 And they wind around the magnetic field lines as such particles are supposed to 213 00:15:03,982 --> 00:15:06,508 do. They wind around the, the magnetic field 214 00:15:06,508 --> 00:15:10,622 lines and are dragged around. So there's this magnetosphere of charged 215 00:15:10,622 --> 00:15:14,383 particles that are dragged around by the rotation of the pulsar. 216 00:15:14,383 --> 00:15:16,851 They wind around the magnetic field lines. 217 00:15:16,851 --> 00:15:20,612 This accelerated motion around the magnetic field lines emits a 218 00:15:20,612 --> 00:15:22,530 characteristic Of. 219 00:15:22,530 --> 00:15:26,809 Curvature radiation which is related to synchrotron radiation. 220 00:15:26,809 --> 00:15:32,606 This a mix preferentially because of the relativistic speeds along the direction 221 00:15:32,606 --> 00:15:37,161 of the magnetic axis. And so we produce this sort of lighthouse 222 00:15:37,161 --> 00:15:40,681 effect. the source of the energy for all of this 223 00:15:40,681 --> 00:15:46,409 emission is the rotation, and this is why the pulsars are observed to slow their 224 00:15:46,409 --> 00:15:50,274 rotation speeds. In fact, this at the end will answer the 225 00:15:50,274 --> 00:15:54,870 question I posed earlier. Why is the crab nebula still glowing a 226 00:15:54,870 --> 00:15:59,726 thousand years after the supernova light pulse as past through. 227 00:15:59,726 --> 00:16:05,614 In fact the energy source for all of the glow of n one is the magnetic field 228 00:16:05,614 --> 00:16:09,220 generated by the pulsar in the middle in fact. 229 00:16:09,220 --> 00:16:13,870 What can computer, or estimate, the kinetic energy. 230 00:16:13,870 --> 00:16:19,170 Included in that rotation, one knows the rate at which the crab pulsar is slowing, 231 00:16:19,170 --> 00:16:24,274 one can figure out how much energy that means its losing and compare that our 232 00:16:24,274 --> 00:16:29,641 luminosity of the crab nebula, its a firm calculation and the results, to within 233 00:16:29,641 --> 00:16:35,072 our uncertainties completely agree so the entire luminosity of a, crab nebula is 234 00:16:35,072 --> 00:16:39,980 powered by the slowing down of the rotating neutron star that is in the 235 00:16:39,980 --> 00:16:43,776 middle of it. since Bells discover, I said that, these 236 00:16:43,776 --> 00:16:49,330 particles should emit, synchrotron or Curvature radiation at all wavelengths. 237 00:16:49,330 --> 00:16:54,388 And indeed, pulsars have been observed in all bands, radio waves, infrared, 238 00:16:54,388 --> 00:16:59,447 ultraviolet, X-rays, visible light. The Crab Pulsar can be seen in visible 239 00:16:59,447 --> 00:17:02,750 light though it's a tricky exercise to find it. 240 00:17:02,750 --> 00:17:09,520 But pulsars do admit at all bends neutron stars are extremely exciting 241 00:17:09,520 --> 00:17:14,186 Systems you can imagine that just like white dwarfs when you put neutron stars 242 00:17:14,186 --> 00:17:17,611 in a binary system, you can have exciting mass transfer. 243 00:17:17,611 --> 00:17:21,510 The physics that describes all of these phenomena is relavalistic. 244 00:17:21,510 --> 00:17:25,290 And the details are going to be a little bit beyond what we can do. 245 00:17:25,290 --> 00:17:29,897 if we have time next week we might return armed with some understanding of 246 00:17:29,897 --> 00:17:32,850 relativity. And we'll certainly meet neutron stars 247 00:17:32,850 --> 00:17:36,158 and pulsars in the sequel but I couldn't not mentioning. 248 00:17:36,158 --> 00:17:40,942 Not mention them as the most exciting almost, second most exciting end product 249 00:17:40,942 --> 00:17:42,239 of. Stellar revolution. 250 00:17:42,239 --> 00:17:46,194 Of course the most exciting. End product of star evolution is what 251 00:17:46,194 --> 00:17:51,289 happens if neutron degeneracy is overcome in the collapse of the core and that will 252 00:17:51,289 --> 00:17:52,927 be the topic for next week.