1 00:00:00,000 --> 00:00:04,988 So the sun has joined the main sequence. Let's remind ourselves of what that 2 00:00:04,988 --> 00:00:07,678 means, that means we have a core in which 3 00:00:07,678 --> 00:00:12,798 hydrogen is fusing generating helium. This is supporting the rest of the 4 00:00:12,798 --> 00:00:18,114 envelope by thermal radiation pressure. And there's a theorem that the luminosity 5 00:00:18,114 --> 00:00:23,496 surface temperature, profile, etcetera is all determined essentially by the mass of 6 00:00:23,496 --> 00:00:28,415 the cloud the, the, the ball of hydrogen you're forming. But there are also 7 00:00:28,415 --> 00:00:32,502 dependencies on the composition. What composition, it's hydrogen and 8 00:00:32,502 --> 00:00:35,430 helium. Yes, but there are those trace amounts of 9 00:00:35,430 --> 00:00:39,334 carbon, nitrogen, oxygen. They adjust delicately both the dynamics 10 00:00:39,334 --> 00:00:43,332 of nuclear reactions and of heat transfer, so metallicity makes a 11 00:00:43,332 --> 00:00:47,528 difference. In addition, the rate at which a star rotates can make a 12 00:00:47,528 --> 00:00:51,975 difference, the existence of a close binary partner, some affects of the 13 00:00:51,975 --> 00:00:56,985 atmosphere of the star and when we're observing it also unaccounted for affects 14 00:00:56,985 --> 00:01:00,743 in the interstellar medium can alter a star's appearance. 15 00:01:00,743 --> 00:01:05,440 This, these causes are why the main sequence is not an infinitesimally thin 16 00:01:05,440 --> 00:01:10,325 line, but rather a strip because we have to account for differences in rate of 17 00:01:10,325 --> 00:01:14,245 rotation, composition, etc. And so the, but other than that the star 18 00:01:14,245 --> 00:01:18,481 settles down and sits there in equilibrium and if its a star with the 19 00:01:18,481 --> 00:01:22,080 mass of the sun it will sit there for about ten billion years. 20 00:01:22,080 --> 00:01:26,392 During which time we saw it, things are not exactly static, 21 00:01:26,392 --> 00:01:31,596 there is some evolution going on. What is going on is that the core is 22 00:01:31,596 --> 00:01:34,867 contracting. And the main reason the core is 23 00:01:34,867 --> 00:01:39,402 contracting, you remember, is because of our old equation p is 24 00:01:39,402 --> 00:01:42,525 (n/v)*(kboltzmann)*t. When we take four protons and form an 25 00:01:42,525 --> 00:01:47,432 alpha particle out of them. And in the process eject two positrons 26 00:01:47,432 --> 00:01:53,130 that take two electrons out of the mix. We have gone from a total of eight 27 00:01:53,130 --> 00:01:59,315 particles, four protons and four electrons, to a total of three particles, 28 00:01:59,315 --> 00:02:03,010 one alpha nucleus and two electrons. And, 29 00:02:03,010 --> 00:02:07,306 the net result of this is that the number of particles is decreasing. 30 00:02:07,306 --> 00:02:11,166 If the core does not contract then the pressure will decrease, 31 00:02:11,166 --> 00:02:15,525 pressure can't decrease because it's holding up the external envelope. 32 00:02:15,525 --> 00:02:20,880 There's no real intuitive reason way I can think of to explain this, but the net 33 00:02:20,880 --> 00:02:25,798 result is that the compression and the resulting heating of the core more than 34 00:02:25,798 --> 00:02:29,597 compensate for the decrease in the concentration of hydrogen. 35 00:02:29,597 --> 00:02:34,329 The rate at which fusion is occurring increases and then the core is now 36 00:02:34,329 --> 00:02:37,734 producing more luminosity, more energy, the need to 37 00:02:37,734 --> 00:02:42,497 puff, push more energy through the envelope puffs the envelope out and so 38 00:02:42,497 --> 00:02:47,718 the radius of the star slowly increases and its luminosity slowly increases and 39 00:02:47,718 --> 00:02:52,678 since the rise in temperature of the outer envelope does not track the main 40 00:02:52,678 --> 00:02:55,810 sequence. the star is starting to turn away from 41 00:02:55,810 --> 00:03:01,227 the main sequence if the temperature not changing it's moving vertically up the HR 42 00:03:01,227 --> 00:03:04,294 diagram. And this is where we pick up our story 43 00:03:04,294 --> 00:03:09,879 and where things start to be interesting. So, we meet our Sun at the ripe old age 44 00:03:09,879 --> 00:03:15,475 of about, almost eleven billion years. It has grown somewhat, as we discussed. 45 00:03:15,475 --> 00:03:20,847 It's got a radius of about 1.6 solar radii, it's got a luminosity that's 46 00:03:20,847 --> 00:03:27,040 almost double what it started with. by now it has been accumulating helium in 47 00:03:27,040 --> 00:03:32,411 the core to the extent that the inner 3%, not by volume but by radius. 48 00:03:32,411 --> 00:03:37,560 So, the first point 03 of the solar radius is essentially a chunk of helium 49 00:03:37,560 --> 00:03:41,114 that's, or ball of helium and the helium just sits 50 00:03:41,114 --> 00:03:43,185 there it's inert, it's not producing energy. 51 00:03:43,185 --> 00:03:46,653 Therefore, there's no temperature gradient, there's no flow of energy out 52 00:03:46,653 --> 00:03:49,255 of the helium. So there's no temperature gradient, it's 53 00:03:49,255 --> 00:03:54,242 all at the same temperature, which is the temperature of the hydrogen immediately 54 00:03:54,242 --> 00:03:59,254 adjacent to it and outside this helium core, of course, is a shell of hydrogen 55 00:03:59,254 --> 00:04:03,680 in which fusion is occurring, and that's what's powering the star. 56 00:04:03,680 --> 00:04:08,822 and the rate of fusion in the shell exceeds the rate that was previously 57 00:04:08,822 --> 00:04:12,727 going on in the core. Which is why the star is more luminous 58 00:04:12,727 --> 00:04:17,486 than it was and over these eleven billion years or so, the envelope 59 00:04:17,486 --> 00:04:22,367 has slowly been expanding. And the core has slowly been growing as 60 00:04:22,367 --> 00:04:27,224 helium, hydrogen fuses in the shell, more and more helium is being deposited into 61 00:04:27,224 --> 00:04:32,021 this inert core, which begins to grow. And this is a picture of the solar system 62 00:04:32,021 --> 00:04:36,756 at this point in time, where we are in terms of the sun's main sequence and 63 00:04:36,756 --> 00:04:41,431 evolutionary tract, is that for the first ten and a half billion years of its 64 00:04:41,431 --> 00:04:44,406 existence the sun sat very happily at this point. 65 00:04:44,406 --> 00:04:49,142 And it is now rising away from the main sequence, its luminosity is increasing, 66 00:04:49,142 --> 00:04:52,360 and its temperature is starting to decrease slightly. 67 00:04:52,360 --> 00:04:58,377 As the, envelope puffs out, so the evolutionary track is turning somewhat to 68 00:04:58,377 --> 00:05:01,386 the right. What's the next thing that happens? 69 00:05:01,386 --> 00:05:06,825 Well there is an issue here and the issue is well maybe have an optional clip or 70 00:05:06,825 --> 00:05:09,740 I'll do a calculation associated to this but. 71 00:05:09,740 --> 00:05:14,849 The core being isothermal means again PV is NKT, you need a higher pressure in the 72 00:05:14,849 --> 00:05:20,082 center of the core than at the outside of the core because the center is supporting 73 00:05:20,082 --> 00:05:23,260 the mass, the weight of the outside against gravity. 74 00:05:23,260 --> 00:05:28,182 This means the center of the core has to be more dense than the outside of the 75 00:05:28,182 --> 00:05:30,924 core. Not too complicated a calculation from 76 00:05:30,924 --> 00:05:35,783 this shows you that if the core is too large a fraction of the star, it cannot 77 00:05:35,783 --> 00:05:40,955 support the weight of the outer layers no matter what density you give it and what 78 00:05:40,955 --> 00:05:44,220 this tells you. Is that as the correlate fact-, the 79 00:05:44,220 --> 00:05:49,280 calculation, if you do it in detail, shows you that a core whose mass is more 80 00:05:49,280 --> 00:05:52,610 than 8% of the mass of the star cannot support. 81 00:05:52,610 --> 00:05:56,951 The atmosphere outside it. When the mass of the inert helium core in 82 00:05:56,951 --> 00:06:01,738 the center of the sun exceeds eight% of the solar mass, and it will, remember 83 00:06:01,738 --> 00:06:06,399 that's about the mass of Jupiter. When it exceeds eight% of the solar mass, 84 00:06:06,399 --> 00:06:11,506 it can no longer sustain the weight of the atmosphere and the core starts to 85 00:06:11,506 --> 00:06:13,166 collapse. Collapse rapidly. 86 00:06:13,166 --> 00:06:16,421 What is rapidly? Rapidly means on the gravitational 87 00:06:16,421 --> 00:06:21,485 scales, tens of millions of years. Does, that was this Kelvin-Helmholtz 88 00:06:21,485 --> 00:06:25,662 Scale we talked about. So the core starts to collapse rapidly. 89 00:06:25,662 --> 00:06:31,209 This releases, of course, a great deal of Kelvin-Helmholtz gravitational potential 90 00:06:31,209 --> 00:06:34,428 energy. It also compresses the hydrogen burning 91 00:06:34,428 --> 00:06:39,153 shell immediately outside the core, because that falls in as the core 92 00:06:39,153 --> 00:06:42,440 collapses. This in turn, increases the luminosity 93 00:06:42,440 --> 00:06:50,086 that, that hydrogen shell is putting out. That puffs out the star's atmosphere and 94 00:06:50,086 --> 00:06:57,100 cools it down and the result. Is that the envelope has puffed up. 95 00:06:57,100 --> 00:07:02,720 It's radius is larger, the external temperature decreases, so the star starts 96 00:07:02,720 --> 00:07:08,932 moving to the right along the HR diagram. This is what the solar system will look 97 00:07:08,932 --> 00:07:14,257 like with a larger, cooler sun. notice the time, 700 million years have 98 00:07:14,257 --> 00:07:17,733 elapsed. And the sun is now a sub giant star, it 99 00:07:17,733 --> 00:07:23,723 is moving, it'll spend these 700 million years moving to the left and slightly 100 00:07:23,723 --> 00:07:26,460 heating up. Moving to the right, sorry. 101 00:07:26,460 --> 00:07:31,556 So, cooling down and slightly increasing in luminosity. 102 00:07:31,556 --> 00:07:35,260 As the envelope puffs up. What's a subgiant star? 103 00:07:35,260 --> 00:07:39,350 Well, an example of a subgiant star is Procyon in Canis Minor. 104 00:07:39,350 --> 00:07:43,977 you can look up its data, that's a good example of a subgiant star. 105 00:07:43,977 --> 00:07:49,476 Notice, the Sun will only last about 700 million years as a subgiant whereas, it 106 00:07:49,476 --> 00:07:52,360 lasted ten billion as a main sequence star. 107 00:07:52,360 --> 00:07:57,591 Subgiants are more rare, but because they are luminous, notice they are, the Sun 108 00:07:57,591 --> 00:08:03,090 will be more luminous at the end of its subgiant phase we can see some of them. 109 00:08:03,090 --> 00:08:09,390 So we've left our core collapsing. What does that do? 110 00:08:09,390 --> 00:08:15,348 Well, once the core starts to collapse, then compression heats the shell, 111 00:08:15,348 --> 00:08:22,144 luminosity of the hydrogen fusion shell increases dramatically, this puffs up the 112 00:08:22,144 --> 00:08:26,160 envelope. As it puffs up it cools out cools down it 113 00:08:26,160 --> 00:08:31,050 cools down to a temperature of a few 1,000 degrees where 114 00:08:31,050 --> 00:08:36,003 Negative hydrogen ion opacity again controls the opacity of the external 115 00:08:36,003 --> 00:08:38,921 atmosphere. So it's approaching that Hiachi 116 00:08:38,921 --> 00:08:44,010 temperature that we talked about, because the external atmosphere is opaque. 117 00:08:44,010 --> 00:08:49,303 That means that instead of radiation transfer at the outer atmosphere, we have 118 00:08:49,303 --> 00:08:54,392 sort of deep convection cells over here. These dredge up to the surface the 119 00:08:54,392 --> 00:08:59,550 products of early fusion in the core. And we see a change in the spectrum of 120 00:08:59,550 --> 00:09:01,450 the star. What comes up, well. 121 00:09:01,450 --> 00:09:06,685 Trace amounts of carbon, nitrogen, and oxygen, whose isotopic abundances have 122 00:09:06,685 --> 00:09:10,687 been slightly shifted by the the CNO processes that have been 123 00:09:10,687 --> 00:09:15,003 going on I'll be at, at a smaller rate in the interior of the star in a bigger 124 00:09:15,003 --> 00:09:17,950 star. We'd see the sea in no abundances 125 00:09:17,950 --> 00:09:22,308 that are adjusted by the action of the CNO cycle. 126 00:09:22,308 --> 00:09:28,806 Now whenever a star puffs up this large, note the sun is acquiring a radius of 160 127 00:09:28,806 --> 00:09:34,512 solar radii, it's doing it rather quickly within about 600 million years. 128 00:09:34,512 --> 00:09:39,270 This quick puffing up is always accompanied by enhanced stellar wind and 129 00:09:39,270 --> 00:09:42,490 mass loss. Notice that the outer layers are now much 130 00:09:42,490 --> 00:09:47,445 farther from the center that they were. Much less strongly gravitationally bound. 131 00:09:47,445 --> 00:09:52,151 So the sun at this point might loose as much as 28% of it's mass in it's red 132 00:09:52,151 --> 00:09:55,185 giant phase. The way this would look in the solar 133 00:09:55,185 --> 00:09:59,954 system, is that poor Mercury will have completely been subsumed in the sun. 134 00:09:59,954 --> 00:10:05,189 Venus and Earth still exist I'll be it temperatures there would be very hot 135 00:10:05,189 --> 00:10:09,869 what's an example of a red giant that we know well the star that we call al 136 00:10:09,869 --> 00:10:15,103 debaron and probably should call a dubron is a red giant with 1.7 solar masses so 137 00:10:15,103 --> 00:10:19,968 its a slightly more massive than the sun red giant with a luminosity about 500 138 00:10:19,968 --> 00:10:25,079 times that of the sun in fact at the peak of its red giant phase and we'll talk 139 00:10:25,079 --> 00:10:30,006 about that the sun with have a luminosity over 2,000 times the correct solar 140 00:10:30,006 --> 00:10:33,270 luminosity and so the sun is puffing up cooling down. 141 00:10:33,270 --> 00:10:35,964 And this goes on, and the core is collapsing. 142 00:10:35,964 --> 00:10:40,557 Now, neither the puffing up and cooling down can go on forever, nor for that 143 00:10:40,557 --> 00:10:42,640 matter can the core collapsing. So. 144 00:10:42,640 --> 00:10:47,608 Something's going to stop the core collapse. 145 00:10:47,608 --> 00:10:57,303 And remember that thermodynamic pressure is not able to do this because of this 146 00:10:57,303 --> 00:11:04,312 Schoenberg-Chandrasekhar limit Before we go there let's remind ourselves where we 147 00:11:04,312 --> 00:11:08,331 are on the HR diagram. We have finished the sub giant phase and 148 00:11:08,331 --> 00:11:13,306 we are now climbing the red giant phase. And this phase is the phase that will 149 00:11:13,306 --> 00:11:16,176 last for the next 600 million years or so. 150 00:11:16,176 --> 00:11:21,215 and the sun becomes more and more bright, more and more luminous at a pretty 151 00:11:21,215 --> 00:11:25,297 constant temperature determined as I said by H minus ionization. 152 00:11:25,297 --> 00:11:28,774 And then what. Well first of all the court cannot 153 00:11:28,774 --> 00:11:32,719 continue to collapse its. Collapses stopped by a quantum effect 154 00:11:32,719 --> 00:11:36,974 called electron degeneracy pressure will meet this effect again and while we 155 00:11:36,974 --> 00:11:40,400 haven't done much quantum mechanics we can explain some of it. 156 00:11:40,400 --> 00:11:44,530 electron degeneracy is the result of the poly exclusion principle. 157 00:11:44,530 --> 00:11:49,177 Which remember tells you that only one electron or two if you account for a spin 158 00:11:49,177 --> 00:11:53,365 states, can occupy a given state. And there is a finite number of electron 159 00:11:53,365 --> 00:11:56,291 states up to a given energy in any volume of space. 160 00:11:56,291 --> 00:12:00,938 This electron degeneracy, if you want, is the reason why when I clap my hands they 161 00:12:00,938 --> 00:12:04,897 don't go through each other. Although low lying states in this region 162 00:12:04,897 --> 00:12:08,454 of space are occupied. All of these electrons would have to be 163 00:12:08,454 --> 00:12:12,136 excited to higher energy states. The neat thing about this is it has 164 00:12:12,136 --> 00:12:15,470 nothing to do with temperature. Even if you have zero temperature, 165 00:12:15,470 --> 00:12:17,881 electrons are all at the lowest possible state. 166 00:12:17,881 --> 00:12:21,779 If you try to squeeze too many of them into too small a volume, some of them 167 00:12:21,779 --> 00:12:24,073 have to. Reach excited states even at zero 168 00:12:24,073 --> 00:12:26,676 temperature. So what this does is it produces a 169 00:12:26,676 --> 00:12:29,612 temperature independent contribution to the pressure. 170 00:12:29,612 --> 00:12:33,822 When you try to squeeze system with electrons in it too tight one of the 171 00:12:33,822 --> 00:12:37,184 things you're doing. It's, you're squeezing some electrons 172 00:12:37,184 --> 00:12:41,204 into higher energy states. In normal systems, this is not, in normal 173 00:12:41,204 --> 00:12:45,530 gases this is an irrelevant contribution, even at the center of the sun. 174 00:12:45,530 --> 00:12:50,647 You can make a calculation that it's less than a fraction of a percent of the total 175 00:12:50,647 --> 00:12:54,972 pressure at the center of the sun. But when this degenerate helium core, 176 00:12:54,972 --> 00:12:59,420 when this helium core collapses, its density becomes so high that in fact. 177 00:12:59,420 --> 00:13:04,986 Electron degeneracy pressure is what ends up supporting the sun's atmosphere. 178 00:13:04,986 --> 00:13:09,768 And what is going on is that, The degeneracy pressure, as I said, is 179 00:13:09,768 --> 00:13:13,771 temperature independent. But it's very strongly dependent on 180 00:13:13,771 --> 00:13:16,173 density. It increases as the density^(5/3). 181 00:13:16,173 --> 00:13:20,576 The constant, ke, is slightly dependent on the details of the model. 182 00:13:20,576 --> 00:13:24,445 And for the parameters relevant to the sun I gave it here. 183 00:13:24,445 --> 00:13:29,382 You plug it in, as I said, you'd find that the sun is highly non-degenerate 184 00:13:29,382 --> 00:13:32,251 today. But that the helium core will become 185 00:13:32,251 --> 00:13:35,720 degenerate, and this is what will cease its collapse. 186 00:13:35,720 --> 00:13:39,190 The important thing about degenerate matter is that. 187 00:13:39,190 --> 00:13:41,778 Its pressure is independent of temperature. 188 00:13:41,778 --> 00:13:45,750 If you heat a gas, it will expand because when T goes up P goes up. 189 00:13:45,750 --> 00:13:50,204 When you heat a degenerate gas it will not expand because P is completely 190 00:13:50,204 --> 00:13:54,778 independent of T, until thermal pressure grows enough to overtake degeneracy 191 00:13:54,778 --> 00:13:58,115 pressure. So this will stop the course collapse it 192 00:13:58,115 --> 00:14:03,364 will stop when it reached degeneracy. What does that do to the outside of the 193 00:14:03,364 --> 00:14:05,478 sun, we'll see in the next clip.