1 00:00:00,980 --> 00:00:05,876 So let's put it all together. We now have four main sequence stars. 2 00:00:05,876 --> 00:00:11,411 An understanding of the relation between, at least empirically, mass, luminosity, 3 00:00:11,411 --> 00:00:15,087 temperature, radius. And now, we can hand this over to the 4 00:00:15,087 --> 00:00:19,743 people who, modeled the Sun and understood the rate of re-fusion inside 5 00:00:19,743 --> 00:00:24,902 the Sun and predicted that neutrino flux and they can adapt their models to study 6 00:00:24,902 --> 00:00:29,935 other main sequence stars and try to test the hypothesis that all of these main 7 00:00:29,935 --> 00:00:33,493 sequence stars are basically. The sun at various sizes. 8 00:00:33,493 --> 00:00:37,515 So, what do we do? We take a ball of hydrogen and model its 9 00:00:37,515 --> 00:00:40,983 behavior. We include all of the properties we know 10 00:00:40,983 --> 00:00:46,323 of hydrogen, and of fusion, and of convection, and of radiation diffusion, 11 00:00:46,323 --> 00:00:49,443 and, of course, a star is a complicated system. 12 00:00:49,443 --> 00:00:54,852 But, the idea is, that a main sequence star is an odd ball of hydrogen which, in 13 00:00:54,852 --> 00:00:58,181 its dense hot core, is fusing hydrogen to helium. 14 00:00:58,181 --> 00:01:02,620 And you work on that assumption and you see, will you predict? 15 00:01:02,620 --> 00:01:06,847 The relation between luminosity and mass, between mass and radius, and mass and 16 00:01:06,847 --> 00:01:09,069 temperature, that the main sequence obeys. 17 00:01:09,069 --> 00:01:11,995 And if you do, then you have an understanding of stars. 18 00:01:11,995 --> 00:01:16,168 And essentially, the point is that the conditions for hydrostatic equilibrium 19 00:01:16,168 --> 00:01:19,907 together with the properties of the plasma of which the star is made 20 00:01:19,907 --> 00:01:23,429 determines everything. Starting from the mass of a star. 21 00:01:23,429 --> 00:01:27,524 And, I'd like to outline this, if this confuses you, skip it. 22 00:01:27,524 --> 00:01:32,820 But in the next slide I'm going to outline how a stellar model, proceeds in 23 00:01:32,820 --> 00:01:36,138 some rough level. So here's how we model a star. 24 00:01:36,138 --> 00:01:39,375 We start out with this picture here. Over star. 25 00:01:39,375 --> 00:01:43,685 And what do we know? Well I am going to assume that I know the 26 00:01:43,685 --> 00:01:45,523 temperature. Outside the star. 27 00:01:45,523 --> 00:01:49,655 And the pressure, the atmospheric pressure of the star, effectively the 28 00:01:49,655 --> 00:01:54,260 atmospheric pressure of the star is essentially zero but I'll start with some 29 00:01:54,260 --> 00:01:57,153 small value. And I'm going to work my way in and try 30 00:01:57,153 --> 00:02:01,757 to understand from equilibrium how the temperature, the pressure and of course 31 00:02:01,757 --> 00:02:06,244 importantly the mass density rho which I'm going to again say is very small on 32 00:02:06,244 --> 00:02:08,783 the outside, atmospheric, how these increase. 33 00:02:08,783 --> 00:02:11,498 I expect all of them to increase as I move in. 34 00:02:11,498 --> 00:02:14,863 So what do I know? A star is a complicated system but I'm 35 00:02:14,863 --> 00:02:18,247 going to imagine. Just for pretend, just so we get a sense 36 00:02:18,247 --> 00:02:22,275 of what's going on, that the interior of a star is an ideal gas. 37 00:02:22,275 --> 00:02:27,070 It's not but if it were an ideal gas, then ideal gases satisfy the equation 38 00:02:27,070 --> 00:02:29,819 that we wrote down, for this precise reason. 39 00:02:29,819 --> 00:02:35,062 Pv is NKT, the product of pressure times volume is the number of particles times a 40 00:02:35,062 --> 00:02:39,474 constant times the temperature. I have pressure in here that's good, I 41 00:02:39,474 --> 00:02:44,588 have temperature, I don't have density, but that's okay if these are all hydrogen 42 00:02:44,588 --> 00:02:47,530 atoms and if M is the mass of a hydrogen atom. 43 00:02:47,530 --> 00:02:55,141 Then since the mass divided by the volume is row, and since the mass in a given 44 00:02:55,141 --> 00:03:01,110 volume is the number of particles times the mass of an hydrogen atom. 45 00:03:01,110 --> 00:03:08,845 I can relate n and v to rho. And I find that, v divided n, which is 46 00:03:08,845 --> 00:03:16,580 the quantity I get that enters into here, is simply n, divided by rho. 47 00:03:16,580 --> 00:03:22,980 And so, putting that into that equation, I find that p, 48 00:03:22,980 --> 00:03:26,715 is equal to, n times rho, times kb times T. 49 00:03:26,715 --> 00:03:33,154 Okay this is a version of the equation of state that I can use, and now what do I 50 00:03:33,154 --> 00:03:36,571 do? Now I need to impose what this tells me 51 00:03:36,571 --> 00:03:43,010 of course, is that as pressure increases, temperature and or density will increase, 52 00:03:43,010 --> 00:03:48,892 now that's one thing I know, and then what I'm going to do is I'm going to 53 00:03:48,892 --> 00:03:54,535 imagine I know the conditions right outside the star, let's try to find 54 00:03:54,535 --> 00:03:59,783 conditions a little distance r inside. So this is the radius of the star. 55 00:03:59,783 --> 00:04:05,447 And I'm going to move a little distance r inside and try and see if you know what 56 00:04:05,447 --> 00:04:08,889 goes on here, how do you know what goes on there. 57 00:04:08,889 --> 00:04:14,051 And there's some things I know. I know the pressure here, p1 has to be 58 00:04:14,051 --> 00:04:15,413 bigger than p0. Why? 59 00:04:15,413 --> 00:04:20,863 Well because I've sunk in this layer underneath is holding up the weight of 60 00:04:20,863 --> 00:04:24,775 the Of the, the bit of the star that is 61 00:04:24,775 --> 00:04:31,623 outside so, I can write some crazy equation that says, P1 minus P0 times the 62 00:04:31,623 --> 00:04:38,289 area of the interface between these layers which is four Pi R squared is 63 00:04:38,289 --> 00:04:42,500 equal to, the. Mass of the gas in this region, 64 00:04:42,500 --> 00:04:46,670 which if I assume that its density is row zero. 65 00:04:46,670 --> 00:04:50,219 That's also four pi r2 squared little r times rho. 66 00:04:50,219 --> 00:04:55,542 That's the mass in there. And then I multiply that by g times the 67 00:04:55,542 --> 00:05:01,220 mass inside the radius R. So that's, in this case, the entire star 68 00:05:01,220 --> 00:05:04,857 divided by r2. square.d And I can, from here, cancelling 69 00:05:04,857 --> 00:05:11,338 these factors, I can find that the pressure changes r 70 00:05:11,338 --> 00:05:16,203 times row times gn over r squared. Okay, now. 71 00:05:16,203 --> 00:05:20,155 That gives me, real, tells me that if I know the 72 00:05:20,155 --> 00:05:23,205 pressure here, I can tell the pressure there. 73 00:05:23,205 --> 00:05:26,949 I want to relate, to figure out the density and the 74 00:05:26,949 --> 00:05:30,900 temperature in here. Of course, since the pressure changed, 75 00:05:30,900 --> 00:05:34,297 the, density and the temperature had to change. 76 00:05:34,297 --> 00:05:37,188 Because, The new pressure, which is higher, is 77 00:05:37,188 --> 00:05:40,202 equal to the product of the new density and temperature. 78 00:05:40,202 --> 00:05:44,754 There's another relation that I know. Which is the important thing that I can 79 00:05:44,754 --> 00:05:49,424 put in, is that I know the luminosity. There's a neck flux of energy the star is 80 00:05:49,424 --> 00:05:53,626 radiating at a luminosity L. And so, that means that, since the 81 00:05:53,626 --> 00:05:58,930 temperature of everything is constant. A net amount of energy, L, is being 82 00:05:58,930 --> 00:06:02,395 transferred through this layer at any given time. 83 00:06:02,395 --> 00:06:07,699 And if I know the properties of the layer, I can figure out how much hotter 84 00:06:07,699 --> 00:06:13,570 it has to be inside in order for an amount of energy L per second, a rate, 85 00:06:13,570 --> 00:06:18,201 the power of L to propagate out. And how this works depends on what the 86 00:06:18,201 --> 00:06:23,485 mechanisms are, if it's convection I need to use the convection properties of the 87 00:06:23,485 --> 00:06:26,616 fluid. If it's radiation diffusion the radiation 88 00:06:26,616 --> 00:06:30,334 diffusion properties of conduction, conductive properties. 89 00:06:30,334 --> 00:06:35,292 But if I know the luminosity I can figure out T1 minus T0, so this allows me, 90 00:06:35,292 --> 00:06:40,009 starting with T0 to figure out T1. And then I use this equation to figure 91 00:06:40,009 --> 00:06:42,957 out P1. And then I use this equation to figure 92 00:06:42,957 --> 00:06:46,353 out row one. And now I understand things one layer in 93 00:06:46,353 --> 00:06:51,480 and then I can proceed in and build the entire model of the star one layer at a 94 00:06:51,480 --> 00:06:54,428 time. If this was not illuminating to you, just 95 00:06:54,428 --> 00:06:58,210 imagine that somebody models stars. So what have we learned? 96 00:06:58,210 --> 00:07:02,711 Well the important thing is, looking way down at the middle of the star at the 97 00:07:02,711 --> 00:07:04,197 core. That there are, 98 00:07:04,197 --> 00:07:08,719 I talked about the PP Chain, which is how the sun produces energy. 99 00:07:08,719 --> 00:07:13,507 And stars with a mass of about one one-half solar masses or more, 100 00:07:13,507 --> 00:07:17,638 so just about the Sun. the core is hotter, the bigger the star 101 00:07:17,638 --> 00:07:22,765 is, because there's more pressure there's more layers to integrate through, and 102 00:07:22,765 --> 00:07:25,993 more mass. And it turns out that at higher, hydrogen 103 00:07:25,993 --> 00:07:31,120 at higher temperature can produce fusion in a much more efficient way through 104 00:07:31,120 --> 00:07:34,727 something called the carbon nitrogen oxygen or CNO chain. 105 00:07:34,727 --> 00:07:40,234 this is a process in which, the steps are, are many, and detailed, and we don't 106 00:07:40,234 --> 00:07:43,335 need to go into them, but you can read up on them. 107 00:07:43,335 --> 00:07:48,757 But basically, the presence of carbon in the core catalyzes fusion, in the sense 108 00:07:48,757 --> 00:07:53,594 that carbon fuses with hydrogen to produce nitrogen, which decays to leave 109 00:07:53,594 --> 00:07:58,431 carbon, a different isotope of carbon, which fuses again to produce another 110 00:07:58,431 --> 00:08:02,287 isotope of nitrogen, which fuses with another hydrogen atom, 111 00:08:02,287 --> 00:08:05,948 producing oxygen, which decays to an isotope of nitrogen, 112 00:08:05,948 --> 00:08:09,870 which fuses with yet another proton, emits an alpha particle, 113 00:08:09,870 --> 00:08:12,070 and returns us to the original carbon atom. 114 00:08:12,070 --> 00:08:16,452 so then end result is one, two, three, four protons go in, two week decays take 115 00:08:16,452 --> 00:08:20,778 place and a helium atom is spat out. The carbon is recycled in this process so 116 00:08:20,778 --> 00:08:25,160 it's not being fused into anything, but at higher temperature, this process goes 117 00:08:25,160 --> 00:08:29,709 much faster than the PP chain the point is that the rate at which this process 118 00:08:29,709 --> 00:08:34,091 goes rises much more is much more temperature dependent than the rate of 119 00:08:34,091 --> 00:08:38,584 the PP chain basically because to start it all off and its several stages in the 120 00:08:38,584 --> 00:08:42,633 middle, you need not to bring two protons close together, overcoming their, 121 00:08:42,633 --> 00:08:44,055 electrostatic. Repulsion. 122 00:08:44,055 --> 00:08:47,410 You need to bring a proton near to a carbon nucleus, 123 00:08:47,410 --> 00:08:53,240 which has charged six and that electrostatic repulsion is much stronger 124 00:08:53,240 --> 00:08:56,392 and so it takes higher temperatures to get the 125 00:08:56,392 --> 00:08:59,497 CNO chain started. This is the qualitative difference 126 00:08:59,497 --> 00:09:03,480 between the big stars and little stars. What are the results of this? 127 00:09:03,480 --> 00:09:08,165 Well it turns out that what happens is that the mechanism by which all of these 128 00:09:08,165 --> 00:09:10,684 stars, main sequence stars indeed can be 129 00:09:10,684 --> 00:09:14,784 explained as a ball of hydrogen, fusing hydrogen to helium in its core. 130 00:09:14,784 --> 00:09:19,774 Details of the model depend on the size of the ball of hydrogen you start with. 131 00:09:19,774 --> 00:09:23,796 Very small stars with a mass less than a half a solar mass. 132 00:09:23,796 --> 00:09:28,001 It turns out that there is no radiation zone as there was in the Sun. 133 00:09:28,001 --> 00:09:31,475 There is just a convection zone. The entire star convects. 134 00:09:31,475 --> 00:09:36,411 This is important for estimating their life time because remember in the core 135 00:09:36,411 --> 00:09:40,860 hydrogen is being converted to helium. Then this helium-enriched hydrogen. 136 00:09:40,860 --> 00:09:45,160 Bubbles up through the entire star. And new fresh hydrogen-poor, helium-poor 137 00:09:45,160 --> 00:09:49,001 hydrogen is convected down. So this star, when it runs out of helium 138 00:09:49,001 --> 00:09:53,474 in the core wil essentially be, when it runs out of hydrogen in the core, will 139 00:09:53,474 --> 00:09:57,660 essentially have converted a large fraction of the entire star to helium. 140 00:09:57,660 --> 00:10:02,057 And that's the way small stars work. Medium mass stars like the sun work we 141 00:10:02,057 --> 00:10:05,359 described. The interior is a radiation diffusion 142 00:10:05,359 --> 00:10:11,139 region then the outer mentor is the convective region where hydrogen atoms 143 00:10:11,139 --> 00:10:16,713 are less ionized, they are therefore more opaque and in and therefore they absorb 144 00:10:16,713 --> 00:10:21,706 the radiation heat up and then well up and its a hydrodynamic process of 145 00:10:21,706 --> 00:10:25,530 convection that brings the heat up to the surface of the star. 146 00:10:25,530 --> 00:10:29,471 In bigger stars it turns out convection and radiation are replaced. 147 00:10:29,471 --> 00:10:33,353 In these stars the entire, the temperature is so high that much of 148 00:10:33,353 --> 00:10:36,000 the interior of the star is actually ionized. 149 00:10:36,000 --> 00:10:39,706 But in the interior because there is a temperature gradient, 150 00:10:39,706 --> 00:10:44,059 the exterior is, of the core, is cool. Still not as hot as the center of the 151 00:10:44,059 --> 00:10:46,765 core. The temperature gradients means, that the 152 00:10:46,765 --> 00:10:49,647 rate at which fusion occurs changes very rapidly. 153 00:10:49,647 --> 00:10:54,353 This leads, to such a power, differences in the power output between different 154 00:10:54,353 --> 00:10:58,165 layers, that in fact the star becomes convected, 155 00:10:58,165 --> 00:11:03,355 so in a star the inner region of the star is heat tran, is 156 00:11:03,355 --> 00:11:07,862 transferred by convection. So this region all gets mixed up, but the 157 00:11:07,862 --> 00:11:11,905 external region is in fact transfers heat by radiation. 158 00:11:11,905 --> 00:11:15,565 the fact that this is what's predicted by the models, 159 00:11:15,565 --> 00:11:19,944 and then predictions of luminosity as the, as it depends on mass. 160 00:11:19,944 --> 00:11:25,042 And radius, as it depends on mass, and temperature as it depends on mass are 161 00:11:25,042 --> 00:11:28,571 reproduced. The, measurements from the main sequence. 162 00:11:28,571 --> 00:11:33,873 Tells us that our models have it right. So we've an understanding of the basic 163 00:11:33,873 --> 00:11:38,521 physics of how, main sequence stars work. They're a ball of hydrogen, fusing 164 00:11:38,521 --> 00:11:43,349 hydrogen to helium at its core and, transmitting the energy to the outside by 165 00:11:43,349 --> 00:11:47,816 convection and radiation diffusion, and then radiating that, radiating that 166 00:11:47,816 --> 00:11:51,105 energy out. we did, are not going to reproduce all of 167 00:11:51,105 --> 00:11:55,759 the details of understanding the nuclear cross sections that go into modeling. 168 00:11:55,759 --> 00:11:59,220 But I think we understand the basic principles, and, the, 169 00:11:59,220 --> 00:12:03,814 rate of fusion in the core, as we said for the sun, is in equilibrium with the 170 00:12:03,814 --> 00:12:06,618 pressure, as we saw, applied by the outer layers, 171 00:12:06,618 --> 00:12:09,781 and therefore the mass determines the rate of fusion. 172 00:12:09,781 --> 00:12:14,150 And as the star, star sits on the main sequence, we'll see next week what 173 00:12:14,150 --> 00:12:17,931 happens before and after. But today let's finish up by discussing 174 00:12:17,931 --> 00:12:22,875 what happens in the 10 billion years, say, for the sun that it sits on the main 175 00:12:22,875 --> 00:12:25,725 sequence. Remember the sun is about 4 1/2 billion 176 00:12:25,725 --> 00:12:29,332 years old, so it's about half done with its main sequence life. 177 00:12:29,332 --> 00:12:34,393 How does the sun today compare to the way it was when it was a brand new fresh zero 178 00:12:34,393 --> 00:12:39,071 age main sequence star, as we call it? So the star has, the Sun formed, as it 179 00:12:39,071 --> 00:12:44,698 was mostly hydrogen. It has a core where, hydrogen starts to 180 00:12:44,698 --> 00:12:49,570 fusing to helium. Over time, as fusion goes on, the 181 00:12:49,570 --> 00:12:53,350 the region, hydrogen in the core becomes enreached, enriched in helium. 182 00:12:53,350 --> 00:12:58,600 So, what that means is that if you have your star over here, and the core in 183 00:12:58,600 --> 00:13:04,200 there there is more and more Helium in the core and correspondingly less and 184 00:13:04,200 --> 00:13:07,369 less Hydrogen. This means that the probability for 185 00:13:07,369 --> 00:13:11,991 collision of two protons in order to initiate fusion decreases, because some 186 00:13:11,991 --> 00:13:15,457 of the time the protons are not running in to each other. 187 00:13:15,457 --> 00:13:20,505 They're running into helium atoms, and in the sum they do not have enough energy to 188 00:13:20,505 --> 00:13:25,370 actually fuse effectively with helium. And so the helium is inert and there's 189 00:13:25,370 --> 00:13:28,168 less and less protons running into each other. 190 00:13:28,168 --> 00:13:32,698 So when we predict that the rate of fusion would decrease in the core this 191 00:13:32,698 --> 00:13:37,014 would decrease the radiation pressure, because the pressure emanating from the 192 00:13:37,014 --> 00:13:41,109 core part of large particles that is radiation pressure or this energy. 193 00:13:41,109 --> 00:13:45,480 furthermore, and this is a tricky. It turns out to be the dominant effect is 194 00:13:45,480 --> 00:13:50,775 that when we particles undergo fusion four hydrogen atoms are converted to one 195 00:13:50,775 --> 00:13:55,740 helium atom, and if you remember our PV equals MKT, 196 00:13:55,740 --> 00:13:59,670 what's really going on is the number of particles is decreasing, 197 00:13:59,670 --> 00:14:05,141 because four protons have only made one alpha particle, when the partic-, the 198 00:14:05,141 --> 00:14:09,240 number of particles decreases, the pressure goes down. 199 00:14:09,240 --> 00:14:12,562 Now this cannot happen. The reason this cannot happen is because 200 00:14:12,562 --> 00:14:16,767 remember the pressure on the inside of the store was predicted and determined by 201 00:14:16,767 --> 00:14:20,245 the need to hold up the outer layers. How can the pressure decrease? 202 00:14:20,245 --> 00:14:23,551 The pressure decreases. The outer layers of the star will 203 00:14:23,551 --> 00:14:27,961 contract the star, the core. Now, this is the first time we're meeting 204 00:14:27,961 --> 00:14:32,805 this sort of a phenomenon that I call expansion by contraction, and it'll come 205 00:14:32,805 --> 00:14:35,538 back. It sounds like a weird economic theory, 206 00:14:35,538 --> 00:14:40,134 but it is a property of stars, so, I want to understand it this first time, 207 00:14:40,134 --> 00:14:45,041 because it will repeat, many times over the course of our study of stars, and 208 00:14:45,041 --> 00:14:49,823 So, what happens is the pressure has not decreased, instead the core contracts. 209 00:14:49,823 --> 00:14:54,730 So, the material that was previously the core is contracted to a smaller radius. 210 00:14:54,730 --> 00:14:58,643 This, in turn, heats it up. Both, because we're, converting 211 00:14:58,643 --> 00:15:02,827 gravitational potential energy. The entire star scrunches down. 212 00:15:02,827 --> 00:15:06,741 And so the entire star undergoes Kelvin-Helmholtz heating. 213 00:15:06,741 --> 00:15:09,912 And of course, this is most extreme in the core. 214 00:15:09,912 --> 00:15:13,924 Moreover. Because a thermodynamically it heats up 215 00:15:13,924 --> 00:15:18,690 the temperature in the core rises and the density rises. 216 00:15:18,690 --> 00:15:22,896 How long does this go on? Well, until fusion rates increase enough 217 00:15:22,896 --> 00:15:27,038 to hold up the rest of the star. So in fact, the pressure here is 218 00:15:27,038 --> 00:15:31,569 essentially equal or larger, in fact, because of the contraction to the 219 00:15:31,569 --> 00:15:35,840 pressure previously obtained there. And density and so on followed. 220 00:15:35,840 --> 00:15:40,888 In that process, something else happened. The region between what the court now 221 00:15:40,888 --> 00:15:44,836 occupies and where the court used to be. Didn't get evacuated. 222 00:15:44,836 --> 00:15:50,272 This is now occupied by an inflow of new hydrogen that used to reside just outside 223 00:15:50,272 --> 00:15:54,172 the court. This new influx of hydrogen is heated and 224 00:15:54,172 --> 00:15:57,596 compressed. It's now closer to the center of the star 225 00:15:57,596 --> 00:16:01,536 than it was before and it, in turn, begins to undergo pressure. 226 00:16:01,536 --> 00:16:06,510 So there are two processes going on. One is the pressure in the core is 227 00:16:06,510 --> 00:16:10,580 maintained by compressing the core. This in turn heats the core. 228 00:16:10,580 --> 00:16:15,484 Increasing the rate of fusion, both by increasing the temperature and the 229 00:16:15,484 --> 00:16:18,575 density. And further more, the amount of fusing 230 00:16:18,575 --> 00:16:23,277 material grows, because some of the hydrogen that was too cold, and not 231 00:16:23,277 --> 00:16:28,316 pressurized enough to fuse is now contracting to the point where it begins 232 00:16:28,316 --> 00:16:31,608 to fuse. The net result is that the core heat, the 233 00:16:31,608 --> 00:16:36,513 fusing region grows, and the total power production of the star increases. 234 00:16:36,513 --> 00:16:39,805 When the core contracts, the luminosity increases. 235 00:16:39,805 --> 00:16:44,921 The increased power output from the core, in turn, applies extra radiation pressure 236 00:16:44,921 --> 00:16:49,470 and extra thermodynamic pressure to the rest of the star, and the star balloons 237 00:16:49,470 --> 00:16:53,345 out a little bit. So over the course of its main sequence 238 00:16:53,345 --> 00:16:57,789 life time, as it runs out slowly of helium, hydrogen in the core, the stars 239 00:16:57,789 --> 00:17:02,166 core contracts and heats, and creates more hydrogen into the core, 240 00:17:02,166 --> 00:17:06,745 resulting in the fact that the outer envelope of the star grows, and 241 00:17:06,745 --> 00:17:10,179 luminosity increases. This is a very important fact. 242 00:17:10,179 --> 00:17:13,344 So, if we apply to the sun, what does it tell us? 243 00:17:13,344 --> 00:17:18,540 It tells us that the sun is now about 25% brighter than when it formed 244 00:17:18,540 --> 00:17:21,774 And the this is halfway through its main sequence lifetime. 245 00:17:21,774 --> 00:17:25,667 the sun is now brighter than when it formed 4 billion years ago. 246 00:17:25,667 --> 00:17:28,792 The sun was a rather dim star compared to what it is now. 247 00:17:28,792 --> 00:17:31,588 this meant that the earth was presumably cooler. 248 00:17:31,588 --> 00:17:35,425 There are all kinds of complications trying to understand how this is 249 00:17:35,425 --> 00:17:39,921 consistent with what we find on earth but it is certainly what our stellar models 250 00:17:39,921 --> 00:17:43,113 predict. Moreover, we can run our simulations and 251 00:17:43,113 --> 00:17:48,413 the core of the sun is now 60% helium. When I said it's depleted in hydrogen, I 252 00:17:48,413 --> 00:17:53,781 meant that of course, there are regions outside the core that are beginning to 253 00:17:53,781 --> 00:17:57,430 fuse as new clean hydrogen, untainted by helium, is 254 00:17:57,430 --> 00:18:01,735 compressed to the densities and temperatures, where it too can begin to 255 00:18:01,735 --> 00:18:05,009 fuse, which is why the sun has a larger luminosity now. 256 00:18:05,009 --> 00:18:09,800 It's going to continue to brighten over the next 5 billion years, making Earth 257 00:18:09,800 --> 00:18:14,651 warmer and warmer, and you can ask global warming, carbon dioxide, will the sun do 258 00:18:14,651 --> 00:18:17,501 us in? And yes, the sun will probably make Earth 259 00:18:17,501 --> 00:18:21,867 uninhabitable, and depending on your estimates, somewhere between 1 and 3 260 00:18:21,867 --> 00:18:25,627 billion years. So, if we managed to control our carbon 261 00:18:25,627 --> 00:18:29,690 emissions for that long, the sun will in any event do life on Earth. 262 00:18:29,690 --> 00:18:34,671 this in fact is a little bit imprecise because once you get into billion year 263 00:18:34,671 --> 00:18:38,054 periods there are other factors that come into account. 264 00:18:38,054 --> 00:18:43,282 The sun loses mass and as it expands, the outer layers are now farther and farther 265 00:18:43,282 --> 00:18:47,095 from the center of the sun. Their escape velocity decreases. 266 00:18:47,095 --> 00:18:51,523 S the solar wind increases. At, in it's last couple a billion years 267 00:18:51,523 --> 00:18:56,320 the sun's lo, mass loss rate increases significantly so that the earth will be 268 00:18:56,320 --> 00:18:59,150 orbiting a star that is less and less massive. 269 00:18:59,150 --> 00:19:03,516 Which means that with it's current energy it will probably be propelled to a higher 270 00:19:03,516 --> 00:19:05,958 orbit. Once you allow orbits to change you have 271 00:19:05,958 --> 00:19:10,220 to also remember that orbits in the solar system, I said are stable to hundreds of 272 00:19:10,220 --> 00:19:13,807 millions, maybe a billion year out. But we do not have really reliable 273 00:19:13,807 --> 00:19:17,653 predictions that maybe in a few billion years there won't be some orbital 274 00:19:17,653 --> 00:19:21,983 residents that will completely throw the orbits out of kilter, and so a billion 275 00:19:21,983 --> 00:19:25,644 years out is a long time. We don't know exactly what will happen, 276 00:19:25,644 --> 00:19:29,935 but at some point in the next three billion years, Earth will probably be a 277 00:19:29,935 --> 00:19:32,738 problem. If we survived that long we have to deal 278 00:19:32,738 --> 00:19:35,312 with this. Another busy week, but I think very 279 00:19:35,312 --> 00:19:38,230 productive. What have you learned by looking at the 280 00:19:38,230 --> 00:19:40,690 stars? For 90% of them, we have a pretty good 281 00:19:40,690 --> 00:19:45,037 physics understanding of how they work and it matches all the data, and this 282 00:19:45,037 --> 00:19:49,248 came from decades of painstaking observations, measuring the positions of 283 00:19:49,248 --> 00:19:53,559 stars over the decades to do astrometric measurements of binaries and proper 284 00:19:53,559 --> 00:19:55,798 motion. Measuring the parallax angles of 285 00:19:55,798 --> 00:19:59,773 thousands of stars in competing their distance carefully, measuring thousands 286 00:19:59,773 --> 00:20:03,860 and thousands of spectra in classifying them and understanding the patterns. 287 00:20:03,860 --> 00:20:07,667 A lot of really, really careful observation, and then detailed in the 288 00:20:07,667 --> 00:20:12,425 miracle modelling with the advent of high speed computing and putting all that 289 00:20:12,425 --> 00:20:16,736 together with experiments under that to determine the properties of there is 290 00:20:16,736 --> 00:20:20,409 nuclear processes, we actually understand a lot about how stars work. 291 00:20:20,409 --> 00:20:24,219 That's good for the 85% that are on the main sequence, what about the rest? 292 00:20:24,219 --> 00:20:28,395 Not all stars are main sequence stars. We need to understand where the rest come 293 00:20:28,395 --> 00:20:30,743 from. A related question it turns out will be, 294 00:20:30,743 --> 00:20:34,136 well what was the sun like before it became a main sequence star? 295 00:20:34,136 --> 00:20:38,259 And, even more excitingly, what happens when the hydrogen runs out, and it can no 296 00:20:38,259 --> 00:20:41,704 longer be a main sequence star. And that is what we're going to start 297 00:20:41,704 --> 00:20:42,435 studying next.