1 00:00:00,000 --> 00:00:03,166 Great. So now we have a catalog, a growing 2 00:00:03,166 --> 00:00:06,795 catalog of stars to which we know the distance. 3 00:00:06,795 --> 00:00:11,120 We have pulled those stars. We, some of them stars nearby, 4 00:00:11,120 --> 00:00:14,899 down off of the celestial sphere. We know the distance to them, we live, they live 5 00:00:14,899 --> 00:00:18,468 in our three-dimensional universe. And what does that tell us about them? 6 00:00:18,468 --> 00:00:21,723 Well, tells us a lot. Let's start by seeing what we can tell 7 00:00:21,723 --> 00:00:25,240 about a star just by looking at it, that's all we can do with stars. 8 00:00:25,240 --> 00:00:29,590 But, assuming that someone tells us because we measure carefully the distance 9 00:00:29,590 --> 00:00:31,990 to it. Well, one thing we can do is we can do a 10 00:00:31,990 --> 00:00:35,288 photometric measurement. We can measure the brightness of a star, 11 00:00:35,288 --> 00:00:39,461 literally aim a telescope with a known aperture area at the star and measure the 12 00:00:39,461 --> 00:00:42,398 rate at which the telescope gets energy from the star. 13 00:00:42,398 --> 00:00:44,613 You correct for dark sky. There's a process, 14 00:00:44,613 --> 00:00:48,372 it's not that difficult. But if we know the brightness, then we 15 00:00:48,372 --> 00:00:53,351 can remember, remind ourself that brightness is related to luminosity of 16 00:00:53,351 --> 00:00:55,544 the star by this expression. Right? 17 00:00:55,544 --> 00:01:00,334 And this is luminosity divided by four pi D^2, if we know the brightness because we 18 00:01:00,334 --> 00:01:03,175 measured it. We know the distance because we measured 19 00:01:03,175 --> 00:01:05,570 it. We can extract an expression by solving 20 00:01:05,570 --> 00:01:09,191 this for the luminosity. So we know the actual luminosity of the 21 00:01:09,191 --> 00:01:11,475 star. Now we can tell you, is this some very 22 00:01:11,475 --> 00:01:14,093 huge, very luminous star, or some very tiny star? 23 00:01:14,093 --> 00:01:19,106 this is norm way to write the equation, a more convenient form in which to write 24 00:01:19,106 --> 00:01:23,396 it is to scale it to something known. In other words, this same equation holds 25 00:01:23,396 --> 00:01:27,360 for any star in particular, it holds for the sum. 26 00:01:27,360 --> 00:01:32,549 And the advantage of writing it in this way is now whether this suggests is if I 27 00:01:32,549 --> 00:01:37,306 divide the left-hand sides and set that equal to the ratio of the right-hand 28 00:01:37,306 --> 00:01:41,877 sides, first of all the, four pis and whatever constants are sitting around 29 00:01:41,877 --> 00:01:46,572 cancel, but more usefully I now get a product of dimensionless quantities. 30 00:01:46,572 --> 00:01:51,514 I get an expression that says that this divided by that is this divided by that 31 00:01:51,514 --> 00:01:55,861 or this expression here, where I have plugged in that the value of the distance 32 00:01:55,861 --> 00:02:00,471 of the sun from earth is one astronomical unit and the sun's brightness is the 33 00:02:00,471 --> 00:02:03,733 solar constant. So we have rate of dimensionless object. 34 00:02:03,733 --> 00:02:08,344 the luminosity of the star in units of solar luminosity written as the product 35 00:02:08,344 --> 00:02:11,267 of two others. Whenever possible, we'll write it that 36 00:02:11,267 --> 00:02:11,774 way. Okay. 37 00:02:11,774 --> 00:02:16,159 Now we know the luminosity of the star. What else can I get just by looking at 38 00:02:16,159 --> 00:02:18,465 it? Well, if I'm careful I can measure the 39 00:02:18,465 --> 00:02:21,993 color, star's color. And the star's color as we know gives us 40 00:02:21,993 --> 00:02:26,331 information about its temperature. If I find the maximum of its black body 41 00:02:26,331 --> 00:02:30,200 spectrum, I can get an estimate from a temperature from Wien's law. 42 00:02:30,200 --> 00:02:33,835 So there is Wien's law. It relates the surface temperature of a 43 00:02:33,835 --> 00:02:37,646 star to the wavelength at which it emits its maximum emission, 44 00:02:37,646 --> 00:02:42,802 this is written in Kelvin. And now, if I know the temperature and I 45 00:02:42,802 --> 00:02:48,000 know the luminosity, I can remind myself that I have yet another expression for 46 00:02:48,000 --> 00:02:53,395 the luminosity of any star. L was equal to the sigma T^4, given by V 47 00:02:53,395 --> 00:02:58,067 Stefan-Boltzmann law for the rate at which each square meter of the star 48 00:02:58,067 --> 00:03:03,331 surface radiates times the surface area of the star, which in terms of the star's 49 00:03:03,331 --> 00:03:07,608 radius is given by four pi R^2, where R is the star's radius. 50 00:03:07,608 --> 00:03:12,017 And now, if I know T and I know L, I can extract an expression for R. 51 00:03:12,017 --> 00:03:22,749 you find that R^2 is L over four pi sigma T^4 or if I just want R, I simply take 52 00:03:22,749 --> 00:03:29,113 the square root of both sides. And I can rewrite that as the square root 53 00:03:29,113 --> 00:03:37,015 of L over four pi sigma times the square root of one over T^4 is T minus two, one 54 00:03:37,015 --> 00:03:40,688 over T^2. And in this form, again I can compare to 55 00:03:40,688 --> 00:03:45,484 the sun by dividing this expression for the star by the same expression for the 56 00:03:45,484 --> 00:03:48,063 sun. The radius of the sun is luminosity of 57 00:03:48,063 --> 00:03:52,319 the sun square root divided [INAUDIBLE] one over the temperature, solar 58 00:03:52,319 --> 00:03:55,737 temperatures square, and this gives me another one of those 59 00:03:55,737 --> 00:03:59,514 nice scaling expressions. But then, bottom line is if I know the 60 00:03:59,514 --> 00:04:04,191 temperature and luminosity, for which I needed observations and the distance, I 61 00:04:04,191 --> 00:04:06,290 can get the radius of the star. Now, 62 00:04:06,290 --> 00:04:11,072 now some stars, a few tens have actually been imaged and this is a recent 63 00:04:11,072 --> 00:04:14,643 development. There's a few tens of stars for which the 64 00:04:14,643 --> 00:04:19,490 radius has actually been measured particularly optically by imaging them 65 00:04:19,490 --> 00:04:24,209 and measuring the angular distance between the left and right side of the 66 00:04:24,209 --> 00:04:27,206 star. This is a new result, but most stars, 67 00:04:27,206 --> 00:04:30,650 when we say we know their radius, we know it from this. 68 00:04:30,650 --> 00:04:35,183 This is brilliant, we can know a lot from a star, about a star if we know it's 69 00:04:35,183 --> 00:04:38,009 distance. the problematic measure here is the 70 00:04:38,009 --> 00:04:41,954 temperature Remember we said the black body spectrum is very broad. 71 00:04:41,954 --> 00:04:46,546 If you have a very broad mountain, identifying exactly where the summit is 72 00:04:46,546 --> 00:04:50,727 can be a problem, in the same way, finding the precise maximum of a very 73 00:04:50,727 --> 00:04:54,259 broad black body spectrum is a difficult and imprecise task. 74 00:04:54,259 --> 00:04:58,675 We want a better thermometer, since measuring the stellar temperature is so 75 00:04:58,675 --> 00:05:01,523 important. And, it turns out that we have a better 76 00:05:01,523 --> 00:05:04,703 thermometer. it's also less subject to distortion, 77 00:05:04,703 --> 00:05:09,271 for example, if there is a cloud of gas or dust between us and the star, we know 78 00:05:09,271 --> 00:05:13,896 that we'll preferentially scatter blue light star viewed through dust or gas 79 00:05:13,896 --> 00:05:18,117 will appear redder than it is and that might mislead us into thinking it is 80 00:05:18,117 --> 00:05:21,239 cooler than it is. In fact, if you looked at the sun at 81 00:05:21,239 --> 00:05:25,344 sunset and tried to devise it's temperature from it's color or even in 82 00:05:25,344 --> 00:05:29,738 the middle of the day, you would conclude that it's yellow rather than green. 83 00:05:29,738 --> 00:05:35,185 Now something that is not distorted by interception intervening 84 00:05:35,185 --> 00:05:38,099 media is the star's absorption line spectrum. 85 00:05:38,099 --> 00:05:43,604 So, we can look and understand something about the chemical composition of the 86 00:05:43,604 --> 00:05:47,230 star's atmosphere. This was known and there was a big 87 00:05:47,230 --> 00:05:52,152 ongoing project late 1930, twentieth centure into the 20s to classify the 88 00:05:52,152 --> 00:05:54,937 forms that stellar absorption spectra take. 89 00:05:54,937 --> 00:05:59,017 It was clear that there was a lot of information there, but isn't clear until 90 00:05:59,017 --> 00:06:03,421 the 20s exactly what it is that we are classifying when we classify stellar 91 00:06:03,421 --> 00:06:06,530 spectrum. we now understand the classification. 92 00:06:06,530 --> 00:06:10,407 Here is a sort of compilation of representative stellar 93 00:06:10,407 --> 00:06:14,220 spectrum arranged in order of what is called spectral type. 94 00:06:14,220 --> 00:06:19,259 And spectral type runs from A through B, A, F, G, K, and M. 95 00:06:19,259 --> 00:06:23,851 And, within each category there are ten subdivisions, 96 00:06:23,851 --> 00:06:29,327 so B0 is on one end and then it goes all the way up to B10, 97 00:06:29,327 --> 00:06:32,330 and A0 up to A10 and so on. and, 98 00:06:32,330 --> 00:06:35,637 if you notice there are sort of properties, 99 00:06:35,637 --> 00:06:41,369 there are spectral lines that are very prominent, say in this region between the 100 00:06:41,369 --> 00:06:46,148 Bs and the As, but almost absent in the O type stars and then disappear in the F 101 00:06:46,148 --> 00:06:48,829 stars. This for example are the spectral lines 102 00:06:48,829 --> 00:06:53,799 of hydrogen, these are [INAUDIBLE] lines of hydrogen and the interpretation that 103 00:06:53,799 --> 00:06:58,772 is understood in the 20s is that this organization, and the reason B, B comes 104 00:06:58,772 --> 00:07:03,745 before A is because there was previously another organizing principle, and this 105 00:07:03,745 --> 00:07:07,749 is, this was understood later. this organization, this organization is 106 00:07:07,749 --> 00:07:12,753 in direction of decreasing temperature. So O stars are the hottest stars and M 107 00:07:12,753 --> 00:07:17,070 stars are the coolest stars. and for example if you look at the 108 00:07:17,070 --> 00:07:23,178 hydrogen in the stellar atmosphere, then O stars are so hot that the hydrogen is 109 00:07:23,178 --> 00:07:27,244 essentially ionized and in B stars much of the hydrogen is ionized. 110 00:07:27,244 --> 00:07:31,613 An ionized hydrogen atom is just a free proton and electron, there is no 111 00:07:31,613 --> 00:07:34,222 absorption line spectrum for a free proton. 112 00:07:34,222 --> 00:07:39,258 So, hydrogen lines are almost completely absent from the spectrum of O and they're 113 00:07:39,258 --> 00:07:42,119 really weak in the spectrum of B type stars. 114 00:07:42,119 --> 00:07:48,899 in the cooler Bs and in the A type stars, hydrogen lines are very permanent because 115 00:07:48,899 --> 00:07:53,796 hydrogen is now atomic. the ambient the, the light that the star 116 00:07:53,796 --> 00:08:00,258 is emitting is at high frequencies so the and the temperature is high enough that 117 00:08:00,258 --> 00:08:04,673 these hydrogen atoms get excited to their excited state in the observed 118 00:08:04,673 --> 00:08:09,460 this language is associated to a hydrogen atom in it's first excited state the 119 00:08:09,460 --> 00:08:14,366 hydrogen atom ground state excitations of the Hydrogen atom from the ground state 120 00:08:14,366 --> 00:08:18,290 are ultraviolet and they don't appear in the visible light spectrum. 121 00:08:18,290 --> 00:08:22,735 And indeed, as we proceed in lowering temperature, once we go from A to F type 122 00:08:22,735 --> 00:08:27,179 stars, the hydrogen lines weaken and eventually disappear, because hydrogen in 123 00:08:27,179 --> 00:08:30,700 the cooler atmosphere of F type stars is in the ground state. 124 00:08:30,700 --> 00:08:34,146 And if it absorbs anything, it absorbs ultraviolet light, 125 00:08:34,146 --> 00:08:38,947 very few of the atoms are in the first excited state where they can absorb 126 00:08:38,947 --> 00:08:42,024 visible light protons, so hydrogen lines disappear. 127 00:08:42,024 --> 00:08:46,579 What starts to appear is the spectral lines over here of ionized metals, 128 00:08:46,579 --> 00:08:49,902 heavier elements. You see these forests with many, many, 129 00:08:49,902 --> 00:08:54,650 many, many lines in them. and these are characteristics of more 130 00:08:54,650 --> 00:09:00,683 complex atoms, so these are the spectral lines of ionized metals, and in cooler 131 00:09:00,683 --> 00:09:06,921 stars, yeah, then cooler Gs and the Ks we find the spectrum of neutral metals. 132 00:09:06,921 --> 00:09:11,731 So now, it's, the temperature is cool enough that heavier atoms do not become 133 00:09:11,731 --> 00:09:14,832 ionized. And in the M types star the cooler M 134 00:09:14,832 --> 00:09:19,913 types stars, we actually find these bands, these ray broadened bands of 135 00:09:19,913 --> 00:09:22,847 absorption. This corresponds to the existence of 136 00:09:22,847 --> 00:09:28,226 molecules with eternal degrees of freedom and so they can absorb light at various 137 00:09:28,226 --> 00:09:31,466 wavelengths. And so, this progression is a progression 138 00:09:31,466 --> 00:09:36,233 in temperature, and once you understand that, we know that we can use this as a 139 00:09:36,233 --> 00:09:39,901 precise thermometer, here is the current list of spectral 140 00:09:39,901 --> 00:09:43,018 types. they are listed according to the color, 141 00:09:43,018 --> 00:09:46,991 the color the perception of stars is very subjective. 142 00:09:46,991 --> 00:09:51,607 Here are the temperatures. Note that the temperatures at stellar 143 00:09:51,607 --> 00:09:57,014 surfaces range from as hot as 50 or 60,000 Kelvin in hot O type stars to 2000 144 00:09:57,014 --> 00:10:00,642 or 3000 Kelvin on the very cool, dark red M type stars. 145 00:10:00,642 --> 00:10:06,391 And, these are the sort of description of the spectral features that characterize 146 00:10:06,391 --> 00:10:09,402 them. This is the prevalence and I should be 147 00:10:09,402 --> 00:10:15,131 careful, this is our understanding of the prevalence of this type of star among all 148 00:10:15,131 --> 00:10:18,429 stars. I'll explain why this needs some 149 00:10:18,429 --> 00:10:23,095 qualification. And note that it is precisely increasing 150 00:10:23,095 --> 00:10:28,565 as you go to cooler stars. So, the coolest M type stars form three 151 00:10:28,565 --> 00:10:34,920 quarters of all known stars, whereas the O type stars form a tiny, tiny fraction 152 00:10:34,920 --> 00:10:39,068 and the cooler the star is the more likely it is to appear. 153 00:10:39,068 --> 00:10:43,015 And here's some examples of stars of each spectral type. 154 00:10:43,015 --> 00:10:49,639 And so dark red Betelgeuse and orange are Arcturus and Aldebaran are examples that 155 00:10:49,639 --> 00:10:52,784 you are familiar with. The sun is a G type star. 156 00:10:52,784 --> 00:10:57,505 In fact, G2 within the internal classification of G type stars and Sirius 157 00:10:57,505 --> 00:11:02,104 and Vega are A type stars and so on. The bright stars of Orion's Belt are O 158 00:11:02,104 --> 00:11:05,538 type stars. some of these stars are listed here in 159 00:11:05,538 --> 00:11:10,320 not in black type and in the next clip, we'll understand what we now have is a 160 00:11:10,320 --> 00:11:14,613 collection of data about stars. We now have a huge population of stars 161 00:11:14,613 --> 00:11:18,660 about which we know their luminosity, their radius, their temperature, 162 00:11:18,660 --> 00:11:22,730 and we can start trying to arrange this data as a sociologist would to do 163 00:11:22,730 --> 00:11:25,310 population study and try to draw conclusions. 164 00:11:25,310 --> 00:11:28,012 We'll figure out how to organize it in the next clip.