1 00:00:01,180 --> 00:00:04,310 We now know how to characterize our population of stars. 2 00:00:04,310 --> 00:00:09,007 We use their luminosity and we use their spectra to determine what type of stars 3 00:00:09,007 --> 00:00:11,858 they are. We give their spectral type that gives us 4 00:00:11,858 --> 00:00:16,219 our, their surface temperature, and we can now try to find correlations between 5 00:00:16,219 --> 00:00:19,910 luminosity and temperature and so on, and do population studies. 6 00:00:19,910 --> 00:00:23,930 what do the statistics tell us? Well first of all we notice that 7 00:00:23,930 --> 00:00:28,550 luminosity varies over huge ranges. We find stars with luminosities less than 8 00:00:28,550 --> 00:00:33,470 1,000 times less than the sun and stars with luminosities more than 100,000 times 9 00:00:33,470 --> 00:00:36,830 more than the sun. At the same time the temperatures are 10 00:00:36,830 --> 00:00:41,150 ranging from 1000 or so Kelvin all the way to 50,000 Kelvin and more. 11 00:00:41,150 --> 00:00:45,830 And stellar radius, which we can compute if we know luminosity and temperature 12 00:00:45,830 --> 00:00:49,829 varies considerably less. how to organize the data was the subject 13 00:00:49,829 --> 00:00:53,179 of much speculation. And the successful presentation that we 14 00:00:53,179 --> 00:00:57,434 used to this day, and will accompany us for much of this class, is in the form of 15 00:00:57,434 --> 00:00:59,827 something called Herzsprung-Russell diagram. 16 00:00:59,827 --> 00:01:02,592 And was invented by Hertzsprung and Russell in 1910. 17 00:01:02,592 --> 00:01:06,685 And here is a Herzsprung-Russell diagram. It's a scatter plot of the stars. 18 00:01:06,685 --> 00:01:11,459 Each dot here represents a star. And in some sample, this is some part of 19 00:01:11,459 --> 00:01:14,396 the [INAUDIBLE] sample, and what do we have here? 20 00:01:14,396 --> 00:01:18,129 Well, the horizontal access is temperature with by convention, 21 00:01:18,129 --> 00:01:22,841 temperature increasing to the left. So the hottest O type stars are over here 22 00:01:22,841 --> 00:01:26,146 on the left. the temperature scale is at the top of 23 00:01:26,146 --> 00:01:29,389 the diagram. And the coolest M type stars are here on 24 00:01:29,389 --> 00:01:32,511 the right. The vertical axis is luminosity, so we're 25 00:01:32,511 --> 00:01:35,693 plotting, if you will, luminosity against temperature. 26 00:01:35,693 --> 00:01:41,230 the most luminous stars with luminosities of over 100,000 solar luminosities are at 27 00:01:41,230 --> 00:01:43,909 the top, the dimmer stars are at the bottom. 28 00:01:43,909 --> 00:01:48,895 And notice that the luminosity scale is logarithmic so that the sun is about in 29 00:01:48,895 --> 00:01:53,444 the center of this diagram. one solar lumnosity over here and above 30 00:01:53,444 --> 00:01:57,370 the next tag above it corresponds to ten solar luminosities. 31 00:01:57,370 --> 00:02:01,047 Similar distance above is 100 solar lumonisities and so on. 32 00:02:01,047 --> 00:02:05,222 And so what do we discern? Well we certainly discern that stars are 33 00:02:05,222 --> 00:02:08,650 not distributed randomly in the spot. We have a pattern. 34 00:02:08,650 --> 00:02:11,109 Good, that's the beginning of understanding. 35 00:02:11,109 --> 00:02:13,854 Now we try to understand it. What is the pattern? 36 00:02:13,854 --> 00:02:18,487 Well about 85% of all the stars lay along this one diagonal strip called the main 37 00:02:18,487 --> 00:02:21,232 sequence because that's where all the stars are. 38 00:02:21,232 --> 00:02:25,750 And this runs from cool, dense stars over here in the lower right, to hot, bright 39 00:02:25,750 --> 00:02:28,667 stars or hot very luminous stars in the upper left. 40 00:02:28,667 --> 00:02:33,357 And that means that if a star's a main sequence star, you know it's temperature 41 00:02:33,357 --> 00:02:37,169 you can predict its luminosity. We see a collection of stars scattered 42 00:02:37,169 --> 00:02:40,463 above the main sequence. What does it mean to be above the main 43 00:02:40,463 --> 00:02:42,502 sequence? That means that if you pick a temperature 44 00:02:42,502 --> 00:02:47,084 by in other words a vertical line, these stars lie above the main sequence, they 45 00:02:47,084 --> 00:02:50,726 are more luminous than our main sequence star with a same temperature. 46 00:02:50,726 --> 00:02:54,992 How do you get more luminous maintaining the same temperature that means they are 47 00:02:54,992 --> 00:02:59,155 radius, their radiating area is bigger. These stars are bigger than main sequence 48 00:02:59,155 --> 00:03:03,421 stars suitably they are called giants, we have this collected population of giants 49 00:03:03,421 --> 00:03:07,428 and still higher above the main sequence are various super giants and bright 50 00:03:07,428 --> 00:03:10,810 giants and even larger stars especially at the high temperatures. 51 00:03:10,810 --> 00:03:14,381 We see the very bright hyper giants and bright giants. 52 00:03:14,381 --> 00:03:18,926 And then there is the, below the main sequence, stars smaller than main 53 00:03:18,926 --> 00:03:22,261 sequence star. It just don't seem to be there except for 54 00:03:22,261 --> 00:03:26,365 this one arc towards the bottom. These are stars that, because they're way 55 00:03:26,365 --> 00:03:30,863 lower than the main sequence, are less luminous even though their temperature is 56 00:03:30,863 --> 00:03:33,562 quite high. And so suitably they're called white 57 00:03:33,562 --> 00:03:35,811 dwarfs. These are very small hot objects. 58 00:03:35,811 --> 00:03:39,915 We'll discuss where they come from later but other than that, the plot is 59 00:03:39,915 --> 00:03:43,739 relatively empty. we should we've talked about the way that 60 00:03:43,739 --> 00:03:47,168 radius plays into this. We can compute radius, of course, given 61 00:03:47,168 --> 00:03:51,779 temperature and luminosity, let's see how the radii of stars end up plotting on 62 00:03:51,779 --> 00:03:54,967 this diagram. This animation is designed to allow you 63 00:03:54,967 --> 00:03:58,101 to explore the HR diagram. Again, we have luminosity, 64 00:03:58,101 --> 00:04:02,648 logarithmically on the left where you can sort of pick a luminosity and a 65 00:04:02,648 --> 00:04:06,764 temperature and move your little cursor along the main sequence. 66 00:04:06,764 --> 00:04:11,495 Note that fixed, changing the temperature at fixed luminosity is a horizontal 67 00:04:11,495 --> 00:04:16,657 motion, changing the luminosity at fixed temperature is a vertical motion and the 68 00:04:16,657 --> 00:04:21,394 red line gives us the main sequence. And what we see is that, for the most 69 00:04:21,394 --> 00:04:26,442 part, stars on the main sequence have radii between one solar radius, this is 70 00:04:26,442 --> 00:04:29,963 where approximately the sun lies, and ten solar radii. 71 00:04:29,963 --> 00:04:34,147 So temperatures of 100,000 illuminosities, 100,000 times the 72 00:04:34,147 --> 00:04:39,660 luminosity of the sun, are achieved with a modest factor of ten increase, or less 73 00:04:39,660 --> 00:04:42,650 increase, in radius. And the, the, the, 74 00:04:42,650 --> 00:04:46,965 main sequence sort of follows a slow increase in radius with luminosity 75 00:04:46,965 --> 00:04:51,700 except, a little bit below the sun's radius. It suddenly dips below the stars 76 00:04:51,700 --> 00:04:56,615 over here on the lower right of the main sequence are cooled and smaller than you 77 00:04:56,615 --> 00:05:01,410 would get by just extending the main sequence they go by the name red dwarfs, 78 00:05:01,410 --> 00:05:05,846 and we see that over here where the giants were are stars with radii of a 79 00:05:05,846 --> 00:05:10,701 hundred and even a thousand solar radii way over here in the upper right hand 80 00:05:10,701 --> 00:05:11,900 side of the plot. So. 81 00:05:11,900 --> 00:05:16,789 This is a useful demonstration. You can plot here some of our nearest 82 00:05:16,789 --> 00:05:20,113 stars to us. We note that most of the nearest stars 83 00:05:20,113 --> 00:05:24,741 are, in fact the sun-like or dimmer. On the other hand, if we plot the 84 00:05:24,741 --> 00:05:29,826 brightest stars, we see that most of the stars we actually see are going to be 85 00:05:29,826 --> 00:05:31,195 giants. This is clear. 86 00:05:31,195 --> 00:05:36,280 We can see giants farther out, where there is more of an opportunity for there 87 00:05:36,280 --> 00:05:39,017 to be more of them. And we'll come back. 88 00:05:39,017 --> 00:05:44,428 We'll be talking about HR diagrams a lot. For now, we have one more investigation 89 00:05:44,428 --> 00:05:47,385 to make. So what we saw is that if you know that a 90 00:05:47,385 --> 00:05:52,024 star, if a star happens to be on the main sequence all you need to do is measure 91 00:05:52,024 --> 00:05:56,142 its spectrum and you can tell its luminosity because being on the main 92 00:05:56,142 --> 00:05:59,795 sequence implies a relation between temperature and luminosity. 93 00:05:59,795 --> 00:06:02,289 But not all stars are on the main sequence. 94 00:06:02,289 --> 00:06:05,710 how do we tell? Is there a way just by looking at a star 95 00:06:05,710 --> 00:06:09,654 to tell if it's a hyper giant, a white dwarf, or a main sequence star? 96 00:06:09,654 --> 00:06:14,184 this was a very interesting A, a question and it was eventually 97 00:06:14,184 --> 00:06:18,858 understood in the 40s by Morgan, Keenan and Kellerman and the result of their 98 00:06:18,858 --> 00:06:23,593 investigations was the following Smaller stars at a given temperature tend 99 00:06:23,593 --> 00:06:26,385 to have denser higher pressure atmospheres. 100 00:06:26,385 --> 00:06:30,573 It's in the atmosphere that we're observing the line, absorption line 101 00:06:30,573 --> 00:06:33,305 spectrum. A denser, higher-pressure atmosphere 102 00:06:33,305 --> 00:06:37,736 exhibits broader spectral lines. As you condense matter more and more the 103 00:06:37,736 --> 00:06:41,621 spectral lines broaden. Of course if you condense it all the way 104 00:06:41,621 --> 00:06:46,246 to a solid you get a black body spectrum. That's sort of the extreme case. 105 00:06:46,246 --> 00:06:51,788 And so you find that you can divide stars into sort of classes by their luminosity 106 00:06:51,788 --> 00:06:56,262 at a given temperature. and these classes range from zero for 107 00:06:56,262 --> 00:07:01,404 hypergiants, way over here in at the top through type one for supergiants, 108 00:07:01,404 --> 00:07:05,477 type two for the bright giants, three are the giants, etcetera. 109 00:07:05,477 --> 00:07:10,700 Five importantly, type V is luminosity class V is the main sequence and down to 110 00:07:10,700 --> 00:07:16,031 luminosity class seven where the white dwarfs lie way below the main sequence. 111 00:07:16,031 --> 00:07:21,625 In this language, we can now say that our sun which had temperature that made it a 112 00:07:21,625 --> 00:07:25,195 G2 star somewhat in the middle of the type G 113 00:07:25,195 --> 00:07:29,818 temperature range since it is a main sequence star is a G25 star. 114 00:07:29,818 --> 00:07:33,730 So that's the spectral class, a combination of three 115 00:07:33,730 --> 00:07:38,935 designations one for spectral type one for the sub type within the type and one 116 00:07:38,935 --> 00:07:43,952 with luminosity class gives you a three parameter two dimensional position of a 117 00:07:43,952 --> 00:07:46,712 star. Roughly the first two letters tell you 118 00:07:46,712 --> 00:07:51,729 where it is horizontally along the the, HR diagram and the last one tells you 119 00:07:51,729 --> 00:07:55,053 where it is. In the vertical direction you can locate 120 00:07:55,053 --> 00:07:59,004 a star based on that. So now that we know how to distinguish 121 00:07:59,004 --> 00:08:03,231 just by looking at the spectrum the position of the star in a joint 122 00:08:03,231 --> 00:08:07,351 diagram, we now have a great idea. Something called spectroscopic parallax. 123 00:08:07,351 --> 00:08:09,947 I warn you it has nothing to do with parallax. 124 00:08:09,947 --> 00:08:13,672 What is spectroscopic parallax? It's a way of determining a star's 125 00:08:13,672 --> 00:08:16,001 distance. Just from looking at the spectrum. 126 00:08:16,001 --> 00:08:20,073 If a star is too far to make parallax measurements can you still give me an 127 00:08:20,073 --> 00:08:23,394 estimate of its distance? The answer is yes, the reason is if I 128 00:08:23,394 --> 00:08:27,501 look at the spectrum and I recognize the presence of a particular set of 129 00:08:27,501 --> 00:08:30,196 absorption lines that gives me a spectral type. 130 00:08:30,196 --> 00:08:33,234 That gives me an estimate of the surface temperature. 131 00:08:33,234 --> 00:08:37,592 Moreover, if I can look at the breadth of those lines, I can figure out which 132 00:08:37,592 --> 00:08:41,261 luminosity class the star belongs to. Is it a main sequence star? 133 00:08:41,261 --> 00:08:44,931 Or is it a hypergiant? And once I do that I can go back to my HR 134 00:08:44,931 --> 00:08:49,345 diagram and pick out the intersection of the corresponding curve with the 135 00:08:49,345 --> 00:08:52,269 corresponding vertical line for the temperature. 136 00:08:52,269 --> 00:08:56,118 And I can obtain a luminosity. So now I can read a star's luminosity 137 00:08:56,118 --> 00:08:58,640 with some accuracy right off of its spectrum. 138 00:08:58,640 --> 00:09:03,078 Now if I know the luminosity I can measure the brightness and of course use 139 00:09:03,078 --> 00:09:07,601 our expression for luminosity bright, brightness and distance to figure out the 140 00:09:07,601 --> 00:09:10,259 distance. So, I can measure a distance to a star 141 00:09:10,259 --> 00:09:13,369 with some accuracy, even if it was too far for parallex. 142 00:09:13,369 --> 00:09:17,723 Note that this is another one of those ladders on the cosmic distanct ladder. 143 00:09:17,723 --> 00:09:22,191 We know the calibration of the HR diagram because we've measured the actual 144 00:09:22,191 --> 00:09:25,019 luminosity of stars to which we knew the distance. 145 00:09:25,019 --> 00:09:29,599 Now we used that to extend the distances to things that are too far for parallex 146 00:09:29,599 --> 00:09:32,880 measurements that will be very useful for us, in the 147 00:09:32,880 --> 00:09:37,664 sequel when we need to know the distances to things that are too far for parallax. 148 00:09:37,664 --> 00:09:40,928 There are many other methods, all calibrated from parallax. 149 00:09:40,928 --> 00:09:45,037 But this is a good example of one and I think we need a little more of a, 150 00:09:45,037 --> 00:09:48,301 calculational example. Let's try to understand the star 151 00:09:48,301 --> 00:09:51,115 Alphecca. This is Alpha Coronae Borealis. 152 00:09:51,115 --> 00:09:55,852 And it's a whitish star. It's not the brightest star in the sky 153 00:09:55,852 --> 00:10:00,045 but it's a bright one. In fact, we can measure its la, photo 154 00:10:00,045 --> 00:10:05,740 measurement tells us that the brightness of, Alphecca is 2.6 times 10 to the -12 155 00:10:05,740 --> 00:10:10,184 times the solar luminosity. we look at its spectral lines, and we can 156 00:10:10,184 --> 00:10:13,626 measure its temperature. Its temperature is 9700 kelvin. 157 00:10:13,626 --> 00:10:17,444 It's star of type A. It's hotter than the sun, a zero, in 158 00:10:17,444 --> 00:10:20,135 fact. And Alphecca is a main sequence star as 159 00:10:20,135 --> 00:10:23,140 determined by the breadth of its spectral lines. 160 00:10:23,140 --> 00:10:27,258 So, we go over to our HR diagram we look at the main sequenc. 161 00:10:27,258 --> 00:10:32,595 We look at the luminosity of an A0 type this is the hottest of the type A stars 162 00:10:32,595 --> 00:10:35,892 and you can estimate a luminosity of 74 solar luminosities. 163 00:10:35,892 --> 00:10:40,196 Alphecca is 74 times as luminous as the sun, and from this if I want, I can 164 00:10:40,196 --> 00:10:44,163 figure out a distance because I have the brightness and the luminosity. 165 00:10:44,163 --> 00:10:48,746 I can also figure out Alphecca's radius. Remember we had a relation between radii, 166 00:10:48,746 --> 00:10:52,211 luminosity and temperature. This is the scaling relation, and I 167 00:10:52,211 --> 00:10:55,956 predict a radius of about three solar luminosities for Alphecca. 168 00:10:55,956 --> 00:11:00,353 Remember we said that this main spectra, the main sequence goes from one solar 169 00:11:00,353 --> 00:11:05,145 radius at the sun all the way up to ten. Alphecca is a part of the way up there. 170 00:11:05,145 --> 00:11:10,061 Three solar radii is pretty reasonable and we can as I said predict a distance 171 00:11:10,061 --> 00:11:15,166 to Alphecca based on using the luminosity and the brightness, brightness is 172 00:11:15,166 --> 00:11:20,518 measured luminosity is predicted from HR. I plug in 74 solar luminosities here I 173 00:11:20,518 --> 00:11:25,723 plug in ten to the minus twelve or whatever for Alphecca's brightness. 174 00:11:25,723 --> 00:11:31,565 And I find five and a half million AU. I can convert that to parsec with our 175 00:11:31,565 --> 00:11:36,765 206, 265 astronomical unit per parsec conversion, and I predict Alphecca's 176 00:11:36,765 --> 00:11:41,610 distance to be 25.7 parsecs. Now with that range, we do have parallax 177 00:11:41,610 --> 00:11:44,816 measurements. And so I can look up the Alphecca's 178 00:11:44,816 --> 00:11:50,016 database, Alphecca's database read off the parallax angle of of Alphecca. 179 00:11:50,016 --> 00:11:55,427 And, of course I remember that the distance in units of parsec is just one 180 00:11:55,427 --> 00:12:01,020 arc second divided by the parallax angle plugging that in I know that we have 181 00:12:01,020 --> 00:12:05,440 measured the actual distance to Alphecca of 22.9 Parsecs. 182 00:12:05,440 --> 00:12:07,937 We have an error of an on the order of 10%.. 183 00:12:07,937 --> 00:12:12,408 This is typical of spectroscopic parallax system its our under there is some 184 00:12:12,408 --> 00:12:17,054 breadth to the main sequence and we'll talk about where that breadth comes from, 185 00:12:17,054 --> 00:12:21,119 stars are not exactly on the line. So the luminosity is not absolutely 186 00:12:21,119 --> 00:12:25,765 precisely determined by spectro-class that being able to measure distances just 187 00:12:25,765 --> 00:12:29,540 from looking at the spectrum of the start within 10% is not that.