1 00:00:00,000 --> 00:00:04,812 . We now have our designated population of 2 00:00:04,812 --> 00:00:07,085 stars. We have a collection of them. 3 00:00:07,085 --> 00:00:11,631 We're going to try to understand whether the way we understood the sun with 4 00:00:11,631 --> 00:00:14,503 modeling, we can understand how these stars work. 5 00:00:14,503 --> 00:00:19,288 We're not quite ready to start with the modeling because if you tell us stellar 6 00:00:19,288 --> 00:00:22,100 modeler, I want you to model a ball of hydrogen. 7 00:00:22,100 --> 00:00:25,510 I know its surface temperature and I know its luminosity. 8 00:00:25,510 --> 00:00:28,538 He's going to ask you well, yeah, how much hydrogen is there? 9 00:00:28,538 --> 00:00:32,379 We need a way to find the mass of a star. So how do you weight the star? 10 00:00:32,379 --> 00:00:35,949 All we can do is look at it. How do you measure the mass of a star 11 00:00:35,949 --> 00:00:39,140 just by looking at it? You recall that we found the mass of 12 00:00:39,140 --> 00:00:43,359 Saturn just by looking not at it, but at a moon orbiting it and using Newton's 13 00:00:43,359 --> 00:00:43,900 laws. Well, 14 00:00:43,900 --> 00:00:47,865 wouldn't it be convenient if we found stars with things orbiting them. 15 00:00:47,865 --> 00:00:50,471 Not moons, but something we could actually see. 16 00:00:50,471 --> 00:00:54,833 So that we could use the same kind of calculation through Newton's law to 17 00:00:54,833 --> 00:00:58,628 measure the mass of stars. Well luckily for us about a fifth of all 18 00:00:58,628 --> 00:01:02,424 the stars in the sky, somewhere around that, are not single stars. 19 00:01:02,424 --> 00:01:05,540 They are gravitationally bound to one or more partners. 20 00:01:05,540 --> 00:01:10,008 And so, if we can see the partners, we can measure orbital parameters, and try 21 00:01:10,008 --> 00:01:14,888 to make an estimate of the mass that way. these, if you recall, the picture on the 22 00:01:14,888 --> 00:01:19,650 right, is our friend Albireo, the head of Cygnus the Swan, back from lecture one. 23 00:01:19,650 --> 00:01:23,883 And you remember that we talked about the fact that these are two stars. 24 00:01:23,883 --> 00:01:27,481 this is what astronomers, amateur astronomers like to call a double star. 25 00:01:27,481 --> 00:01:31,378 but not all double stars are binaries. A double star is just two stars that are 26 00:01:31,378 --> 00:01:34,561 very near each other in the sky. There are two ways this can happen. 27 00:01:34,561 --> 00:01:38,030 The two stars could actually be near each other in the world or they could happen 28 00:01:38,030 --> 00:01:41,927 to lie in the same direction in the Earth but it's vastly different distances, and 29 00:01:41,927 --> 00:01:45,158 be nowhere near each other. As we saw for example, for the members of 30 00:01:45,158 --> 00:01:48,010 the big dipper, which are nowhere near each other in the sky. 31 00:01:48,010 --> 00:01:52,935 In that case, by the way, we call a false double star or a double star that is not 32 00:01:52,935 --> 00:01:57,150 a binary is an optical double. A visual binary like Albireo is a binary 33 00:01:57,150 --> 00:02:01,280 where the two members of the pair can actually be seen and separated. 34 00:02:01,280 --> 00:02:04,051 So is Albireo a visual binary or an optical double? 35 00:02:04,051 --> 00:02:06,767 The answer is we're not quite sure. How do we tell? 36 00:02:06,767 --> 00:02:09,593 Well we can measure parallax angles to these stars. 37 00:02:09,593 --> 00:02:12,092 And they are quite near each other in the sky. 38 00:02:12,092 --> 00:02:14,809 Though it's not quite certain that they are bound. 39 00:02:14,809 --> 00:02:19,264 For that we measure their motions and try to see whether their total energy is 40 00:02:19,264 --> 00:02:22,687 negative or positive. it's not clear whether these stars are 41 00:02:22,687 --> 00:02:25,241 bound or not. But they're close to that so that, 42 00:02:25,241 --> 00:02:29,178 they're at about the same distance. And, with that in mind, let's stop for a 43 00:02:29,178 --> 00:02:32,816 minute, and appreciate what we've learned, just looking at this picture. 44 00:02:32,816 --> 00:02:36,973 What can we say that we couldn't say a few weeks ago, when we started out, and 45 00:02:36,973 --> 00:02:40,039 looked at Albireo? Well, we see two stars, we clearly see 46 00:02:40,039 --> 00:02:43,884 that one is orange and one is blue. So, we realize black body spectra tells 47 00:02:43,884 --> 00:02:46,639 us that the blue star is hotter than the orange star. 48 00:02:46,639 --> 00:02:49,393 We also see that one appears brighter than the other. 49 00:02:49,393 --> 00:02:53,186 Since I told you their parallex angles are about the same, that tells you that 50 00:02:53,186 --> 00:02:56,824 they're about the same distance. The one that appears brighter is more 51 00:02:56,824 --> 00:03:00,150 luminous, so the orange star is more luminous than the blue star. 52 00:03:00,150 --> 00:03:04,007 That tells us a third thing. These cannot both be main sequence stars. 53 00:03:04,007 --> 00:03:08,479 Our long domain sequence, the harder the star is the more luminous since here we 54 00:03:08,479 --> 00:03:12,057 have a cooler orange star more luminous than a harder blue star. 55 00:03:12,057 --> 00:03:16,361 We have no doubt that one or more of these stars is not a main sequence star 56 00:03:16,361 --> 00:03:21,113 just looking at the picture combining it with things we have learned systematized 57 00:03:21,113 --> 00:03:25,361 we ca say some things about this. we'll see later that we have many other 58 00:03:25,361 --> 00:03:28,156 techniques. Binary stars are so important that you've 59 00:03:28,156 --> 00:03:30,840 develop many techniques for discovering them 60 00:03:30,840 --> 00:03:33,750 binaries discovered through non visual techniques. 61 00:03:33,750 --> 00:03:36,111 Where we can't resolve, even in a telescope. 62 00:03:36,111 --> 00:03:40,174 The two members are going to be non visual binaries and we'll talk about how 63 00:03:40,174 --> 00:03:43,139 to find them. But for now let's talk about a famous 64 00:03:43,139 --> 00:03:45,720 visual binary to see what we can learn from it. 65 00:03:45,720 --> 00:03:48,410 the star in question is called Alpha Centauri. 66 00:03:48,410 --> 00:03:52,363 Alpha Centauri is famous because it's one of the nearest stars to Earth. 67 00:03:52,363 --> 00:03:55,987 It's only, about a parsec. A little more than a parsec away from 68 00:03:55,987 --> 00:03:58,185 Earth. it has, in fact two members. 69 00:03:58,185 --> 00:04:01,904 It's a binary star. The two members are Alpha Centauri A and 70 00:04:01,904 --> 00:04:05,437 B, A being the brighter, the primary, B being the secondary. 71 00:04:05,437 --> 00:04:08,784 And in fact we think that the system is a triple star. 72 00:04:08,784 --> 00:04:13,123 The third member would be Proxima Centauri, the actual closest star to 73 00:04:13,123 --> 00:04:17,152 Earth very famous. we're not quite sure if Proxima Centauri 74 00:04:17,152 --> 00:04:21,243 is bound to these two or not. If it is it's a very large, very slow 75 00:04:21,243 --> 00:04:23,970 orbit. Let's ignore Proxima Centauri for now, 76 00:04:23,970 --> 00:04:27,100 focus on Alpha Centauri. you see here a plot. 77 00:04:27,100 --> 00:04:31,103 We can see both stars. So what we've done here is we've plotted, 78 00:04:31,103 --> 00:04:34,279 we've fixed the brighter A component at one point. 79 00:04:34,279 --> 00:04:38,282 And then plotted where in the sky the B component would appear. 80 00:04:38,282 --> 00:04:43,682 These are right ascension and declination axis and the scale or the angles are 81 00:04:43,682 --> 00:04:47,240 marked in arc seconds since we know the stars are about. 82 00:04:47,240 --> 00:04:54,036 Both, are about, 1.3 parsecs from Earth. Well, at a distance of a parsec, an 83 00:04:54,036 --> 00:04:58,362 angular separation of one arc second corresponds to an astronomical unit. 84 00:04:58,362 --> 00:05:02,511 So the ticks on the scale, the arcsec ticks on the scale, correspond to 85 00:05:02,511 --> 00:05:05,000 distances of about 1.3 astronomical units. 86 00:05:05,000 --> 00:05:09,628 That means that these stars are orbiting within planetary distances they're 87 00:05:09,628 --> 00:05:14,401 orbiting as close to each other, as our planets orbit the sun. This is a very 88 00:05:14,401 --> 00:05:18,106 close binary system. and because we know the small angle 89 00:05:18,106 --> 00:05:23,130 formula we can translate angles to distances, that's glorious in fact this 90 00:05:23,130 --> 00:05:27,715 is not the actual orbit. the actual orbit, the apparent orbit is tilted 91 00:05:27,715 --> 00:05:32,802 elipse here, the actual orbit if you flatten it out so that you see it face on 92 00:05:32,802 --> 00:05:36,581 would be this more broader, that's here, how do we know 93 00:05:36,581 --> 00:05:39,836 that? Well we can extract the radial velocity 94 00:05:39,836 --> 00:05:44,852 of B Centauri, B Alpha Centauri, by measuring doppler shifts, and that tells 95 00:05:44,852 --> 00:05:48,310 us how fast it's moving towards us, or away from us. 96 00:05:48,310 --> 00:05:52,988 Combine that with what we see in the tangent plane and we get a full 97 00:05:52,988 --> 00:05:57,463 description of the motion. Just as we did for other proper motions. 98 00:05:57,463 --> 00:06:02,480 And this is, in fact the ellipse seen head-on and we can measure the 99 00:06:02,480 --> 00:06:06,937 Eccentricity of this ellipse is about 5.. It's a rather eccentric motion. 100 00:06:06,937 --> 00:06:10,246 The semi-major axis is 23 astronomical units approximately. 101 00:06:10,246 --> 00:06:14,108 That's about the radius of Saturn at their closest approach these stars are 102 00:06:14,108 --> 00:06:17,970 only eleven astronomical units apart and their period is about eighty years. 103 00:06:17,970 --> 00:06:20,970 we can basically, you know we can plot an ellipse. 104 00:06:20,970 --> 00:06:23,510 We measure the speed. We know exactly how 105 00:06:23,510 --> 00:06:28,169 fast these stars are going to move and so we have an 80-year period at a semi-major 106 00:06:28,169 --> 00:06:31,996 axis of 23 astronomical units. Now, before we go how to take advantage 107 00:06:31,996 --> 00:06:36,377 of this, I should tell you I didn't pick this system, just because it is nearest 108 00:06:36,377 --> 00:06:40,870 to, to earth, it is also, well of course as such it has been of interest to many 109 00:06:40,870 --> 00:06:45,307 science fiction writers but it is also recently been of interests to scientists 110 00:06:45,307 --> 00:06:49,356 because in October 2012 an earth size planet was detected orbiting Alpha 111 00:06:49,356 --> 00:06:53,960 Centauri B remember we said that it was strange to find stable orbits in binary 112 00:06:53,960 --> 00:06:56,511 systems. Even in this very close binary system 113 00:06:56,511 --> 00:07:00,519 there is a stable orbit. Note that the planet orbits very, very 114 00:07:00,519 --> 00:07:05,444 near to its star at a distance ten times closer than Mercury to the sun. 115 00:07:05,444 --> 00:07:08,658 it's period is only three and a half days, or so. 116 00:07:08,658 --> 00:07:13,562 This is a very close in much too hot for liquid water to exist, but the 117 00:07:13,562 --> 00:07:17,858 discovery of an Earth sized planet, in a binary system is exciting nonetheless. 118 00:07:17,858 --> 00:07:22,260 All the imaginations of what it would be like to live on a planet with two suns 119 00:07:22,260 --> 00:07:24,710 get fired up and so on. So, 120 00:07:24,710 --> 00:07:27,965 so much for Alpha Centauri. Why do we like binary stars? 121 00:07:27,965 --> 00:07:32,523 We like binary stars, because when we have a visual binary we can measure the 122 00:07:32,523 --> 00:07:35,778 positions. we can actually predict just as we did. 123 00:07:35,778 --> 00:07:38,560 A projection of the orbit on the, tangent plane. 124 00:07:38,560 --> 00:07:43,000 Remember the tangent plane is the plane, perpendicular to our line of sight. 125 00:07:43,000 --> 00:07:47,882 If we can augment this with radial measurements of the radial velocity from 126 00:07:47,882 --> 00:07:52,146 doppler shift, we can figure out both the motion in the tangent plane. 127 00:07:52,146 --> 00:07:54,865 Remember, if this is us, and here is the star. 128 00:07:54,865 --> 00:07:58,264 This is the tangent plane. This is the radial direction. 129 00:07:58,264 --> 00:08:03,789 Doppler shifts give us the measurement of in this direction the astrometry where we 130 00:08:03,789 --> 00:08:08,288 take the distance and the angle and convert it to distance over here with the 131 00:08:08,288 --> 00:08:12,384 small angle formula, give us the projection of the orbit on the tangent 132 00:08:12,384 --> 00:08:15,269 plane. We can actually produce the orbit of the 133 00:08:15,269 --> 00:08:20,032 planet and in particular we can measure the orbit of the stars, and we can then 134 00:08:20,032 --> 00:08:22,725 measure semi major axis and certainly periods. 135 00:08:22,725 --> 00:08:26,822 And if we know semi major axis and period, we can use Kepler's formula, 136 00:08:26,822 --> 00:08:31,212 scale it to the motion say, of the motion of the Earth around the sun. 137 00:08:31,212 --> 00:08:35,895 And find that the total mass of the star divided by the total mass of the Earth 138 00:08:35,895 --> 00:08:40,636 sun system, which to our approximation is the mass of the sun is the ratio of the 139 00:08:40,636 --> 00:08:44,031 radii cubed divided by the ratio of the period squared. 140 00:08:44,031 --> 00:08:48,889 So we have if since we measured the radius and we measured the period, we can 141 00:08:48,889 --> 00:08:53,321 find the total mass of the system. We can do better than that because we 142 00:08:53,321 --> 00:08:57,345 plot the motion of both partners in the sky, relative to the fixed stars far 143 00:08:57,345 --> 00:08:59,940 behind them. We actually find our one and our two 144 00:08:59,940 --> 00:09:02,588 separately. Remember, the two stars orbit each in a 145 00:09:02,588 --> 00:09:06,454 circle, or an ellipse in this case of semi major axis or radius in our 146 00:09:06,454 --> 00:09:09,949 approximation. R1 and R2 and since they're both orbiting 147 00:09:09,949 --> 00:09:13,550 their center of mass these radial satisfy M1, R1 is M1, R2. 148 00:09:13,550 --> 00:09:15,880 That's the distance from the center of mass. 149 00:09:15,880 --> 00:09:19,324 We know the ratio of the two masses, because we measured the radii. 150 00:09:19,324 --> 00:09:22,821 We know their sum, because we measured the period between these two. 151 00:09:22,821 --> 00:09:26,997 We can write an easy algebraic equation, and find the individual masses of stars. 152 00:09:26,997 --> 00:09:30,233 We have a way of weighting stars. This is why we like binaries. 153 00:09:30,233 --> 00:09:34,095 not always are binaries so close that we can distinguish both partners. 154 00:09:34,095 --> 00:09:37,175 It's worth figuring out other ways to study binary systems. 155 00:09:37,175 --> 00:09:37,958 Let's try that.