1 00:00:00,012 --> 00:00:03,517 Well let us start climbing the distance ladder. 2 00:00:03,517 --> 00:00:09,354 First, we'll talk about, methods that we can find distances to nearby stars, or 3 00:00:09,354 --> 00:00:13,458 star clusters. The Trigonometric Parallax is the most 4 00:00:13,458 --> 00:00:16,749 basic measurement of distance in astronomy. 5 00:00:16,749 --> 00:00:20,764 And, hopefully all of you are, well famililar with it. 6 00:00:20,764 --> 00:00:25,332 It is pure geometry, and there is nothing uncertain about it. 7 00:00:25,332 --> 00:00:30,532 So by measuring the annual apparent slooshing on the sky of a star, we can 8 00:00:30,532 --> 00:00:36,287 figure out how far it is, if we know the distance between earth and the sun, which 9 00:00:36,287 --> 00:00:41,377 we do know, with a great percision. So the method by itself is safe, the 10 00:00:41,377 --> 00:00:46,922 problem is that, these are very small angles, and the current state of the art 11 00:00:46,922 --> 00:00:52,648 is that we can measure distances using parallaxes To about one kiloparsec out, 12 00:00:52,648 --> 00:00:58,524 more or less, and that's well within our own galaxy, never mind external galaxies. 13 00:00:58,524 --> 00:01:01,988 The next one is so-called moving cluster method. 14 00:01:01,988 --> 00:01:06,999 This is a statistical method. Stars do come in clusters, clusters move 15 00:01:06,999 --> 00:01:11,502 relative to the solar system, and stars have internal motions. 16 00:01:11,502 --> 00:01:15,971 Within a cluster itself. Since, ostensibly, all cluster stars are 17 00:01:15,971 --> 00:01:20,984 moving roughly in the same direction. If we look from afar, we will see them 18 00:01:20,984 --> 00:01:26,292 converging toward some distant point. Which is direction which they are going. 19 00:01:26,292 --> 00:01:31,527 By measuring the spread of those angles, we can figure out, what's the angle of 20 00:01:31,527 --> 00:01:37,229 their actual velocity vector to the line of sight? We also measure proper motions 21 00:01:37,229 --> 00:01:42,574 of stars in angular seconds, per unit time on Sky, as well as their radial 22 00:01:42,574 --> 00:01:46,489 velocities. We can assume that random motions within 23 00:01:46,489 --> 00:01:51,028 the cluster are same both in radial and tangential direction. 24 00:01:51,028 --> 00:01:56,798 So by knowing what the, what the angle is between The radial and tangential 25 00:01:56,798 --> 00:02:01,163 components, we can figure out what is the parallax to the cluster. 26 00:02:01,163 --> 00:02:05,843 Note that this makes some assumptions about the internal motions of the 27 00:02:05,843 --> 00:02:09,502 cluster, and it is basically a statistical technique. 28 00:02:09,502 --> 00:02:14,086 So the more stars you have the better, but cluster's have finite number of 29 00:02:14,086 --> 00:02:16,864 stars. By measuring distances to a number of 30 00:02:16,864 --> 00:02:22,088 stars using either one of two techniques, we can calibrate the Hertzsprung-Russell 31 00:02:22,088 --> 00:02:26,760 or polar magnitude diagram for stars. Hopefully this is something you know 32 00:02:26,760 --> 00:02:30,303 about very well. It is a lot of stellar luminosity versus 33 00:02:30,303 --> 00:02:33,859 temperature. Temperature is sometimes measured through 34 00:02:33,859 --> 00:02:36,990 color. The important, thing to note here, is 35 00:02:36,990 --> 00:02:42,375 that stellar luminosities are distance dependent according to the inverse square 36 00:02:42,375 --> 00:02:45,860 law from given measurements of apparent brightness. 37 00:02:45,860 --> 00:02:49,908 Temperature, measured from spectra, or from colors, is not. 38 00:02:49,908 --> 00:02:53,956 Star will have exact same temperature no matter how hot it is. 39 00:02:53,956 --> 00:02:58,278 So, once we calibrate The main sequence of this Hipparcos's diagram. 40 00:02:58,278 --> 00:03:02,874 If we can measure stellar colors or temperatures, then we can read off their 41 00:03:02,874 --> 00:03:06,809 absolute magnitudes. From absolute and apparent magnitudes, we 42 00:03:06,809 --> 00:03:11,229 can figure out how far they are. In a given cluster you may have thousands 43 00:03:11,229 --> 00:03:16,361 of stars, and therefore you can determine the distance very precisely, the distance 44 00:03:16,361 --> 00:03:20,717 to the cluster itself. Now this works fairly well for young 45 00:03:20,717 --> 00:03:26,877 stellar clusters in the galactic disc. However, no globular cluster is as yet 46 00:03:26,877 --> 00:03:33,062 close enough to measure parallaxes to it. And so something else will have to be 47 00:03:33,062 --> 00:03:37,472 done about those. There what we do is we measure, we use 48 00:03:37,472 --> 00:03:42,527 Field stars of the same type as those that live in globular clusters, the 49 00:03:42,527 --> 00:03:46,677 population 2 stars. HR diagram measurement is a collective 50 00:03:46,677 --> 00:03:50,203 measurement. But not all stars are created equal. 51 00:03:50,203 --> 00:03:55,935 Between the temperature luminosity plane, there is a strip within which stars are 52 00:03:55,935 --> 00:03:59,622 unstable to pulsation. So called instability strip. 53 00:03:59,622 --> 00:04:04,109 On the main sequence, those will be the Cepheids, or delta Cepheid stars. 54 00:04:04,109 --> 00:04:08,906 Among the globular clusters, horizontal branch, those will be RR Lyrae stars. 55 00:04:08,906 --> 00:04:12,012 There are many different kinds of pulsating stars. 56 00:04:12,012 --> 00:04:16,407 But those are the principal ones. And indeed, physics of Cepheids and RR 57 00:04:16,407 --> 00:04:22,024 Lyrae is probably the best understood of all It turns out that there are 58 00:04:22,024 --> 00:04:28,197 correlations between observed period, which again does not depend on distance, 59 00:04:28,197 --> 00:04:31,518 and luminosities of these stars, which do. 60 00:04:31,518 --> 00:04:37,630 Those are empirical relations and they can be calibrated if you had distances to 61 00:04:37,630 --> 00:04:43,142 a number of these pulsating stars using one of the previous techniques. 62 00:04:43,142 --> 00:04:48,768 At first, people did not know that there are different kinds of pulsating stars, 63 00:04:48,768 --> 00:04:53,745 they all thought it was one kind. And the first star that Hubble figured 64 00:04:53,745 --> 00:04:59,399 out in Andromeda was Cepheid, pulsating star that produced the first distance to 65 00:04:59,399 --> 00:05:03,982 another galaxy. But people are confusing RR Lyrae which 66 00:05:03,982 --> 00:05:10,457 are much dimmer than surface with surface themselves and that confusion were 67 00:05:10,457 --> 00:05:13,342 through a an error of factor of 2 in the distance scale. 68 00:05:14,792 --> 00:05:20,081 Once Walter Baade understood that there really are two different kinds of period 69 00:05:20,081 --> 00:05:23,420 luminosity relations. That error was corrected. 70 00:05:23,420 --> 00:05:28,442 Let's talk about cepheids in more detail. Because they remain among the most 71 00:05:28,442 --> 00:05:33,364 important distance indicators altogether. They're young luminous stars. 72 00:05:33,364 --> 00:05:36,832 Therefore, they'll be found in star forming discs. 73 00:05:36,832 --> 00:05:41,837 And star forming regions, whereas Delta Ceti itself is relatively bright one 74 00:05:41,837 --> 00:05:45,784 within our own galaxy. It was Henrietta Leavitt working with 75 00:05:45,784 --> 00:05:50,764 Harold Shapley who recognized that there is a correlation between period and 76 00:05:50,764 --> 00:05:55,650 luminosity, as they were studying stars in the Magellanic Clouds, about 50 77 00:05:55,650 --> 00:05:59,381 kiloparsecs away. Since all of them were roughly the same 78 00:05:59,381 --> 00:06:02,817 distance. Apparent magnitude would correlate with 79 00:06:02,817 --> 00:06:07,737 period and then they understood that comparing that with nearby Cepheids they 80 00:06:07,737 --> 00:06:10,647 can find out how far the Magellanic Couds are. 81 00:06:10,647 --> 00:06:15,527 Surface are important because they are bright and so we can see them far away, 82 00:06:15,527 --> 00:06:19,552 we can find them in galaxies up to maybe 25 mega parsecs or so. 83 00:06:19,552 --> 00:06:25,033 So we can calibrate distances to a number of nearby galaxies using Cepheids, which 84 00:06:25,033 --> 00:06:29,552 is not easy but it's possible. And then we can use distances to those 85 00:06:29,552 --> 00:06:32,539 galaxies to calibrate some other relations. 86 00:06:32,539 --> 00:06:37,645 It isn't all perfectly safe. The position of stars must depend on 87 00:06:37,645 --> 00:06:43,972 their internal composition and opacity, and therefore metallicity. the exact 88 00:06:43,972 --> 00:06:48,702 effects of metallicity are not firmly established as here. 89 00:06:48,702 --> 00:06:52,502 Moreover, there are external problems such as extinction. 90 00:06:52,502 --> 00:06:57,254 Cepheids are found in star-forming regions and they also tend to be dusty. 91 00:06:57,254 --> 00:06:59,897 So one has to make a, a correction for it. 92 00:06:59,897 --> 00:07:04,745 In very distant galaxies, they may be blended by other stars giving us wrong 93 00:07:04,745 --> 00:07:08,211 luminosity. Cepheids remain keystones of the distant 94 00:07:08,211 --> 00:07:12,320 scale and that also applies for the measurements with the Hubble space 95 00:07:12,320 --> 00:07:16,090 telescope. Here are some examples of Cepheid period 96 00:07:16,090 --> 00:07:20,342 luminosity relations in the modulaic clouds in different filters. 97 00:07:20,342 --> 00:07:25,183 The scatter is biggest in the blue band and the smallest in the near infra red. 98 00:07:25,183 --> 00:07:29,510 However the amplitudes are biggest in blue and smallest in infra red. 99 00:07:29,510 --> 00:07:34,342 It's a good idea to observe them in different bands so that the The effects 100 00:07:34,342 --> 00:07:38,952 of extinction can be taken out. Until Hipparchus satellite flew, we did 101 00:07:38,952 --> 00:07:41,754 not have parallax calibration of Cepheids. 102 00:07:41,754 --> 00:07:46,740 Distances to Cepheids until then were based on the distances through clusters 103 00:07:46,740 --> 00:07:50,707 in which they live. And distances through those clusters were 104 00:07:50,707 --> 00:07:54,182 by in large use, determined using the cluster map. 105 00:07:54,182 --> 00:07:58,998 However, with the Hipparcos, a handful of cepheids was within reach. 106 00:07:58,998 --> 00:08:04,149 And these are the actual calibration relations for distances to cepheids. 107 00:08:04,149 --> 00:08:09,577 As you can see, they're fairly noisy. But in any case, for the first time, they 108 00:08:09,577 --> 00:08:15,192 gave us an absolute calibration of the period luminosity relations for cepheid. 109 00:08:15,192 --> 00:08:20,752 This is going to get a lot better with the Gaia satellite, which is an astronomy 110 00:08:20,752 --> 00:08:26,291 mission which will measure Cepheids to a much larger number of pulsating stars 111 00:08:26,291 --> 00:08:31,173 with a much greater precision. The other important kind of pulsating 112 00:08:31,173 --> 00:08:35,212 stars are RR Lyrae. Their also named after the prototype star 113 00:08:35,212 --> 00:08:39,267 that was first recognized. Their at a population to stars, their not 114 00:08:39,267 --> 00:08:43,477 on the main sequence, but on the horizontal branch, which is the helium 115 00:08:43,477 --> 00:08:48,077 burning may sequence, and their found in old stellar populations, such as the 116 00:08:48,077 --> 00:08:51,382 globular clusters. They do have an advantage that their 117 00:08:51,382 --> 00:08:54,672 periods are short. So, it's much easier to observe full 118 00:08:54,672 --> 00:08:58,952 periodic Pulsating curve for an RR Lyrae Star than it is for a cepheid. 119 00:08:58,952 --> 00:09:03,295 Because they're dimmer, they can be really used, only within the local group 120 00:09:03,295 --> 00:09:06,360 of galaxies. But that's still useful, and it provides 121 00:09:06,360 --> 00:09:09,735 a welcome check, on the distances measure using Cepheids. 122 00:09:09,735 --> 00:09:13,818 Now, let's take a closer look to what happens when a star is pulsating. 123 00:09:13,818 --> 00:09:16,982 It's photosphere expands, but the temperature changes. 124 00:09:18,121 --> 00:09:21,331 As well. So the radius changes, the temperature 125 00:09:21,331 --> 00:09:24,318 changes therefore, luminosity must change. 126 00:09:24,318 --> 00:09:29,626 If we observe stars spectroscopically, we can observe the velocity of the photo 127 00:09:29,626 --> 00:09:32,732 sphere. Come storage us and go away from us. 128 00:09:32,732 --> 00:09:37,137 So we can measure stellar temperatures using colors or spectroscopy. 129 00:09:37,137 --> 00:09:42,362 We can measure velocity of the pulsating photosphere using spectroscopy and we can 130 00:09:42,362 --> 00:09:45,362 measure the changes in the apparent brightness. 131 00:09:45,362 --> 00:09:49,082 This forms the basis of so called Baade-Wesselink Method. 132 00:09:49,082 --> 00:09:54,477 If the pulsating stars were perfect black bodies, this would be an excellent pure 133 00:09:54,477 --> 00:09:57,852 physics based method to determine distances to them. 134 00:09:57,852 --> 00:10:02,917 Unfortunately, real stars are not perfect black bodies, but they're not too far 135 00:10:02,917 --> 00:10:05,832 either. So, at any given time, the flux from a 136 00:10:05,832 --> 00:10:10,617 star will be it's luminosity, which is in itself, given by Stefan Boltzmann 137 00:10:10,617 --> 00:10:13,757 formula. It's proportional to the temperature to 138 00:10:13,757 --> 00:10:17,011 the fourth power. And to the surface area of the star, 139 00:10:17,011 --> 00:10:20,033 which is proportional to the square of its radius. 140 00:10:20,033 --> 00:10:23,938 And it's universally proportional to the square of the distance. 141 00:10:23,938 --> 00:10:28,107 We can measure those quantities all throughout the pulsation period. 142 00:10:28,107 --> 00:10:31,607 So temperatures are directly observable from photometry. 143 00:10:31,607 --> 00:10:35,323 But so are the fluxes. And the only remaining question is, can 144 00:10:35,323 --> 00:10:41,024 we find out the radius? We can, in a way, because if we integrate motion of the 145 00:10:41,024 --> 00:10:46,462 photosphere as traced by the radial velocity, we can find out how much the 146 00:10:46,462 --> 00:10:51,294 radius has been changing. So we have 3 equations in 3 unknowns and 147 00:10:51,294 --> 00:10:56,101 we can solve for that. Therefore, we can obtain distances purely 148 00:10:56,101 --> 00:11:00,200 from measurements. And assumptions about black body nature 149 00:11:00,200 --> 00:11:04,277 of stellar photospheres. The problem is, the stars are not perfect 150 00:11:04,277 --> 00:11:06,956 black bodies. And some modelling of stellar 151 00:11:06,956 --> 00:11:11,351 photospheres has to be done in order to actually make the method to work. 152 00:11:11,351 --> 00:11:15,722 So there is model dependence. And that's where the uncertainties come. 153 00:11:15,722 --> 00:11:18,267 From. There are a couple more statistical 154 00:11:18,267 --> 00:11:21,080 methods that are based on stellar indicators. 155 00:11:21,080 --> 00:11:25,484 Globular star clusters themselves have a distribution of luminosities. 156 00:11:25,484 --> 00:11:30,005 It turns out that their distribution function, the luminosity function of 157 00:11:30,005 --> 00:11:34,911 globular clusters, seems to be universal among galaxies for reasons that are not 158 00:11:34,911 --> 00:11:39,122 really well understood at all. Actually you can think of many reasons 159 00:11:39,122 --> 00:11:44,123 why this shouldn't be the case. But empirically, the do seem to be very 160 00:11:44,123 --> 00:11:47,859 similar. Thus, if we can calibrate the luminosity 161 00:11:47,859 --> 00:11:52,865 function of globular clusters in the milky way using local distance 162 00:11:52,865 --> 00:11:58,668 indicators, then we can apply it to luminosity functions of globular clusters 163 00:11:58,668 --> 00:12:02,736 in other galaxies. A good thing about this is the globual 164 00:12:02,736 --> 00:12:07,847 clusters are much brighter than most stars, and so they're easier to find and 165 00:12:07,847 --> 00:12:11,551 easier to measure. Now one problem is that the number of 166 00:12:11,551 --> 00:12:14,933 globular clusters vary widely among the galaxies. 167 00:12:14,933 --> 00:12:19,952 Elliptical galaxies, early type spirals, have most, late type spirals. 168 00:12:19,952 --> 00:12:25,922 Hardly have any and therefore there be a statistical uncertainty for those 169 00:12:25,922 --> 00:12:30,172 galaxies. A similar method uses luminosity function 170 00:12:30,172 --> 00:12:34,357 of planetary neubli. As you recall planetary nebuli 171 00:12:34,357 --> 00:12:38,227 represents. Stellar envelopes that have been shed by 172 00:12:38,227 --> 00:12:41,527 a star, following it's horizontal branch phase. 173 00:12:41,527 --> 00:12:46,402 They are illuminated and iodized by the incandescent core that remains. 174 00:12:46,402 --> 00:12:50,962 And most of their light emerges in recombination emission lines. 175 00:12:50,962 --> 00:12:57,045 A very prominent line among those, is the line of ionized oxygen at 5007 angstroms. 176 00:12:57,045 --> 00:13:02,807 We can measure luminositys of those lines alone and then we can form luminosity 177 00:13:02,807 --> 00:13:08,330 function that is distribution of luminosities for that emission line alone 178 00:13:08,330 --> 00:13:13,322 for planetary nebula. That too, turns out to be more or less 179 00:13:13,322 --> 00:13:19,454 the same for the nearby galaxies. Ostensibly, that reflects the way in 180 00:13:19,454 --> 00:13:24,506 which stars evolve. But there isn't solid strong physical 181 00:13:24,506 --> 00:13:27,842 basis. This is an empirical relation. 182 00:13:27,842 --> 00:13:33,315 And again It, it is statistical. It can work up to the distance of the 183 00:13:33,315 --> 00:13:37,424 vertigo cluster, which is not so bad, but not beyond. 184 00:13:37,424 --> 00:13:41,644 And finally, there is, the tip of the red giant branch. 185 00:13:41,644 --> 00:13:46,859 The stars cannot get more luminous than certain amount. 186 00:13:46,859 --> 00:13:51,995 This is related to the, so called Eddington Luminosity, which, hopefully, 187 00:13:51,995 --> 00:13:55,551 you have heard about, and which we can address later. 188 00:13:55,551 --> 00:14:00,292 So, empirically, they don't seem to get brighter than a certain limit. 189 00:14:00,292 --> 00:14:05,650 And, if we can observe stars in other galaxies, nearby galaxies like Andromeda, 190 00:14:05,650 --> 00:14:08,678 and find out what are the most luminous ones. 191 00:14:08,678 --> 00:14:13,944 Where does luminosity stop? Then that threshold can be used as standard candle. 192 00:14:13,944 --> 00:14:18,261 The advantage of this is, of course, that these stars are bright. 193 00:14:18,261 --> 00:14:22,868 The disadvantage is that it is not a terribly well-defined indicator. 194 00:14:22,868 --> 00:14:28,255 There aren't very many of those stars so the numerical fluctuations can affect the 195 00:14:28,255 --> 00:14:30,942 result. That is it about the stellar. 196 00:14:30,942 --> 00:14:34,717 Distance indicator. Next time we will talk about so called 197 00:14:34,717 --> 00:14:37,605 Distance Indicator Relations for galaxies.