1 00:00:00,012 --> 00:00:03,613 Hello. Last time, we saw how we can use, various 2 00:00:03,613 --> 00:00:08,424 relationships to measure distances to stars, or star clusters. 3 00:00:08,424 --> 00:00:14,016 Chief among them, relations between period, and luminosity for pulsating 4 00:00:14,016 --> 00:00:19,742 variables like Cepheids, but also fitting of the main sequence for the star 5 00:00:19,742 --> 00:00:23,159 clusters. These are examples of a really more 6 00:00:23,159 --> 00:00:27,288 general idea of Distance indicator relations. 7 00:00:27,288 --> 00:00:31,041 So let's just recap what that really means. 8 00:00:31,041 --> 00:00:37,540 In general, if we can find a correlation between some distance independent 9 00:00:37,540 --> 00:00:43,843 quantity, like color or temperature or stars or period was for pulsating 10 00:00:43,843 --> 00:00:50,012 variables, this correlates well with something that Does depend on distance 11 00:00:50,012 --> 00:00:54,156 like, stellar luminosity. And we can calibrate that relation, then 12 00:00:54,156 --> 00:00:58,802 we can see how stars in, other clusters, of different distances, fit on that 13 00:00:58,802 --> 00:01:01,238 relation. So now when we compare, these 14 00:01:01,238 --> 00:01:06,245 correlations inapparent quantities, say apparent magnitudes instead of absolute 15 00:01:06,245 --> 00:01:10,987 magnitudes, clusters of different distances Will systematically shift from 16 00:01:10,987 --> 00:01:14,082 each other. From magnitude of shift, we can find out 17 00:01:14,082 --> 00:01:16,687 what the relative distance is between them. 18 00:01:16,687 --> 00:01:21,117 So thus, we can use these distance to indicate the relations as a measure of 19 00:01:21,117 --> 00:01:24,732 relative distance. If we can actually calibrate them, in the 20 00:01:24,732 --> 00:01:29,007 absolute sense, then of course we can get the optimal distances as well. 21 00:01:29,007 --> 00:01:32,942 In this is how Cepheids work. So now the question is, can we do the 22 00:01:32,942 --> 00:01:37,997 same for galaxies, and the answer is yes. The first relation, that we'll consider, 23 00:01:37,997 --> 00:01:40,944 is so called, surface brightness fluctuations. 24 00:01:40,944 --> 00:01:45,808 And, conceptually, it's fairly simply. Suppose we are looking at some galaxies 25 00:01:45,808 --> 00:01:50,454 with a detector that has square pixels, like, typically they do, and each of 26 00:01:50,454 --> 00:01:53,852 these pixels would cover, a certain number of stars. 27 00:01:53,852 --> 00:01:59,191 Now if we, remove the galaxy twice as far, then there'll be, four times as many 28 00:01:59,191 --> 00:02:02,582 stars in each pixel, and that will look smoother. 29 00:02:02,582 --> 00:02:06,682 The mathematical reason be, behind this is, fairly simply. 30 00:02:06,682 --> 00:02:12,200 For elliptical galaxies and bulges, most of the light comes from luminous red 31 00:02:12,200 --> 00:02:17,045 giants. And it's the fluctuations in the numbers 32 00:02:17,045 --> 00:02:23,078 of the red giants that will determine what's going on here. 33 00:02:23,078 --> 00:02:28,576 So if we have, say, stars, that contribute most of the light and the 34 00:02:28,576 --> 00:02:28,576 average flux is f and the number of them in a pixel is, and the total amount of 35 00:02:28,576 --> 00:02:33,507 flux from the pixel will be n*f. And the variance of that will be due, 36 00:02:33,507 --> 00:02:36,317 given by the square root of the number of stars. 37 00:02:36,317 --> 00:02:40,982 It's simple statistics. So, if we move galaxy further, the number 38 00:02:40,982 --> 00:02:45,697 will, go as the distance squared, but flux will decline as the distance square. 39 00:02:45,697 --> 00:02:49,212 And, therefore, the variance will scale with the square. 40 00:02:49,212 --> 00:02:53,904 Of the distance, universally. And square root of that, which is rms or 41 00:02:53,904 --> 00:02:58,201 sigma as the first power. This is why a galaxy that's twice as far 42 00:02:58,201 --> 00:03:03,485 would appear twice as smooth. So now, if we actually knew what real 43 00:03:03,485 --> 00:03:08,082 luminosity is for an average star that corresponds to that. 44 00:03:08,082 --> 00:03:11,218 Average f, then we can determine the distance. 45 00:03:11,218 --> 00:03:16,822 Roughly speaking, the absolute mag, mean the absolute magnitude M corresponding to 46 00:03:16,822 --> 00:03:21,861 that main flux F, is the one at the top of the Red Giant branch, and we can try 47 00:03:21,861 --> 00:03:27,292 to calibrate that using Andromeda Galaxy to which we measure distance using other 48 00:03:27,292 --> 00:03:30,175 techniques. Using that gives the following 49 00:03:30,175 --> 00:03:34,369 calibrating relationship here. Note that this a purely empirically 50 00:03:34,369 --> 00:03:38,681 calibrated relationship using a galaxy to which we know the distance. 51 00:03:38,681 --> 00:03:43,383 However, there is likely to be some dependence on the actual coefficients of 52 00:03:43,383 --> 00:03:47,745 this equation, or I should say correlation, that will depend on things 53 00:03:47,745 --> 00:03:51,982 like the mean metallicity of stars in a given population, and so on. 54 00:03:51,982 --> 00:03:56,137 We also have to take care of things like removing the effects of foreground, 55 00:03:56,137 --> 00:04:00,782 extinction, presence of foreground stars in our galaxy, background galaxies behind 56 00:04:00,782 --> 00:04:04,962 the galaxy we're studying, and so on. Nevertheless, this is a very powerful 57 00:04:04,962 --> 00:04:08,912 method, and can be used to measure distances up to 100 megaparsecs using 58 00:04:08,912 --> 00:04:13,191 Hubble-Space telelscope. Here is a simulation of how that works. 59 00:04:13,191 --> 00:04:18,802 The 2 columns of pictures correspond to 2 galaxies, fictitious galaxies that 1 of 60 00:04:18,802 --> 00:04:23,951 which is twice as far as the other. Top panels schematically show where the 61 00:04:23,951 --> 00:04:26,871 stars would be relative to the pixel grid. 62 00:04:26,871 --> 00:04:32,147 Now if we average the fluxes we can see in the grey scale images the second row 63 00:04:32,147 --> 00:04:34,360 what say. Picture might look like. 64 00:04:34,360 --> 00:04:37,974 Now let's add more pixels or alternatively we can move galaxies 65 00:04:37,974 --> 00:04:42,041 further out and so we see those grainy structure which is indeed what is 66 00:04:42,041 --> 00:04:44,446 observed. Finally, we convolve this with 67 00:04:44,446 --> 00:04:48,904 atmospheric turbulence thus seeing because we are not observing in a vacuum. 68 00:04:48,904 --> 00:04:52,912 Don't have to do this last step if observing with a space telescope. 69 00:04:52,912 --> 00:04:57,447 And the last row shows selected images of 2 different galaxies, of 2 different 70 00:04:57,447 --> 00:05:00,922 distances from us. Obviously the one that's further away is 71 00:05:00,922 --> 00:05:04,116 much smoother. 100 megaparsecs is a good distance but 72 00:05:04,116 --> 00:05:07,762 we'd like to push even further into what's called pure Hubble. 73 00:05:07,762 --> 00:05:12,467 So remember, the definition of Hubble's Law is that distance is proportional to 74 00:05:12,467 --> 00:05:16,082 the recession of velocity. That's due to the expansion of the 75 00:05:16,082 --> 00:05:19,087 universe. However, in reality, galaxies do move. 76 00:05:19,087 --> 00:05:23,857 Since the time they form, they acquired so called peculiar velocities because of 77 00:05:23,857 --> 00:05:28,522 the mutual gravitational attraction. You can imagine, that if there is a large 78 00:05:28,522 --> 00:05:33,187 concentration of mass, in some direction from a galaxy, it will be accelerated 79 00:05:33,187 --> 00:05:36,367 towards it. And over time it will develop certain 80 00:05:36,367 --> 00:05:39,577 velocity. So the actual observed radio velocities 81 00:05:39,577 --> 00:05:44,102 of galaxies have these two components, the components that's due to the 82 00:05:44,102 --> 00:05:48,937 expansion of the universe, the Hubble flow, and the other one which has to do 83 00:05:48,937 --> 00:05:53,985 with dynamics of large scale structure. Now, typically Today these peculiar 84 00:05:53,985 --> 00:05:58,094 velocities of galaxies are a few hundred kilometers per second. 85 00:05:58,094 --> 00:06:02,512 For example Milky Way moves 600 kilometers per second relative to the 86 00:06:02,512 --> 00:06:06,912 cosmic micro background which is a good physical embodiment of the combo and 87 00:06:06,912 --> 00:06:09,372 coordinate grid, and galaxies new cluster. 88 00:06:09,372 --> 00:06:14,332 So, in our case, we are a member of the local group, and that is part of a larger 89 00:06:14,332 --> 00:06:19,467 concentration, the local super cluster. And our entire local group is falling to 90 00:06:19,467 --> 00:06:22,917 it with a speed of a few hundred kilometers per second. 91 00:06:22,917 --> 00:06:27,627 Since these large scale non-uniformities extend out to scales of maybe 100 92 00:06:27,627 --> 00:06:32,166 megaparsecs or so. Up until that scales, or thereabouts, 93 00:06:32,166 --> 00:06:36,541 there, there are going to be peculiar velocity components. 94 00:06:36,541 --> 00:06:42,082 Going to larger scales, things pretty much average out, and if the peculiar 95 00:06:42,082 --> 00:06:47,630 velocity is few hundred kilometers per second, few thousand kilometers per 96 00:06:47,630 --> 00:06:51,452 second hubble flow would make that 10% if we go to. 97 00:06:51,452 --> 00:06:54,975 Tens of thousands of kilometers per second of recession velocity. 98 00:06:54,975 --> 00:06:58,465 Then the peculiar velocities will only matter on a percent level. 99 00:06:58,465 --> 00:07:02,295 This is why I would like to measure Hubble constant to distances that are 100 00:07:02,295 --> 00:07:06,871 considerably larger than 100 megaparsecs. And for that, we need some very luminous 101 00:07:06,871 --> 00:07:10,026 objects. Galaxies and supernovae are such luminous 102 00:07:10,026 --> 00:07:14,861 objects and both have been used to push measurement of the Hubble constant all 103 00:07:14,861 --> 00:07:19,213 the way out to the Hubble flow. This is where galaxy scaling relations 104 00:07:19,213 --> 00:07:22,179 come in. Remember we explain how it works at the 105 00:07:22,179 --> 00:07:27,177 beginning of this clip and if we can find a quantity for galaxies that correlates 106 00:07:27,177 --> 00:07:31,542 with another one What the first one, with being distance dependant, such as 107 00:07:31,542 --> 00:07:34,587 luminosity. The outer one being distance independent. 108 00:07:34,587 --> 00:07:38,167 Then we can, actually do the same trick, as we did with cephates. 109 00:07:38,167 --> 00:07:42,237 There are 2 examples, of such, distant indicator relations for galaxies. 110 00:07:42,237 --> 00:07:45,922 1 for spiral galaxies, called the Tully-Fisher relation, and 1 for 111 00:07:45,922 --> 00:07:48,822 elliptical galaxies, called the fundamental plane. 112 00:07:48,822 --> 00:07:53,112 Because these distance indicator relations, provide a relative Distance of 113 00:07:53,112 --> 00:07:56,515 galaxies from each other, they do have to be calibrated locally. 114 00:07:56,515 --> 00:08:00,545 So, for example, the Tully-Fisher relation can be calibrated with distances 115 00:08:00,545 --> 00:08:02,936 to spirals that are now unsafe from Cepheids. 116 00:08:02,936 --> 00:08:07,080 Or as the Fundamental Plane relation can be calibrated from the distances using 117 00:08:07,080 --> 00:08:10,711 surface brightness fluctuations. Each of which, of course, has been 118 00:08:10,711 --> 00:08:13,742 calibrated with the lower ranks of the distance ladder. 119 00:08:13,742 --> 00:08:18,942 Now one thing to note here is that we have some idea where these relations come 120 00:08:18,942 --> 00:08:23,692 from, but their exact physical standing for evolution are not yet well 121 00:08:23,692 --> 00:08:25,992 understood. So we have to beware. 122 00:08:25,992 --> 00:08:31,342 We're using a tool whose origins and the right functions are not perfectly well 123 00:08:31,342 --> 00:08:34,657 understood. The Tully-Fisher relation, for spirals, 124 00:08:34,657 --> 00:08:39,267 is a very useful one, it, connects the luminosity of a galaxy, with its maximum 125 00:08:39,267 --> 00:08:42,333 rotational speed. When we talk about, properties of 126 00:08:42,333 --> 00:08:47,021 galaxies, later on in the class, we will address these relations in much greater 127 00:08:47,021 --> 00:08:51,553 detail, but, for now, just take it for granted, that this is indeed the case, 128 00:08:51,553 --> 00:08:55,514 and I'll show you the plot. The luminosity of spiral galaxies are 129 00:08:55,514 --> 00:08:59,881 well protected with rotational speeds, and the relation has the power of slope 130 00:08:59,881 --> 00:09:04,389 of 4, namely luminosity is proportional to the fourth power of the circular 131 00:09:04,389 --> 00:09:07,163 velocity. Roughly speaking, the power varies 132 00:09:07,163 --> 00:09:10,422 depending on the filter that is used and so on. 133 00:09:10,422 --> 00:09:15,802 We can also express that in terms of magnitudes, because log of the luminosity 134 00:09:15,802 --> 00:09:21,105 * -2.5 gives the absolute magnitude, will manifest itself as the width of the 135 00:09:21,105 --> 00:09:26,793 observed radio line of neutral hydrogen. Because as the hydrogen atoms move in the 136 00:09:26,793 --> 00:09:32,332 galaxy their Doppler shifted this way or that and faster the rotation speed. 137 00:09:32,332 --> 00:09:36,202 More of the Doppler Browniung rays. So we can establish this, this 138 00:09:36,202 --> 00:09:40,829 correlation using spiral galaxies with well measured distances nearby and then 139 00:09:40,829 --> 00:09:43,255 try to apply it to much more distant ones. 140 00:09:43,255 --> 00:09:47,459 In practice the scatter of the Tully-Fisher relations is typically 10 to 141 00:09:47,459 --> 00:09:50,102 20%. The very best that has been done is about 142 00:09:50,102 --> 00:09:53,232 9% and that's including all the measurement errors. 143 00:09:53,232 --> 00:09:56,497 It's actually a very good correlation when done well. 144 00:09:56,497 --> 00:10:00,055 There are some problems. The light from spiral galaxies is 145 00:10:00,055 --> 00:10:04,517 affected by the extinction in them. There is lots of dust that absorbs the 146 00:10:04,517 --> 00:10:08,962 blue light, or absorbs light at all wavelengths, but more so in the blue. 147 00:10:08,962 --> 00:10:13,667 And, the fluctuation in star formation can affect the luminosity of galaxy on 148 00:10:13,667 --> 00:10:16,932 short time scales. So here is the actual Tally-Fisher 149 00:10:16,932 --> 00:10:20,772 relation for a set of galaxies nearby, in 3 different filters. 150 00:10:20,772 --> 00:10:23,910 There is a gradual change in slope. But that's okay. 151 00:10:23,910 --> 00:10:27,048 Whatever we do, we can just calibrate to that slope. 152 00:10:27,048 --> 00:10:31,656 But also note that the scatter improves, the further in the red we go, for the 153 00:10:31,656 --> 00:10:35,611 reasons I just mentioned. There is less effect of the extinction, 154 00:10:35,611 --> 00:10:40,135 and less susceptibility fluctuations due to the very luminous young stars. 155 00:10:40,135 --> 00:10:44,082 The other important correlation is so called fundamental plane. 156 00:10:44,082 --> 00:10:49,152 This is actually a set of bivariate correlations, which connect one property 157 00:10:49,152 --> 00:10:52,906 of elliptical galaxies with the combination of 2 others. 158 00:10:52,906 --> 00:10:57,872 But it's usually shown in this form, where a distance dependent quantity. 159 00:10:57,872 --> 00:11:02,276 Radius determining a certain consistent fashion is correlated against a 160 00:11:02,276 --> 00:11:07,023 combination of velocity dispersion. Which, again, is the Doppler broadening 161 00:11:07,023 --> 00:11:09,677 of spectroscopic lines in galaxy spectrum. 162 00:11:09,677 --> 00:11:14,131 And it means surface brightness. Surface brightness not depending on the 163 00:11:14,131 --> 00:11:16,704 distance, at least in Euclidean. Space. 164 00:11:16,704 --> 00:11:21,928 The observed scatter of the fundamental plane visible bands say a is about 10%. 165 00:11:21,928 --> 00:11:25,946 So it is as good as the Tully-Fisher. It may be even slightly lower and 166 00:11:25,946 --> 00:11:30,450 actually why is it so small is an interesting problem enough itself, which 167 00:11:30,450 --> 00:11:34,842 will come back to when we talk about properties of elliptical galaxies. 168 00:11:34,842 --> 00:11:39,437 Its zero point nowadays, tends to be calibrated with surface brightness 169 00:11:39,437 --> 00:11:42,949 fluctuations. The fundamental plane comes in another 170 00:11:42,949 --> 00:11:47,885 flavor, so called DN sigma relation, where DN is the diameter of a galaxy at 171 00:11:47,885 --> 00:11:51,372 which its surface brightness reaches certain value. 172 00:11:51,372 --> 00:11:56,571 This turns out to be a slightly oblique projection of the fundamental plane, but 173 00:11:56,571 --> 00:12:01,075 it basically works in the same way. Next time we will talk about use of 174 00:12:01,075 --> 00:12:05,251 supernova as a standard candle, a very popular method these days.