1 00:00:00,012 --> 00:00:05,139 You will recall that, value of Hubble's constant, was fairly unsettled all the 2 00:00:05,139 --> 00:00:08,704 way through 1980s. The reason for this, is that, these 3 00:00:08,704 --> 00:00:13,155 measurements are difficult. There are so many different relations, 4 00:00:13,155 --> 00:00:18,426 then one has to be calibrated against the other, and there are many opportunities 5 00:00:18,426 --> 00:00:21,608 for errors. And systematic errors in particular. 6 00:00:21,608 --> 00:00:26,496 And that resulted in the values of Hubble constants scattering by a factor of 2, 7 00:00:26,496 --> 00:00:31,291 which means that distances will be also uncertain by a factor 2 and things like 8 00:00:31,291 --> 00:00:35,542 luminosity by a factor of 4 and that, clearly, was not a satisfactory 9 00:00:35,542 --> 00:00:38,643 situation. So when the Hubble space telescope was 10 00:00:38,643 --> 00:00:43,531 launched, measuring Hubble constant was seen as one of it's key goals and it was 11 00:00:43,531 --> 00:00:47,893 a subject of a so called distance scale or Hubble Constant key project. 12 00:00:47,893 --> 00:00:52,112 This took ten years of very diligent measurements using Hubble space 13 00:00:52,112 --> 00:00:55,168 telescope. And even today Hubble space telescope 14 00:00:55,168 --> 00:00:59,182 continues to be used for this purpose, improving the results. 15 00:00:59,182 --> 00:01:04,268 The idea here was to observe Cepheids in a number of nearby spiral galaxies, and 16 00:01:04,268 --> 00:01:09,212 the reason why Hubble was needed is that these stars are faint, and they're in 17 00:01:09,212 --> 00:01:13,989 crowded fields, so the superb resolving power of HST was needed in order to 18 00:01:13,989 --> 00:01:18,522 actually measure their brightness and populate their light curves. 19 00:01:18,522 --> 00:01:23,847 Then, using the locally calibrated Cepheid relation, understand the distance 20 00:01:23,847 --> 00:01:28,522 to these galaxies and then use those to calibrate other things such as 21 00:01:28,522 --> 00:01:32,022 supernovae. A choice was made to use the distance to 22 00:01:32,022 --> 00:01:36,907 the Large Magellanic Cloud to establish The zero point to the Cepheid period 23 00:01:36,907 --> 00:01:40,497 luminosity relation. You recall that, that was the original 24 00:01:40,497 --> 00:01:45,307 discovered period luminosity relation by Henrietta Leavitt, and it still plays a 25 00:01:45,307 --> 00:01:48,067 role. And so any uncertainties in the distance 26 00:01:48,067 --> 00:01:52,772 to the Large Magellanic Cloud would then map directly into the inserted piece in 27 00:01:52,772 --> 00:01:54,304 the Hubble. Constant. 28 00:01:54,304 --> 00:01:58,981 Now not only did this team perform wonderful measurements, but they're also 29 00:01:58,981 --> 00:02:03,887 very careful about their analysis, and they tried to honestly account for every 30 00:02:03,887 --> 00:02:08,163 source of error they can think of. And the final result is shown here. 31 00:02:08,163 --> 00:02:12,865 Hubble constant turned out to be right in the middle of the disputed interval 32 00:02:12,865 --> 00:02:16,379 between 50 and 100 kilometers per second per megaparsec. 33 00:02:16,379 --> 00:02:21,874 It's 72 + or - 3 in just random errors, but also + or - 7 kilometers per second 34 00:02:21,874 --> 00:02:27,718 per megaparsec plus potential systematic errors and that's an honest result. 35 00:02:27,718 --> 00:02:32,915 In fact this is still perfectly consistent with all of the more modern 36 00:02:32,915 --> 00:02:38,491 measurements, Note, however, that there is still dependance, on the assumed to 37 00:02:38,491 --> 00:02:41,702 the [UNKNOWN] clouds. And that is osmething that people 38 00:02:41,702 --> 00:02:45,051 continue to improve. So here is a sample image of what they 39 00:02:45,051 --> 00:02:48,047 were looking at. The picture on the left, is 1 of the 40 00:02:48,047 --> 00:02:52,605 spiral galaxies used in their study, and superimposed on that, is an outline of 41 00:02:52,605 --> 00:02:56,558 the field of view of the camera, of a space telescope, that was used. 42 00:02:56,558 --> 00:03:00,708 This was the original White field Blanthery camera, and has the strange B2 43 00:03:00,708 --> 00:03:03,545 bumper shape. The picture on the right, shows a zoom 44 00:03:03,545 --> 00:03:07,603 in, on one of those images, with some of the candidates Cepheid's circled. 45 00:03:07,603 --> 00:03:11,298 As you can see, this would be a very hard thing to do from the ground. 46 00:03:11,298 --> 00:03:15,306 Some of these Cepheid's, occur in star-forming regions, so there may well 47 00:03:15,306 --> 00:03:19,423 be other bright stars that are blended with them and that has to be taken care 48 00:03:19,423 --> 00:03:21,938 of. And here are some light curves of 49 00:03:21,938 --> 00:03:27,056 cepheids discovered by the key project. These represent many measurements of 50 00:03:27,056 --> 00:03:31,371 different times that we folded together into the best fit period. 51 00:03:31,371 --> 00:03:35,882 And you can see that those really look like those of nearby cepheids. 52 00:03:35,882 --> 00:03:39,540 So here are some Hubble diagrams they obtain in the end. 53 00:03:39,540 --> 00:03:44,492 The bottom left one shows only that one. For galaxies, whose distance was derived 54 00:03:44,492 --> 00:03:47,243 from Cepheid's. The one on the right includes all 55 00:03:47,243 --> 00:03:50,274 possible calibration sources they could come up with. 56 00:03:50,274 --> 00:03:54,650 And here is a table that accounts for different sources of uncertainty in their 57 00:03:54,650 --> 00:03:57,620 measurement. I'm just showing for information only, 58 00:03:57,620 --> 00:04:01,974 and you can see how many things they can think of And here is their final error 59 00:04:01,974 --> 00:04:06,574 probability distribution around hubble constant This is actually a good 60 00:04:06,574 --> 00:04:10,893 scientific way of presenting result. It's not a number, it's a probability 61 00:04:10,893 --> 00:04:15,212 distribution for that number The peak value is the one that's quoted and the 62 00:04:15,212 --> 00:04:18,962 width of that distribution is indicative of that uncertainty. 63 00:04:18,962 --> 00:04:23,180 People continued, to try to determine Hubble constant, using any 1 of the 64 00:04:23,180 --> 00:04:27,676 number of methods and combinations of different indicators and callibrators, 65 00:04:27,676 --> 00:04:32,019 and here is again, a table of those. Not there for you to remember all of it, 66 00:04:32,019 --> 00:04:36,703 but just to see how, much the different measurements, scatter around each other. 67 00:04:36,703 --> 00:04:41,022 Most of them are certainly within the error bars of the value determined by 68 00:04:41,022 --> 00:04:44,778 Hubble key project. Now recall that the basis for the whole 69 00:04:44,778 --> 00:04:49,337 thing was distance to the Large Magellanic Cloud which is about 50 kpc 70 00:04:49,337 --> 00:04:53,287 from the Milky Way. So the uncertainty of this distance maps 71 00:04:53,287 --> 00:04:56,626 directly onto the uncertainty on Hubble Constant. 72 00:04:56,626 --> 00:05:01,940 And the distance to The Magellanic Cloud was measured many different ways by many 73 00:05:01,940 --> 00:05:05,607 different authors. That alone, has a spread of + or - 10%. 74 00:05:05,607 --> 00:05:10,167 There is maybe about, 10 different methods, by which this was attempted, and 75 00:05:10,167 --> 00:05:13,042 here is the table that shows some of the results. 76 00:05:13,042 --> 00:05:17,792 Again, not there for you to remember all of it, but just to see the, roughly, the 77 00:05:17,792 --> 00:05:21,407 spread of the numbers, and the accuracies that are involved. 78 00:05:21,407 --> 00:05:26,921 A more important Check, which is actually becoming a very powerful new method is, 79 00:05:26,921 --> 00:05:32,615 as follows: in the neclei, of many, large spiral galaxies, there is a massive black 80 00:05:32,615 --> 00:05:35,677 hole. Which, for all practical purposes, is 81 00:05:35,677 --> 00:05:40,510 like a point mass, just like, essentially, all of the mass in the solar 82 00:05:40,510 --> 00:05:44,725 system is in the sun. Now, if we have test particles moving 83 00:05:44,725 --> 00:05:49,532 around that black hole. From measuring their orbits, we can find 84 00:05:49,532 --> 00:05:54,115 out how far the galaxy is. The orbits can be well-assumed to be 85 00:05:54,115 --> 00:05:57,635 Keplerian. And the suitable test particles are 86 00:05:57,635 --> 00:06:03,031 so-called interstellar masers. These are interstellar clouds that have 87 00:06:03,031 --> 00:06:08,952 very sharp line due to the coherent emission, and as they're moving around, 88 00:06:08,952 --> 00:06:14,461 the center of this galaxy, they can be used to measure the central mass, But 89 00:06:14,461 --> 00:06:19,262 also they can be used to measure the semi-major axes of these orbits. 90 00:06:19,262 --> 00:06:24,002 This was the first case in which this was done, since then there have been more, 91 00:06:24,002 --> 00:06:28,419 and the distance to this particular galaxy was found to be consistent with 92 00:06:28,419 --> 00:06:33,068 that one determined by the Cepheids. Now wouldn't it be nice, if we can bypass 93 00:06:33,068 --> 00:06:37,601 all this messy distance scale ladder climbing from one to another and so on, 94 00:06:37,601 --> 00:06:42,311 and go directly into the tuple flow. Well, there're 2 methods by which death 95 00:06:42,311 --> 00:06:46,013 can be accomplished, that do not require any other calibration. 96 00:06:46,013 --> 00:06:50,773 They're both based on physical reasoning. The first one is gravitational lens time 97 00:06:50,773 --> 00:06:54,312 delay and the second one is so-called Senile of Gorbachev effect. 98 00:06:54,312 --> 00:06:58,993 Whereas these are based on physics, they're still very much model-dependent. 99 00:06:58,993 --> 00:07:03,790 Initially, at least, we are producing values that were somewhat lower than that 100 00:07:03,790 --> 00:07:08,480 when measured by the Hubble Key Project, but since then, they have converged a 101 00:07:08,480 --> 00:07:11,634 little more. Any of these small discrepancies can be 102 00:07:11,634 --> 00:07:16,381 understood in terms of systematic errors. So firstly, gravitational lens time 103 00:07:16,381 --> 00:07:19,322 delays. Assuming that we understand the geometry 104 00:07:19,322 --> 00:07:23,804 of the lensing, and I'll show this in a moment, we can in principal derive the 105 00:07:23,804 --> 00:07:28,378 distance between the lens and the lensed object using the measured time delay. 106 00:07:28,378 --> 00:07:31,636 Modeling the lens geometry is the key uncertainty here. 107 00:07:31,636 --> 00:07:35,637 Because masses responsible for gravitational lensing are not always 108 00:07:35,637 --> 00:07:40,200 perfectly straightly symmetric and there can be combination of many potential 109 00:07:40,200 --> 00:07:42,832 wells of say galaxies in a cluster or group. 110 00:07:42,832 --> 00:07:47,265 So here is how it works,.Here's a schematic diagram showing what 111 00:07:47,265 --> 00:07:51,902 gravitational source might be. There is a background source, say a 112 00:07:51,902 --> 00:07:56,512 quasar, There is a foreground which could be a galaxy or a cluster. 113 00:07:56,512 --> 00:08:01,877 It bends the lights rays coming from the original source and One usually sees 114 00:08:01,877 --> 00:08:06,177 mulitple images, on the sky. Each of these images correspond to 115 00:08:06,177 --> 00:08:11,527 particular path of light rays that came around the gravitational lens and there 116 00:08:11,527 --> 00:08:16,852 will generally difference in length. The difference in length would translate 117 00:08:16,852 --> 00:08:19,777 itself in to a difference in arrival times. 118 00:08:19,777 --> 00:08:25,002 So we are going to see in our ability in the place are we will first see it in one 119 00:08:25,002 --> 00:08:27,791 image And then some time later in the other. 120 00:08:27,791 --> 00:08:31,508 These time delays are typically in the range of weeks or months. 121 00:08:31,508 --> 00:08:36,018 The path difference between different rays, assuming that you know, know the 122 00:08:36,018 --> 00:08:40,286 geometry will scale directly with everything else, every other length in 123 00:08:40,286 --> 00:08:43,313 the system. And the ratio of this path difference to 124 00:08:43,313 --> 00:08:48,169 the, distance to the lens or the source. Is also something that the model will 125 00:08:48,169 --> 00:08:50,867 tell you. So by measuring the time delay, 126 00:08:50,867 --> 00:08:55,825 multiplying by the speed of light, we directly measure the difference in the 127 00:08:55,825 --> 00:08:59,030 path length. And if we knew the lens model, we can 128 00:08:59,030 --> 00:09:03,390 then use it to infer the distance to the lens, or the lensed object. 129 00:09:03,390 --> 00:09:07,352 Synyaev-Zeldovich Effect is something entirely different. 130 00:09:07,352 --> 00:09:11,357 Clusters of galaxies contain galaxies, dark matter. 131 00:09:11,357 --> 00:09:16,100 But also a lot of hot gas. Gas that was expelled from galaxies or 132 00:09:16,100 --> 00:09:20,986 accreted by the cluster. And since that gas is in a potential well 133 00:09:20,986 --> 00:09:24,680 of a cluster, the speed of individual particles. 134 00:09:24,680 --> 00:09:27,884 Protons. Electrons has to be such that the kinetic 135 00:09:27,884 --> 00:09:32,367 energy balances the potential energy. It turns out that [UNKNOWN] responds to 136 00:09:32,367 --> 00:09:36,812 temperatures of millions or tens of millions of degrees, which means that the 137 00:09:36,812 --> 00:09:40,816 gas will emit in the X-rays. Now we're looking at the cosmic microwave 138 00:09:40,816 --> 00:09:45,773 background [UNKNOWN] cluster Cluster. The photons of the micro background will 139 00:09:45,773 --> 00:09:49,906 come through, and some of them will scatter off these hot energetic 140 00:09:49,906 --> 00:09:53,055 electrons. In the cases of forward scattering this 141 00:09:53,055 --> 00:09:56,730 will generally result in an increased energy of the photon. 142 00:09:56,730 --> 00:10:01,314 The energy's been gained from the electrons in the cluster.Of course there 143 00:10:01,314 --> 00:10:04,382 is equal amounts going out from the other side. 144 00:10:04,382 --> 00:10:09,722 So essentially what you see on the micro background sky is there's going to be a 145 00:10:09,722 --> 00:10:12,658 bump that corresponds to this X-ray cloud. 146 00:10:12,658 --> 00:10:17,999 And the entire spectrum of the cosmic micro background will be shifted towards 147 00:10:17,999 --> 00:10:23,073 a somewhat higher energies. By measuring that shift We can find out, 148 00:10:23,073 --> 00:10:30,153 how long was the path? Because the longer the path along the line of sight, more 149 00:10:30,153 --> 00:10:37,183 chances the photons have to be scattered. Therefore, we can, derive from this 150 00:10:37,183 --> 00:10:43,352 measurement directly, physical we can measure the apparent size of the cluster 151 00:10:43,352 --> 00:10:46,902 on the sky. In an average, we expect the cluster will 152 00:10:46,902 --> 00:10:50,552 have the size in radial direction or orthogonal to it. 153 00:10:50,552 --> 00:10:55,502 So since we have observed apparant angular size of the cluster in the sky. 154 00:10:55,502 --> 00:11:00,327 And we know how much that is in physical units, the cluster's red shift. 155 00:11:00,327 --> 00:11:04,941 We can derive the angular diameter distance Now, any given cluster is not 156 00:11:04,941 --> 00:11:09,281 likely to be spherically symmetric, but the whole ensemble, on average, will 157 00:11:09,281 --> 00:11:12,570 probably work out. A beautiful thing about this method, is 158 00:11:12,570 --> 00:11:16,092 that it does not depend, on the distance to the cluster itself. 159 00:11:16,092 --> 00:11:19,514 The source that's observed, is cosmic microwave background. 160 00:11:19,514 --> 00:11:22,548 Cluster could be near by, or it could be very far away. 161 00:11:22,548 --> 00:11:26,132 So the method can work over a very broad range of redshift's. 162 00:11:26,132 --> 00:11:31,036 There are uncertainties in modelling the process because the gas could be clumpy, 163 00:11:31,036 --> 00:11:35,858 there are some density gradients, all of that has to be accounted for before we 164 00:11:35,858 --> 00:11:40,011 can derive the actual diameter of a cluster that photon goes through. 165 00:11:40,011 --> 00:11:43,731 Next we will talk about measurements of the age of the universe.