1 00:00:00,012 --> 00:00:04,870 We now turn to Measurement of Cosmological Parameters. 2 00:00:04,870 --> 00:00:10,596 The first one of which, is Hubble Constant, or Hubble Parameter. 3 00:00:10,596 --> 00:00:16,514 It sets, both the spatial and temporal scales for the whole universe. 4 00:00:16,514 --> 00:00:23,634 In a given cosmological model, specified by values of different, omegas, or little 5 00:00:23,634 --> 00:00:26,604 w as well. All distances and all times scale 6 00:00:26,604 --> 00:00:30,398 linearly with Hubble's constant. And thus, its importance. 7 00:00:30,398 --> 00:00:34,957 So, the inverse of the Hubble constant is the characteristic time unit of 8 00:00:34,957 --> 00:00:36,763 cosmology. The Hubble time. 9 00:00:36,763 --> 00:00:40,375 Multiplied by the speed of light, it gives Hubble length. 10 00:00:40,375 --> 00:00:44,532 Which is commensurate with the size of the observable universe. 11 00:00:44,532 --> 00:00:50,932 Note that, Hubble's constant, is independent of all other cosmological 12 00:00:50,932 --> 00:00:55,457 parameters. We have this neat separation, between 13 00:00:55,457 --> 00:01:02,563 Hubble constant that sets the scale, and all under parameters that Describe the 14 00:01:02,563 --> 00:01:08,712 qualitative behavior of the universe. So distances to anything, galaxies, 15 00:01:08,712 --> 00:01:14,447 quasars, anything cosmology. Scale with Humboldt's constant and it's 16 00:01:14,447 --> 00:01:16,372 importance. Moreover. 17 00:01:16,372 --> 00:01:21,144 Physical parameters of, objects like galaxies or anything else, such as their 18 00:01:21,144 --> 00:01:25,606 total luminosity, or their masses or physical sizes, all scale, with the 19 00:01:25,606 --> 00:01:30,445 distance, with the appropriate power. And in order to understand these objects 20 00:01:30,445 --> 00:01:34,848 better, and how they form, how they evolve, we need, distances to them. 21 00:01:34,848 --> 00:01:39,486 However, measuring the distances in cosmology is, a very difficult thing to 22 00:01:39,486 --> 00:01:42,767 do. Because galaxies are very far away. 23 00:01:42,767 --> 00:01:48,327 And, in fact, the only distances in astronomy that are measured cleanly, 24 00:01:48,327 --> 00:01:54,517 without recourse 20 models or statistics, are trigonometric paralexes to stars. 25 00:01:54,517 --> 00:02:00,147 Everything else requires some sort of physical modeling or assumptions or 26 00:02:00,147 --> 00:02:03,948 statistics. Because we have a concept of the distance 27 00:02:03,948 --> 00:02:06,936 ladder. Which means, that we first measure, 28 00:02:06,936 --> 00:02:12,196 distances to objects that, where we're sure how to do it, such as nearby stars. 29 00:02:12,196 --> 00:02:17,233 Then we use that, to calibrate distances to some objects further away, star 30 00:02:17,233 --> 00:02:22,246 clusters say, and, so on and so on. So we calibrate the distance indicators 31 00:02:22,246 --> 00:02:26,958 relevant to each other. And this is what's known as the distance 32 00:02:26,958 --> 00:02:30,463 ladder. Locally, those will be various stellar 33 00:02:30,463 --> 00:02:35,733 types of indicators, say, based on pulsating stars or star clusters and 34 00:02:35,733 --> 00:02:41,224 things like that, then properties of nearby galaxies, using their scaling 35 00:02:41,224 --> 00:02:46,602 relations And sun, until we reach what is called pure Hubble flow, where only the 36 00:02:46,602 --> 00:02:51,057 recession of velocities matter. And that is where the expansion of the 37 00:02:51,057 --> 00:02:55,157 universe, unperturbed by local non-infirmities really sets in. 38 00:02:55,157 --> 00:02:59,651 Now the age of the universe, can be actually estimated Independent of 39 00:02:59,651 --> 00:03:04,917 Hubble's constant.The look back times, objects cannot, but the total age of the 40 00:03:04,917 --> 00:03:08,356 universe can. We can, for example, estimate ages of 41 00:03:08,356 --> 00:03:13,501 stars or clusters, or chemical elements and that gives a lower limit to the age 42 00:03:13,501 --> 00:03:16,938 of the universe. Independent of any measurements or 43 00:03:16,938 --> 00:03:20,167 distances. This is a hard thing to do, and thus, 44 00:03:20,167 --> 00:03:24,592 measurements of Hubble constant have somewhat disreputable history. 45 00:03:24,592 --> 00:03:29,612 Hubble's own estimate of it was an order of magnitude off from what we know today 46 00:03:29,612 --> 00:03:34,473 is more or less the correct value. And through the history, people always 47 00:03:34,473 --> 00:03:37,290 thought they knew it to about 10% accuracy. 48 00:03:37,290 --> 00:03:41,190 Even though its value changed by a whole order of magnitude. 49 00:03:41,190 --> 00:03:46,148 The reason for this is that they didn't really account properly for errors of 50 00:03:46,148 --> 00:03:49,829 measurement. And especially for the systematic errors. 51 00:03:49,829 --> 00:03:54,752 So, for example, when Hubble first measured value of Hubble's Constant. 52 00:03:54,752 --> 00:03:59,747 One over that was a couple billion years, and already then people knew that there 53 00:03:59,747 --> 00:04:04,297 were rocks on planet Earth that are three or four billion years old. 54 00:04:04,297 --> 00:04:08,872 So planet Earth was older than the universe, and that was a problem. 55 00:04:08,872 --> 00:04:14,112 Ever since then, the value of the Hubble constant was revised, usually downward. 56 00:04:14,112 --> 00:04:19,162 The first major revision was due to Walter Baddey who recognized that there 57 00:04:19,162 --> 00:04:24,562 are really two very different kinds of pulsating stars, one of which is confused 58 00:04:24,562 --> 00:04:29,287 for the other, and he came up with the concept of stellar populations. 59 00:04:29,287 --> 00:04:33,112 That immediately halved the value of Hubble's constant. 60 00:04:33,112 --> 00:04:37,940 Then improved measurements. Pushed it further down, and down. 61 00:04:37,940 --> 00:04:44,305 And in 1970's, it go down to the range of, between roughly 50 and 100 kilometers 62 00:04:44,305 --> 00:04:49,610 per second, per mega-parsec. There were two prominent schools of 63 00:04:49,610 --> 00:04:53,662 thought on this. One, led by Allen Sandage, the. 64 00:04:53,662 --> 00:04:59,032 The disciple of Hubble, pushed for the lower values, around 50 kilometers per 65 00:04:59,032 --> 00:05:02,289 second per megaparsec. The other one, led by Gerard de 66 00:05:02,289 --> 00:05:07,300 Vaucouleurs and his collaborators in Texas and elsewhere, pushed for twice 67 00:05:07,300 --> 00:05:11,125 that much, about 100 kilometers per second per megaparsec. 68 00:05:11,125 --> 00:05:14,407 And the 2 just could not just get into an agreement. 69 00:05:14,407 --> 00:05:19,276 The reasons for this were the. They made different assumptions, they 70 00:05:19,276 --> 00:05:24,178 used different calibrations, and things went like that until 1980's. 71 00:05:24,178 --> 00:05:27,729 But even in the modern days, the spread continued. 72 00:05:27,729 --> 00:05:33,330 People started being more careful about the error bars, and yet still the actual 73 00:05:33,330 --> 00:05:38,335 spread of quoted values in the literature was always larger error bars. 74 00:05:38,335 --> 00:05:44,028 That persisted until roughly, 1990's. There are two kinds of methods to measure 75 00:05:44,028 --> 00:05:47,484 distances. There are methods that obstensibly give 76 00:05:47,484 --> 00:05:53,038 absolute distances to particular kind of objects, like trigonometric parallax for 77 00:05:53,038 --> 00:05:58,420 stars, or using physical models to derive distances to supernovae or clusters of 78 00:05:58,420 --> 00:06:01,449 galaxies Galaxies. Parallax is the only safe one. 79 00:06:01,449 --> 00:06:04,937 The geometry is well-understood, and there are no problems. 80 00:06:04,937 --> 00:06:09,634 However, we cannot measure parallaxes of stars more than about kiloparsec from us 81 00:06:09,634 --> 00:06:15,467 now, well within sight of our own galaxy. There is so-called moving cluster method, 82 00:06:15,467 --> 00:06:18,747 but that relies on statistics and certain assumptions. 83 00:06:18,747 --> 00:06:22,897 There is so-called Baade-Wesselink method that uses pulsating stars. 84 00:06:22,897 --> 00:06:27,802 That too makes assumptions about stellar atmospheres and thing, things like that. 85 00:06:27,802 --> 00:06:31,823 A very simliar to it, is so called expanding photosphere method for 86 00:06:31,823 --> 00:06:34,606 supernova. They are one also has to make some, 87 00:06:34,606 --> 00:06:39,287 non-trivial assumptions, about physics, of what's really an exploding star. 88 00:06:39,287 --> 00:06:43,217 Pushing further into Hubble flow, there are 2 important methods. 89 00:06:43,217 --> 00:06:47,412 One is based on so called Sunyaev-Zeldovich effect, which measures 90 00:06:47,412 --> 00:06:52,727 Distances to clusters of galaxies using observations of cosmic microbackground. 91 00:06:52,727 --> 00:06:57,857 And of the x ray mission from clusters. We will talk about those in more detail. 92 00:06:57,857 --> 00:07:01,660 And the other one is using gravitational lens time delays. 93 00:07:01,660 --> 00:07:04,358 We will also address that one in due time. 94 00:07:04,358 --> 00:07:08,452 The other kind of distance indicators is the secondary ones. 95 00:07:08,452 --> 00:07:11,441 Which require callibration from somewhere else. 96 00:07:11,441 --> 00:07:15,987 They can be used to measure relative distances say things there are objects 97 00:07:15,987 --> 00:07:20,784 which may be further away but there zero point has to be obtained from something 98 00:07:20,784 --> 00:07:23,538 else. And there are many of those, both using 99 00:07:23,538 --> 00:07:26,401 stars and galaxies and we will address them all. 100 00:07:26,401 --> 00:07:30,877 So here is schematically what the distance ladder is like Each method, 101 00:07:30,877 --> 00:07:34,767 operates in certain range of possible, plausible distances. 102 00:07:34,767 --> 00:07:39,647 And hopefully it overlaps in part, at least, with another method, which then 103 00:07:39,647 --> 00:07:44,062 can reach deeper, and so on. That is what we call the distance ladder. 104 00:07:44,062 --> 00:07:48,892 Nearest to us, trigonometric parallaxes, can be used to measure distances. 105 00:07:48,892 --> 00:07:51,622 Proper motions of stars, can also be used. 106 00:07:51,622 --> 00:07:55,959 Looking at statistical sense. Then we can measure distances to some of 107 00:07:55,959 --> 00:07:59,931 the nearby star clusters. And use properties of star clusters to 108 00:07:59,931 --> 00:08:02,715 measure distances to even more distant ones. 109 00:08:02,715 --> 00:08:07,324 In particular, this leads to measurement to distances to pulsating stars. 110 00:08:07,324 --> 00:08:12,459 Cephids and so called RR-Lyrae Stars, which are key step in the measurements of 111 00:08:12,459 --> 00:08:16,512 the Hubble Constant. But notice that several steps precede. 112 00:08:16,512 --> 00:08:20,909 With those, we can measure distances to a number of nearby galaxies. 113 00:08:20,909 --> 00:08:25,277 And then we can calibrate distance indicator relations for galaxies 114 00:08:25,277 --> 00:08:28,221 themselves. Those are correlations between 2 115 00:08:28,221 --> 00:08:31,691 quantities. One of which does not depend on distance. 116 00:08:31,691 --> 00:08:36,305 Say, rotational speed of a galaxy. And the other one of which does, like 117 00:08:36,305 --> 00:08:40,459 luminosity. So these important distance relations can 118 00:08:40,459 --> 00:08:46,420 be used to measure distances to galaxies far away, but they have to be calibrated 119 00:08:46,420 --> 00:08:51,609 locally, with something else. Then super novae come in, and those are 120 00:08:51,609 --> 00:08:56,362 currently favorite ways of measuring distances in cosmology. 121 00:08:56,362 --> 00:08:59,501 From near to far. We will cover them in some detail. 122 00:08:59,501 --> 00:09:04,231 Once we go beyond the regime where it's easy to do galaxy distance indicators, 123 00:09:04,231 --> 00:09:07,789 two other methods come in, on really cosmological scales. 124 00:09:07,789 --> 00:09:11,699 The Sunyaev–Zel'dovich effect, and the Gravitational Lensing. 125 00:09:11,699 --> 00:09:16,161 In principle, they do not depend on the distance ladder, however they are 126 00:09:16,161 --> 00:09:20,804 model-dependent. And therefore, previous calibrations are 127 00:09:20,804 --> 00:09:25,243 important as a check. So, here is a schematic flow chart. 128 00:09:25,243 --> 00:09:31,286 It's not there to confuse you, it's just to show you, a little bit, how complex 129 00:09:31,286 --> 00:09:37,080 the network of measurments has to be, with mutual checks to find out how far 130 00:09:37,080 --> 00:09:40,182 things are in the universe. It starts. 131 00:09:40,182 --> 00:09:45,548 With nearer stars and goes all the way to supernovean and cosmological, truely 132 00:09:45,548 --> 00:09:49,749 cosmological scale. Well that's it for now, next time we will 133 00:09:49,749 --> 00:09:53,079 actually talk about stellar distance indicators.