1 00:00:00,012 --> 00:00:05,010 We will now talk about gravitational lensing, which is a very powerful 2 00:00:05,010 --> 00:00:10,731 technique to find about distribution of mass in the universe, whether it's 3 00:00:10,731 --> 00:00:14,408 visible or not. As you will recall from the general 4 00:00:14,408 --> 00:00:20,235 relativity, it predicts that the presence of the mass, again whether you can see 5 00:00:20,235 --> 00:00:26,152 it, invisible light or not, will distort the paths of the light rays passing by. 6 00:00:26,152 --> 00:00:32,351 Therefore we have a method of learning about mass distribution, regardless of 7 00:00:32,351 --> 00:00:37,507 whether we can see it in any way. this was originally considered, 8 00:00:37,507 --> 00:00:44,137 considered by Chowlson and Einstein, and also Zwicky, but it took until the 1979 9 00:00:44,137 --> 00:00:49,317 to find the first real example. This was measurement of a quasar, which 10 00:00:49,317 --> 00:00:52,712 we have to have 2 images which are just mirages. 11 00:00:52,712 --> 00:00:58,342 They're both the same quasar and after that hundreds if not thousands of lenses 12 00:00:58,342 --> 00:01:02,477 have been found. So, the geometry shown here, if we have a 13 00:01:02,477 --> 00:01:07,652 perfect alignment of the observer, the background source and the lens. 14 00:01:07,652 --> 00:01:13,052 And distributional symmetric, then each azimuth will be equal and, and so the 15 00:01:13,052 --> 00:01:18,177 image of the background object will be now distorted in to a ring, called the 16 00:01:18,177 --> 00:01:21,766 Einstein ring. If we deviate from that symmetry, either 17 00:01:21,766 --> 00:01:26,085 by moving the lens a little bit in the lens plane, or by changing the mass 18 00:01:26,085 --> 00:01:29,396 distribution to be asymmetric, the ring will break up, 19 00:01:29,396 --> 00:01:32,443 and we'll see multiple images of the lens source. 20 00:01:32,443 --> 00:01:36,951 and this is indeed what's seen in a case of multiple image gravitationalized 21 00:01:36,951 --> 00:01:40,449 quasar. So Zwicky already in 1937 predicted that 22 00:01:40,449 --> 00:01:45,894 gravitational lensing should not only be detected, but it can be used to probe 23 00:01:45,894 --> 00:01:51,364 mass distribution in galaxies in the universe, as well as to use clusters or 24 00:01:51,364 --> 00:01:56,809 galaxies as telescopes to magnify more even distant ones and after all, it can 25 00:01:56,809 --> 00:02:01,864 also be used to test the theory of gravity, all of those predictions have 26 00:02:01,864 --> 00:02:04,953 come true. As far as measuring masses using 27 00:02:04,953 --> 00:02:10,194 gravitational lensing, that took until the 1990's, and Hubble Space Telescope, 28 00:02:10,194 --> 00:02:12,951 in order to be able to really do this well. 29 00:02:12,951 --> 00:02:18,290 These are Hubble Space Telescope images of a particular cluster, that serves as a 30 00:02:18,290 --> 00:02:21,996 gravitational lens. All of these blue arches, arcs and 31 00:02:21,996 --> 00:02:27,387 arclets are images of background galaxies that have been lensed by this cluster, 32 00:02:27,387 --> 00:02:32,661 split and distorted, and thus the cluster itself is essentially a gigantic lens in 33 00:02:32,661 --> 00:02:35,772 space that magnifies and distorts their images. 34 00:02:35,772 --> 00:02:40,950 From the distribution and shape of these arcs and arclets, one can reconstruct the 35 00:02:40,950 --> 00:02:45,632 mass distribution in the cluster regardless of where the galaxies are. 36 00:02:45,632 --> 00:02:50,835 So the gravitational bending of light in general of theory is twice what you heard 37 00:02:50,835 --> 00:02:54,944 from the utonian gravity. Most importantly if it's achromatic, 38 00:02:54,944 --> 00:02:58,840 protons in any wavelength are deflected in exactly same way. 39 00:02:58,840 --> 00:03:02,385 And this is unlike say, plans that were made out of box. 40 00:03:02,385 --> 00:03:06,807 This adds to the power of the method because it's been used not just in 41 00:03:06,807 --> 00:03:09,952 invisible light but in radio and also x-rays. 42 00:03:09,952 --> 00:03:14,583 Obviously the effects would be the strongest for the strongest gravitational 43 00:03:14,583 --> 00:03:17,300 field. and the strongest you can get is if you 44 00:03:17,300 --> 00:03:21,924 compress the lens mass into a black hole. Then you get maximum effect right at 45 00:03:21,924 --> 00:03:25,474 Schwarzschild radius, but in reality that doesn't happen. 46 00:03:25,474 --> 00:03:30,378 Most of the physical objects in galixies are clusters are vastly larger than their 47 00:03:30,378 --> 00:03:34,122 Schwarzschild radii, so the effect isn't quite as strong. 48 00:03:34,122 --> 00:03:37,062 Here is a simple schematic geometry shown. 49 00:03:37,062 --> 00:03:42,177 It is fairly obvious there is observer, the lengths and the source in the 50 00:03:42,177 --> 00:03:47,795 background and destortion of the light path shown here that straight lines must 51 00:03:47,795 --> 00:03:53,646 really curve can be respresented as the angle by which, between the direction to 52 00:03:53,646 --> 00:03:58,210 the lens and the lens image. All these angles are small, usually arc 53 00:03:58,210 --> 00:04:02,916 seconds, or even fractions thereof, and so small angle approximations apply. 54 00:04:02,916 --> 00:04:07,622 There is some fairly straightforward geometry, that then, you can derive from 55 00:04:07,622 --> 00:04:11,825 here, and in the end, you have a quadratic equation that describes the 56 00:04:11,825 --> 00:04:15,862 deflection of light rays, in this particular geometrical setting. 57 00:04:15,862 --> 00:04:21,363 We can simplify that expression a little bit, by introducing Acquainted he called 58 00:04:21,363 --> 00:04:27,559 the Einstein radius, it's really an angle, angular radius if you will and 59 00:04:27,559 --> 00:04:33,078 it's given by this formula. Essentially this is the characteristic 60 00:04:33,078 --> 00:04:39,872 radius in projection away from the lens where distortions will be strongest and. 61 00:04:39,872 --> 00:04:44,937 It may not be a perfect circle, depending on the mass distribution, so the, the 62 00:04:44,937 --> 00:04:50,090 line that connects points to satisfy this criterion, regardless of whatever the 63 00:04:50,090 --> 00:04:53,155 mass distribution is, is called critical line. 64 00:04:53,155 --> 00:04:58,362 Generally speaking, for deflections within Einstein radius or thereabouts, 65 00:04:58,362 --> 00:05:02,385 the, you'll see multiple images, that's called strong lens. 66 00:05:02,385 --> 00:05:07,528 for deflections further out you'll see only distortions but generally not 67 00:05:07,528 --> 00:05:11,086 multi-split images, that's called the weak lensing regime. 68 00:05:11,086 --> 00:05:16,108 So quadratic equation is not shown very simply and it has 2 obvious solutions 69 00:05:16,108 --> 00:05:20,612 that, this is high school math. And so, in the cases where a lens isn't 70 00:05:20,612 --> 00:05:25,187 perfectly aligned, there are at least two solutions, corresponds to, to different 71 00:05:25,187 --> 00:05:27,897 images. One inside, and one outside the Einstein 72 00:05:27,897 --> 00:05:30,557 radius. I mentioned different lensing regimes. 73 00:05:30,557 --> 00:05:34,832 If the deflection is strong, hence the image splitting, that is called strong 74 00:05:34,832 --> 00:05:38,047 lensing regime. however, deflections will occur even 75 00:05:38,047 --> 00:05:42,422 further out, and obviously, the further out you go, the weaker the effect. 76 00:05:42,422 --> 00:05:46,902 But, nevertheless, they'll be detectable in the form of image distortion. 77 00:05:46,902 --> 00:05:51,395 And that's called the weak lensing urgings, that turns out to be a very 78 00:05:51,395 --> 00:05:54,790 important for studies of cluster mass distribution. 79 00:05:54,790 --> 00:05:59,024 If you can map all of the distorted images, you can, in principle, 80 00:05:59,024 --> 00:06:04,335 reconstruct the distribution of mass that led to the lensing This has been done on 81 00:06:04,335 --> 00:06:09,989 galaxies as well as cluster with galaxies we're talking about something in the of 82 00:06:09,989 --> 00:06:14,507 the order of an arc second. Observations with Hubel telescopes were 83 00:06:14,507 --> 00:06:18,161 essential to do this. A particular group called SLACS 84 00:06:18,161 --> 00:06:22,672 collaboration is one of them. they studied fairly large sample of 85 00:06:22,672 --> 00:06:27,658 galaxies acting as lenses to some background galaxies that appearing as are 86 00:06:27,658 --> 00:06:32,836 thin lenses or as segments thereof, and with some reasonable assumptions they can 87 00:06:32,836 --> 00:06:37,396 infer the mass distributions in projection for the lensing galaxies. 88 00:06:37,396 --> 00:06:41,842 The results are sh, shown schematically here for a handful of cases. 89 00:06:41,842 --> 00:06:47,727 The lines on the plots describe density distribution as a function of radius, for 90 00:06:47,727 --> 00:06:53,300 visible matter, which is just measured stars, or other massive stars, for, the 91 00:06:53,300 --> 00:06:59,687 whole thing that causes the distortion, and the difference which represents 92 00:06:59,687 --> 00:07:05,194 contribution of the dark matter halo. as you can see, a smaller radii, visible 93 00:07:05,194 --> 00:07:10,353 material dominates, something we already learned from kinematical studies. 94 00:07:10,353 --> 00:07:15,859 As you go further out in radius, the dark matter component becomes inevitable, and 95 00:07:15,859 --> 00:07:19,717 dominates the geometry. We can simulate the effects of 96 00:07:19,717 --> 00:07:25,559 gravitationalizing, by taking an image of the sky, placing fictitious lens of given 97 00:07:25,559 --> 00:07:31,066 mass distribution in front, and seeing what it will do to the picture behind it. 98 00:07:31,066 --> 00:07:36,036 From that, we can then learn how to invert actual observations to derive 99 00:07:36,036 --> 00:07:39,202 distribution of mass That is doing the lensing. 100 00:07:39,202 --> 00:07:43,517 These are simulations so you can see that clearly that the effects are the 101 00:07:43,517 --> 00:07:47,792 strongest in the middle and get weaker and weaker the further out you go. 102 00:07:47,792 --> 00:07:50,812 This is another simulatio used to illustrate this. 103 00:07:50,812 --> 00:07:54,732 Imagine that somehow there is a gigantic graph paper in the sky. 104 00:07:54,732 --> 00:07:59,466 and then you put a cluster of galaxies in front of it, then it will distort the 105 00:07:59,466 --> 00:08:04,261 geometry of the background as shown here. It is complicated because it's not a 106 00:08:04,261 --> 00:08:08,641 simple, simple mass distribution. There are many different galaxies. 107 00:08:08,641 --> 00:08:12,545 Each of them acts like little lensing, in, you know, of itself, and together 108 00:08:12,545 --> 00:08:16,814 they have a collective effect. So inverting these geometries can be a 109 00:08:16,814 --> 00:08:20,775 very complicated business. Nevertheless, the metal is well 110 00:08:20,775 --> 00:08:24,318 understood now and a lot of good data have been obtained. 111 00:08:24,318 --> 00:08:27,717 Many clusters have been studied using this technique. 112 00:08:27,717 --> 00:08:32,414 Here is an example of a particular cluster, where different contours show, 113 00:08:32,414 --> 00:08:35,222 say, average distribution of galaxy light, 114 00:08:35,222 --> 00:08:40,572 or the number density, or the inferred galaxy mass, or mass distribution for the 115 00:08:40,572 --> 00:08:43,717 whole cluster. This was done for quite a number of 116 00:08:43,717 --> 00:08:46,252 clusters. A small subset is shown here, 117 00:08:46,252 --> 00:08:50,567 and lensing gives a new independent estimate of the lensing mass in a 118 00:08:50,567 --> 00:08:55,492 cluster, regardless of whether it's baryons, or dark baryons, or dark matter 119 00:08:55,492 --> 00:08:59,205 or anything. As long as it's some matter of any kind 120 00:08:59,205 --> 00:09:02,940 that exerts gravitational pull, it will contribute. 121 00:09:02,940 --> 00:09:08,385 And remarkably enough, the inferred mass to light ratios for clusters, are in 122 00:09:08,385 --> 00:09:13,340 excellent agreement with those we inferred from using very old theorem 123 00:09:13,340 --> 00:09:17,867 arguments, from either X-ray gas or Galaxy velocity dispersion. 124 00:09:17,867 --> 00:09:22,792 This is completely different physics and different kind of measurement, 125 00:09:22,792 --> 00:09:28,067 and this is why we believe, that indeed, there is some kind of dark mass there. 126 00:09:28,067 --> 00:09:33,965 We see its effects not just in kinematics of test particles like galaxies or 127 00:09:33,965 --> 00:09:40,480 protons or electrons but also in manifestations of general activity. 128 00:09:40,480 --> 00:09:45,842 The geometry of the images seen as the lensing mass. 129 00:09:45,842 --> 00:09:50,662 For this reason, people really believe that we are, indeed, dealing with dark 130 00:09:50,662 --> 00:09:53,106 matter, and it's not something like the 131 00:09:53,106 --> 00:09:56,935 distortion of gravity, because that will spoil gravitational 132 00:09:56,935 --> 00:09:59,930 lensing, and you never get the same result as you 133 00:09:59,930 --> 00:10:02,893 would for measurements using variable care. 134 00:10:02,893 --> 00:10:07,672 This is one thing, for example, that Monde cannot possibly reproduce. 135 00:10:07,672 --> 00:10:12,152 This kind of study is, is now done not just for big clusters of galaxies, but 136 00:10:12,152 --> 00:10:16,932 just in general deep field surveys, where we measure a lot of faint galaxies, and 137 00:10:16,932 --> 00:10:19,902 sometimes get measurements of their redshifts. 138 00:10:19,902 --> 00:10:24,900 The, what's shown here is a snapshot from one such survey called COSMOS, and what's 139 00:10:24,900 --> 00:10:29,340 show on the left is the smoother distribution of light that's observing 140 00:10:29,340 --> 00:10:31,980 galaxies. What's shown on the right is the 141 00:10:31,980 --> 00:10:36,809 reconstructed distribution of mass in projection that is determined from the 142 00:10:36,809 --> 00:10:40,632 distortions of the images of galaxies in the background. 143 00:10:40,632 --> 00:10:45,552 Because, they measured distance's to galaxies, then they can actually 144 00:10:45,552 --> 00:10:51,344 constructed 3-dimensional dark matter in space, and the resolution isn't very good 145 00:10:51,344 --> 00:10:55,698 still, but here it is. It's actually remarkable that we can map 146 00:10:55,698 --> 00:11:00,747 mass distribution in space, because the physiological distances in full 147 00:11:00,747 --> 00:11:04,432 3-dimension's, even though we don't see the mass. 148 00:11:04,432 --> 00:11:09,320 This is likely to become a very powerful tool in our underst, our understanding of 149 00:11:09,320 --> 00:11:12,911 structure formation. Next we will talk about Gravitational 150 00:11:12,911 --> 00:11:16,131 Microlensing. That's lensing of stars by stars and it 151 00:11:16,131 --> 00:11:19,590 was used to constrain contributions of matches to the dark mass.