1 00:00:00,012 --> 00:00:05,100 We now turn to the subject of Evolution of Galaxy Clustering. 2 00:00:05,100 --> 00:00:11,046 But before we get into that subject proper, we have to introduce another 3 00:00:11,046 --> 00:00:14,967 concept. This is the concept of galaxy biasing 4 00:00:14,967 --> 00:00:20,202 which we did mention before. And the way it works is like this. 5 00:00:20,202 --> 00:00:27,138 In principle, visible material, galaxies, stars in them, may not be distributed in 6 00:00:27,138 --> 00:00:33,637 exactly the same way as the dark matter. It turns out that by and large they are, 7 00:00:33,637 --> 00:00:37,187 but at some scales that may not be the case. 8 00:00:37,187 --> 00:00:44,222 And so we simply Introduce the possibility that density contrast in variance is some 9 00:00:44,222 --> 00:00:48,817 factor b times the density contrast in the dark matter. 10 00:00:48,817 --> 00:00:56,196 And, when expressed through the two point correlation function, then the correlation 11 00:00:56,196 --> 00:01:03,367 function of visible material, is factor of b squared times the correlation function 12 00:01:03,367 --> 00:01:07,945 of the dark matter. Note that There is no assumption that one 13 00:01:07,945 --> 00:01:12,225 is stronger than the other. If B is greater than 1 than baryons, or 14 00:01:12,225 --> 00:01:17,250 visible light are plus or more strongly than dark matter, it's less than 1 and the 15 00:01:17,250 --> 00:01:20,519 other way. And so, it is possible that the visible 16 00:01:20,519 --> 00:01:26,207 material is not entirely representative of the underlying mass distribution, but it 17 00:01:26,207 --> 00:01:30,543 gives you a biases answer and does, does the name of Galaxy bias. 18 00:01:30,543 --> 00:01:35,800 Now, one, why could that be? And so one possibility is that as the 19 00:01:35,800 --> 00:01:42,687 structure forms, it forms in density peaks of the primordial density field and it may 20 00:01:42,687 --> 00:01:47,375 start forming faster or go further in the densest spots. 21 00:01:47,375 --> 00:01:51,754 So those would be the high peaks of the density field. 22 00:01:51,755 --> 00:01:56,931 Instead of average or one sigma deviations or two sigma deviations. 23 00:01:56,931 --> 00:02:02,841 This could be five sigma deviations. And that turns out that for just about any 24 00:02:02,841 --> 00:02:09,573 type of noise it is true that the highest density peaks are clustered more strongly. 25 00:02:09,574 --> 00:02:15,944 So here is an example of this. Lets take just, exaggerated density cut 26 00:02:15,944 --> 00:02:22,472 through a density field in your universe and you can think of it as small scale 27 00:02:22,472 --> 00:02:27,496 fluctuations riding on top of large scale fluctuations. 28 00:02:27,497 --> 00:02:32,366 Or large scale fluctuations lifting the small ones even further. 29 00:02:32,366 --> 00:02:38,424 So if you impose a threshold and saying it has to be at least this dense for galaxies 30 00:02:38,424 --> 00:02:44,387 to really form, to ignite star formation and so on, then it's those fluctuations 31 00:02:44,387 --> 00:02:49,665 that are lifted by the large waves. That will start doing it first. 32 00:02:49,665 --> 00:02:56,056 And, by the construction of this, they will be clustered strongly together. 33 00:02:56,056 --> 00:03:02,762 And so you'd expect, then, that the first structure galaxies form in the highest 34 00:03:02,762 --> 00:03:07,231 spot of the density field. Deepest potential wells. 35 00:03:07,231 --> 00:03:12,360 And that you might see a formation of proto-clusters on the other hand. 36 00:03:12,360 --> 00:03:17,894 On the hand there could be proto-voids which are negative fluctuations. 37 00:03:17,894 --> 00:03:21,598 Things that are less dense than the other places. 38 00:03:21,599 --> 00:03:27,348 Let me give you a metaphor for this. Imagine asking that one the planet earth, 39 00:03:27,348 --> 00:03:31,205 what are the highest points. Above the sea level. 40 00:03:31,205 --> 00:03:36,887 And, if you are to put that cut at few kilometers elevation, you'll find out that 41 00:03:36,887 --> 00:03:42,219 all of them are concentrated in areas like Rocky Mountains or Himalayas or 42 00:03:42,219 --> 00:03:46,611 Cordilleras and so on. And then as you slowly lower down the 43 00:03:46,611 --> 00:03:49,718 threshold. More and more lands enclosed and 44 00:03:49,718 --> 00:03:53,481 eventually the entire surface of the planet is enclosed. 45 00:03:53,481 --> 00:03:58,723 Same thing here, the highest points will be by nature clustered together because 46 00:03:58,723 --> 00:04:03,138 they correspond to smaller fluctuations. A top of larger ones. 47 00:04:03,138 --> 00:04:08,966 Here is a direct illustration of this, not from real universe, but from simulated one 48 00:04:08,966 --> 00:04:13,410 done by Ray Carlberg. So, he followed formation of the structure 49 00:04:13,410 --> 00:04:19,082 and then asked, there is an average value of the density and their deviations of it. 50 00:04:19,082 --> 00:04:24,582 So what is the distribution of all data points and just those that are higher than 51 00:04:24,582 --> 00:04:28,552 1 sigma above the mean? 2 sigma, 3 sigma and you can see as you 52 00:04:28,552 --> 00:04:33,663 increase the threshold that they get to be clustered more and more strongly. 53 00:04:33,663 --> 00:04:36,762 They'll pile up in just 1 part of, of the slice. 54 00:04:36,762 --> 00:04:40,078 So now we can estimate this from redshift surveys. 55 00:04:40,078 --> 00:04:45,089 The redshift surveys as you recall will give us actual measurement of the mass 56 00:04:45,089 --> 00:04:50,116 distribution because. By the coupling Hubble expansion peculiar 57 00:04:50,116 --> 00:04:56,217 velocities, we can find out where the mass really is that causes galaxies to move. 58 00:04:56,217 --> 00:04:59,516 And, we can also see where the galaxies are. 59 00:04:59,516 --> 00:05:04,802 So we can directly compare the distribution inferred from the redshift 60 00:05:04,802 --> 00:05:11,324 surveys with those of galaxies themselves. And so here is a plot from slong retro sky 61 00:05:11,324 --> 00:05:16,870 survey, and he plots the value of the, of the bias as a function of galaxy 62 00:05:16,870 --> 00:05:20,485 luminosity. And you find out that, past certain 63 00:05:20,485 --> 00:05:26,997 luminosity, clustering grows dramatically, more luminous galaxies are Fostered more 64 00:05:26,997 --> 00:05:30,114 strongly. And this makes sense in the previously 65 00:05:30,114 --> 00:05:34,806 described scenario because the earliest forming ones will eventually grow to be 66 00:05:34,806 --> 00:05:39,429 the largest ones and they did form at, at the highest peaks of the denisty field and 67 00:05:39,429 --> 00:05:43,817 they will be clustered more strongly. As it turns out, this is also the case 68 00:05:43,817 --> 00:05:47,420 with all redshifts and it's even stronger at high redshifts. 69 00:05:47,420 --> 00:05:50,716 So now let's look at evolution of clustering itself. 70 00:05:50,717 --> 00:05:57,217 Generally speaking, you expect clustering to grow in time as the structures collapse 71 00:05:57,217 --> 00:06:02,309 to density contrast increases. Remember, it starts as a few parts in a 72 00:06:02,309 --> 00:06:08,117 million at the time of the recombination and now grows to factor of a million in, 73 00:06:08,117 --> 00:06:12,686 in galaxies themselves or few 100 in a large scale structure. 74 00:06:12,686 --> 00:06:16,586 So. The general expectation is that clustering 75 00:06:16,586 --> 00:06:22,687 has to get stronger in time or conversely, it'll be weaker at higher redshifts. 76 00:06:22,687 --> 00:06:27,996 A way to quantify this is to follow the 2 point correlation function. 77 00:06:27,996 --> 00:06:33,042 And a simple model is shown here, it changes the aptitude of correlation 78 00:06:33,042 --> 00:06:36,949 function or some power of the expansion factor 1 plus z. 79 00:06:36,949 --> 00:06:42,493 And it's written in the following form so different values of this parameter epsilon 80 00:06:42,493 --> 00:06:46,492 correspond to different types of clustering evolution as. 81 00:06:46,492 --> 00:06:50,511 Indicated here. If epsilon is equal to minus 1.2, then the 82 00:06:50,511 --> 00:06:53,689 plus string is fixed in comoving coordinates. 83 00:06:53,689 --> 00:06:56,469 It doesn't change. It just expands. 84 00:06:56,469 --> 00:07:01,438 If epsilon is 0, then clustering is fixed in proper coordinates. 85 00:07:01,438 --> 00:07:06,238 The universe expands but the structures stay just as they are. 86 00:07:06,238 --> 00:07:11,456 And, pushing further if epsilon is positive, that means the clustering will 87 00:07:11,456 --> 00:07:14,821 grow in time, in proper coordinates themselves. 88 00:07:14,821 --> 00:07:19,174 And the observation indicate that, that's in, indeed the case. 89 00:07:19,174 --> 00:07:24,364 But, any one single value of epsilon describes this process at all different 90 00:07:24,364 --> 00:07:26,829 scales. So let's look at some data. 91 00:07:26,829 --> 00:07:32,207 What's plotted here is the amplitude of projected angular two point correlation 92 00:07:32,207 --> 00:07:35,396 function, as a function of depth of the serving. 93 00:07:35,396 --> 00:07:38,927 Now the deeper you look the fainter galaxies you see. 94 00:07:38,927 --> 00:07:42,579 And so on average, fainter galaxies are further away. 95 00:07:42,579 --> 00:07:46,068 At higher edges. And you can see that this it's exactly 96 00:07:46,068 --> 00:07:49,562 what you expect. As you go deeper, meaning further, the 97 00:07:49,562 --> 00:07:54,857 strength of the clustering diminishes. But because we actually have redshifts for 98 00:07:54,857 --> 00:07:59,657 those, we can follow the, follow the strength of the clustering as a function 99 00:07:59,657 --> 00:08:02,051 of redshift. And here it's plotted. 100 00:08:02,051 --> 00:08:08,270 As clustering length are not, which you may recall, is work correlation function 101 00:08:08,270 --> 00:08:14,194 has amplitude of 1 and it's about 5 megaparsec divided by little h, near us. 102 00:08:14,194 --> 00:08:17,758 And, then as you go deeper redshift, it goes down. 103 00:08:17,758 --> 00:08:21,592 The lower clustering length means weaker clustering. 104 00:08:21,592 --> 00:08:27,142 And so, here are the redshifts of about unity or slightly beyond this is exactly 105 00:08:27,142 --> 00:08:31,279 what we expect, but then something interesting happens. 106 00:08:31,279 --> 00:08:36,779 Going to larger redshifts, past redshift of 1, the clustering start increasing 107 00:08:36,779 --> 00:08:42,191 again with redshift meaning it's been decreasing in time, which is exactly the 108 00:08:42,191 --> 00:08:46,683 opposite of what you expect. So, even in the deepest redshift survey 109 00:08:46,683 --> 00:08:51,927 measurements over very small fields going very deep, pencil being surveys, we see 110 00:08:51,927 --> 00:08:57,095 spikes, as you may recall by having pencil being survey going through large scale 111 00:08:57,095 --> 00:09:01,807 structure, spikes correspond to intersections with filaments or void in 112 00:09:01,807 --> 00:09:04,399 sun. And here you see them occurring of 113 00:09:04,399 --> 00:09:07,202 redshifts of three or four and even beyond. 114 00:09:07,202 --> 00:09:12,521 Turns out, the strength of clustering back then when the universe was only a couple 115 00:09:12,521 --> 00:09:16,401 gill, couple giga-years old is about the same as it is today. 116 00:09:16,401 --> 00:09:20,180 So the clustering got weaker, and then got stronger again. 117 00:09:20,180 --> 00:09:24,465 And it's not just galaxies. You could use quazars, which we can see 118 00:09:24,465 --> 00:09:27,291 very far away, and they tell the same story. 119 00:09:27,291 --> 00:09:32,753 Beyond redshifts of one, going to higher redshifts, clustering strength increases. 120 00:09:32,753 --> 00:09:38,521 Exactly the opposite from your What you expect from naiive picture of structure 121 00:09:38,521 --> 00:09:41,537 formation. So how can this possibly be? 122 00:09:41,537 --> 00:09:45,894 And the answer is it's due to the evolution of bias itself. 123 00:09:45,894 --> 00:09:50,576 And here is how it works. Consider the fate of fluctuations of 124 00:09:50,576 --> 00:09:56,855 different amplitude, here shown with thin black lines and dashed red lines the 125 00:09:56,855 --> 00:10:02,679 highest fluctuations say 5 sigma lines will evolve fastest, they will reach 126 00:10:02,679 --> 00:10:09,231 higher values sooner, the lower contract fluctuations will get there eventually but 127 00:10:09,231 --> 00:10:15,237 takes longer time Now if the structures form according to the biased contrast, 128 00:10:15,237 --> 00:10:21,131 then as you look back is you'll be looking at different type of fluctuations. 129 00:10:21,131 --> 00:10:26,191 Nearest you might be looking at 1 or 2 signal fluctuations to see which. 130 00:10:26,192 --> 00:10:30,649 Clustered however they are. If you work, be, if you could follow them 131 00:10:30,649 --> 00:10:36,031 to higher redshifts, you would see that they, their clustering indeed was lower at 132 00:10:36,031 --> 00:10:38,279 larger redshifts. But you don't. 133 00:10:38,279 --> 00:10:42,997 You'll see structures that are corresponding to higher contrast as you go 134 00:10:42,997 --> 00:10:46,941 to deeper redshifts. Against two sigma peaks, you may be 135 00:10:46,941 --> 00:10:51,823 looking at five sigma peaks because that's where galaxies are back then. 136 00:10:51,823 --> 00:10:56,604 And those peaks were clustered more strongly, in other words, at different 137 00:10:56,604 --> 00:11:01,562 redshifts, you're looking at a different sample of objects and this is again why 138 00:11:01,562 --> 00:11:06,344 this is called biased galaxy clustering. So this is almost certainly what's 139 00:11:06,344 --> 00:11:09,548 happening. By working at high redshifts, we're 140 00:11:09,548 --> 00:11:14,327 looking at the highest peaks of the density field and they're strongly 141 00:11:14,327 --> 00:11:19,511 clustered and then as you look at lower ratchets, then you see lower contrast 142 00:11:19,511 --> 00:11:24,551 peaks and they're clustered less. And this is why there is an apparent 143 00:11:24,551 --> 00:11:27,992 effect of clustering getting weaker in time. 144 00:11:27,992 --> 00:11:31,930 It's not. It's just that you are changing the sample 145 00:11:31,930 --> 00:11:37,754 to which you're looking at, from say 5 sigma peaks to 3, 2 sigma peaks and so on, 146 00:11:37,754 --> 00:11:40,536 but all of them increase. In time. 147 00:11:40,536 --> 00:11:45,726 Each of these density contreras, get ho, stronger in time, it's just that the 148 00:11:45,726 --> 00:11:50,512 highest ones get there first. And indeed, this can be proved with large 149 00:11:50,512 --> 00:11:55,552 deep regid surveys and here is a result from one of them from European Sultan 150 00:11:55,552 --> 00:12:00,444 Observatory deep survey. It shows the value of the effective, or 151 00:12:00,444 --> 00:12:06,541 average, biased parameter for galaxies, starting from retch of unity to about 1 152 00:12:06,541 --> 00:12:10,356 and a half. And you can see that it was higher in the 153 00:12:10,356 --> 00:12:14,007 past. So galaxies near us are almost an unbiased 154 00:12:14,007 --> 00:12:18,898 tracer of underlying mass. Near us when we look at large scale 155 00:12:18,898 --> 00:12:25,785 structures, as painted by galaxies we see exactly how the dark matter is distributed 156 00:12:25,785 --> 00:12:29,547 as well. But as we go deeper in the past, higher 157 00:12:29,547 --> 00:12:33,437 ridges, then we see a. A more biased set of tracers. 158 00:12:33,437 --> 00:12:38,657 Galaxies are more clustered than the underlying dark matter back then because 159 00:12:38,657 --> 00:12:43,634 it's those that are higher density contrast that lighted up and so these are 160 00:12:43,634 --> 00:12:46,686 what you see. So to summarize the evolution of 161 00:12:46,686 --> 00:12:51,584 clustering and bias, the generic expectation is that clustering grows in 162 00:12:51,584 --> 00:12:55,484 time, and it does. But the rate at which it does depends on 163 00:12:55,484 --> 00:12:59,618 the mass or the density contrast of the initial conditions. 164 00:12:59,618 --> 00:13:02,807 The type of the objects that you're following. 165 00:13:02,807 --> 00:13:06,123 And it's fastest for the highest-contrast ones. 166 00:13:06,123 --> 00:13:11,738 We can quantify this through the evolution of the two point correlation function, as 167 00:13:11,738 --> 00:13:17,189 shown here, and observationally, we can follow clustering to the highest reaches 168 00:13:17,189 --> 00:13:21,401 we can probe. What we observe is always light, not mass. 169 00:13:21,401 --> 00:13:26,911 And so this is my introduce concept of biasing to allow for a possibility that 170 00:13:26,911 --> 00:13:32,329 light, visible parts of galaxies, are clustered in a different way from the 171 00:13:32,329 --> 00:13:37,729 underlying mass distribution. The simplest way of quantifying this is 172 00:13:37,729 --> 00:13:43,870 saying that they're proportional and the factor of proportionality is B, and it's 173 00:13:43,870 --> 00:13:48,137 greater than 1. If light is clustered more strongly than 174 00:13:48,137 --> 00:13:53,415 mass, and it turns out usually is. Now B is not really a constant, it is a 175 00:13:53,415 --> 00:13:59,876 function of all manner of things, not just time, but also the density contrast itself 176 00:13:59,876 --> 00:14:03,627 and so on. And there is no antalytical theory for its 177 00:14:03,627 --> 00:14:09,105 change but it is something that we can reproduce for numerical simulations and 178 00:14:09,105 --> 00:14:14,144 then compare to the observations. And it turns out that the low redshifts, 179 00:14:14,144 --> 00:14:18,186 galaxies are pretty unbiased tracer of the underlying mass. 180 00:14:18,186 --> 00:14:23,798 Galaxies have formed fully by and large. Of course they keep merging and so on, but 181 00:14:23,798 --> 00:14:29,620 as you look at higher redshifts, galaxies become an increasingly more biased tracer 182 00:14:29,620 --> 00:14:34,913 of the underlying mass distribution. That is, the deeper in the past you go, 183 00:14:34,913 --> 00:14:39,112 the more biased sample of the higher density peaks you see. 184 00:14:39,112 --> 00:14:46,558 Next, we'll talk about clusters of galaxies.