1 00:00:00,012 --> 00:00:06,484 Let's now turn to use of supernovae as a standard candle to measure distances in 2 00:00:06,484 --> 00:00:10,506 cosmology. This is today one of the most powerful 3 00:00:10,506 --> 00:00:16,326 tools in the observation of cosmology arsenal, to measure distances or 4 00:00:16,326 --> 00:00:21,307 cosmological scales. We keep using the term, standard candle. 5 00:00:21,307 --> 00:00:26,082 And this is where it comes from. Actually, there used to be such a thing 6 00:00:26,082 --> 00:00:30,232 as standard candle. And such standard candles ostensibly had 7 00:00:30,232 --> 00:00:34,407 the same brightness. Now, a supernova is a lot brighter than a 8 00:00:34,407 --> 00:00:39,782 candle, but the same concept applies. So if, somehow, a supernova or something 9 00:00:39,782 --> 00:00:44,300 else has a constant luminosity. If we put it at different distances from 10 00:00:44,300 --> 00:00:49,122 us, its brightness will decline according to inverse square law or rather, the 11 00:00:49,122 --> 00:00:53,423 relativistic version thereof. So if we can measure relative brightness 12 00:00:53,423 --> 00:00:56,577 of the standard candle, at two different distances. 13 00:00:56,577 --> 00:01:00,572 We can derive, what's the ratio of their luminosity distance. 14 00:01:00,572 --> 00:01:05,709 Similarly, if we have objects of a standard size, like a ruler is always the 15 00:01:05,709 --> 00:01:10,745 same size, and observe it at the different distances from us, the ratio of 16 00:01:10,745 --> 00:01:15,857 the angle, or diameters will be, equal to the ratio of the angular diameter 17 00:01:15,857 --> 00:01:19,172 distances. So we could use, standard rulers, to 18 00:01:19,172 --> 00:01:23,322 determine relative distances to objects we'ere looking at. 19 00:01:23,322 --> 00:01:27,882 So how are the supernovae playing this? They are certainly very bright, can be 20 00:01:27,882 --> 00:01:32,328 seen very far away which makes them useful for cosmological tools and, turns 21 00:01:32,328 --> 00:01:36,760 out, they can be actually standardized. Now, there are 2 different kinds of 22 00:01:36,760 --> 00:01:41,064 supernovae, and both can be used, although one of them is much more useful 23 00:01:41,064 --> 00:01:44,283 than the other. First, there's so called supernovae of 24 00:01:44,283 --> 00:01:47,348 type 1A. They correspond to detonating white dwarf 25 00:01:47,348 --> 00:01:51,627 stars, which have accreted too much material for their own good, either from 26 00:01:51,627 --> 00:01:55,465 their companion or by merging with another white dwarf, which causes 27 00:01:55,465 --> 00:01:59,106 instability and explosion. They're pretty good standard candles 28 00:01:59,106 --> 00:02:03,252 already, and they can be made even better using a trick that I'll show you. 29 00:02:03,252 --> 00:02:07,382 We use their light curves. Brightness is a function of time to put 30 00:02:07,382 --> 00:02:11,162 them to a standard. The other type of supernovae are type 2. 31 00:02:11,162 --> 00:02:15,082 Those are very massive stars that are at the end of their life. 32 00:02:15,082 --> 00:02:17,872 And explode, because their core collapses. 33 00:02:17,872 --> 00:02:21,227 Now, they have a much larger spread of luminosities. 34 00:02:21,227 --> 00:02:24,432 And that will not make them good standard candle. 35 00:02:24,432 --> 00:02:28,537 However, they can be used in a slightly different test called expanding 36 00:02:28,537 --> 00:02:32,781 photosphere method which is similar to the Baade-Wesselink method that we 37 00:02:32,781 --> 00:02:36,370 mentioned earlier when we were talking about pulsating stars. 38 00:02:36,370 --> 00:02:40,412 And thus they can be used as an independent check to those measurements 39 00:02:40,412 --> 00:02:44,467 made with supernovae type 1A. So here is schematically shown, the 40 00:02:44,467 --> 00:02:48,717 difference between, average light curves of the supernovae of 2 kind. 41 00:02:48,717 --> 00:02:53,122 In both cases, their brightness increases, as the star explodes, and then 42 00:02:53,122 --> 00:02:56,087 declines. But the, the shape of the light curve is 43 00:02:56,087 --> 00:03:00,712 different, because it's powered by slightly different physical mechanism. 44 00:03:00,712 --> 00:03:04,992 Supernova classification is actually a little more intricate business. 45 00:03:04,992 --> 00:03:09,332 There are these 2 basic channels. Either massive stars at the end of their 46 00:03:09,332 --> 00:03:13,662 life that exploded because they, no longer produced nuclear reactions in 47 00:03:13,662 --> 00:03:18,312 their core or white dwarfs that are pushed over their stability limit by an, 48 00:03:18,312 --> 00:03:22,572 an additional accretion. They come in many different varieties. 49 00:03:22,572 --> 00:03:27,672 In terms of spectra and so on but they still are, these 2 basic mechanisms, 50 00:03:27,672 --> 00:03:32,997 although they can manifest themselves, in a broader fundamentalogical sense. 51 00:03:32,997 --> 00:03:38,247 So type 1a Supernovae are believed to come, from detonating white dwarfs, and 52 00:03:38,247 --> 00:03:43,347 I'll tell you why that is in a moment. A white dwarf Is a low mass star that has 53 00:03:43,347 --> 00:03:46,307 shed its envelopes. Its at the end of its life. 54 00:03:46,307 --> 00:03:51,442 It, its core just slowly cooling down they are not making energy in the around 55 00:03:51,442 --> 00:03:54,772 there are not thermal nuclear reactions in the core. 56 00:03:54,772 --> 00:03:59,627 But, sometimes or often they can be in binary systems since majority of the 57 00:03:59,627 --> 00:04:04,861 stars in binary systems and if the binary is close enough and their companion, Is 58 00:04:04,861 --> 00:04:09,190 not yet, white dwarf. The gravitational field of a white dwarf 59 00:04:09,190 --> 00:04:14,620 can, pull the outer envelopes of the companion, and accrete, on the surface of 60 00:04:14,620 --> 00:04:17,744 it. Once the, mass of the white dwarf crosses 61 00:04:17,744 --> 00:04:23,124 the so called Chandrasekhar limit, which is the highest mass a white dwarf can 62 00:04:23,124 --> 00:04:27,412 have, and be stable collapse, due to the generousity pressure. 63 00:04:27,412 --> 00:04:31,338 The star explodes. Another way of dumping more matter on it 64 00:04:31,338 --> 00:04:35,857 is if there is a binary white dwarf. And they lose energy by emitting 65 00:04:35,857 --> 00:04:39,857 gravitational waves. They spiral in as the two stars merge. 66 00:04:39,857 --> 00:04:43,881 You get something that's twice a big as then what's sustainable. 67 00:04:43,881 --> 00:04:47,222 As the two stars merge, the effect is the same. 68 00:04:47,222 --> 00:04:52,122 So, we're pretty sure that type 1A suprenovae come from detonating light 69 00:04:52,122 --> 00:04:55,322 force, although this is not yet a 100% certain. 70 00:04:55,322 --> 00:04:58,997 The reasons why we think this is the case is as follows. 71 00:04:58,997 --> 00:05:04,147 There are no hydrogen lines in the explosions of type 1A supernovae. Meaing 72 00:05:04,147 --> 00:05:09,797 they have shed all of their envelopes, so it has to be an old stellar remnant which 73 00:05:09,797 --> 00:05:14,844 would be just like a white dwarf. There are also strong lines of silicon, 74 00:05:14,844 --> 00:05:20,078 which means that nuclear burning in the progenitor has to have reached at least 75 00:05:20,078 --> 00:05:23,338 that stage. Second, they are seen in all kinds of 76 00:05:23,338 --> 00:05:28,631 galaxies, elliptical as well as spiral. Young massive stars That are responsible 77 00:05:28,631 --> 00:05:33,365 for type 2 explosions, are only found, in star forming regions that is like discs 78 00:05:33,365 --> 00:05:36,790 or spiral galaxies. But not in all stellar populations like 79 00:05:36,790 --> 00:05:40,152 bulges or ellipticals. Type 1A supernovae are seen in all 80 00:05:40,152 --> 00:05:44,559 environments, so they have to come from some kind of old progenitor and white 81 00:05:44,559 --> 00:05:48,482 dwarfs, fit that bill. Furthermore, they do have remarkably 82 00:05:48,482 --> 00:05:53,802 similar set of properties, unlike type 2s which suggests that there is single 83 00:05:53,802 --> 00:05:57,667 projenitor mechanism. Their lightcurves are powered by the 84 00:05:57,667 --> 00:06:00,622 radioactive decay of an isotope of mik nickel. 85 00:06:00,622 --> 00:06:04,092 It's about one solar mass worth of radioactive nickel. 86 00:06:04,092 --> 00:06:07,847 However, this is an explosion of the whole star. 87 00:06:07,847 --> 00:06:11,801 And that, by definition, is a very messy business. 88 00:06:11,801 --> 00:06:17,744 We can model supernova explosions in super computers but that is still not a 89 00:06:17,744 --> 00:06:23,003 perfectly well solved problem. This is a very complex phenomenon of 90 00:06:23,003 --> 00:06:24,062 nature. And, 91 00:06:24,062 --> 00:06:28,117 can you imagine it would be kind of hard to standardize an explosion. 92 00:06:28,117 --> 00:06:32,587 So how is it possible that these are standard candles? There is an empirical 93 00:06:32,587 --> 00:06:37,267 relationship between the shapes of light curves of these supernovae, and their 94 00:06:37,267 --> 00:06:40,622 peak luminosity. And it goes in the sense that those that 95 00:06:40,622 --> 00:06:44,332 are intrinsically more luminous are also slower in decaying. 96 00:06:44,332 --> 00:06:48,708 Since the light curves have similar shape, they can be parameterized by a 97 00:06:48,708 --> 00:06:52,176 stretch factor. 1 can be stretched into another, and then 98 00:06:52,176 --> 00:06:56,577 they can be shfited vertically. When you do this, the following happens. 99 00:06:56,577 --> 00:07:01,433 Here we show on the top, a set of actual light curves of, some type 1A supernovea. 100 00:07:01,433 --> 00:07:06,245 And the second panel shows what happens when we normalize them and correct them 101 00:07:06,245 --> 00:07:10,146 with the stretch factor. Suddenly, they all seem to fit this one 102 00:07:10,146 --> 00:07:13,645 universal shape. It turns out that, by doing this, we can 103 00:07:13,645 --> 00:07:18,350 standardize the peak luminosity of a type 1A supernova to 10% or even slightly 104 00:07:18,350 --> 00:07:22,422 better, which is plenty good enough for cosmological purposes. 105 00:07:22,422 --> 00:07:26,612 Note again, that we have to calibrate this, standard luminosity, using 106 00:07:26,612 --> 00:07:30,087 distances to galaxies that were measured in some other way. 107 00:07:30,087 --> 00:07:33,701 Say, with cephates. There aren't very many of those, maybe 20 108 00:07:33,701 --> 00:07:37,265 or so, that have both cephate measurements, and supernovae. 109 00:07:37,265 --> 00:07:41,722 A very similar, result can be obtained by looking not only at the shape of the 110 00:07:41,722 --> 00:07:45,032 light curve, but also behavior of different colors. 111 00:07:45,032 --> 00:07:49,641 The more luminous supernova, tend to be decaying slower, but also, have, 112 00:07:49,641 --> 00:07:54,432 systematically different colors. Either way, supernova, or type 1A can be 113 00:07:54,432 --> 00:07:59,035 standardized, so their peak brightness is nearly constant to within 10%. 114 00:07:59,035 --> 00:08:03,061 And that's what makes them really useful, as cosmological tool. 115 00:08:03,061 --> 00:08:07,965 Not just for the measurement of Hubble constant, but also other cosmological 116 00:08:07,965 --> 00:08:11,113 parameters. And for example they have played a key 117 00:08:11,113 --> 00:08:15,710 role in the Recent confirmation of the existence of the dark energy. 118 00:08:15,710 --> 00:08:20,700 Here is an example of a supernova 1A Hubble diagram, corrected for the stretch 119 00:08:20,700 --> 00:08:23,957 factor and so on. The scatter is remarkably small. 120 00:08:23,957 --> 00:08:28,872 What's plotted here is the distance, luminosity distance in formal distance 121 00:08:28,872 --> 00:08:33,127 modules, raises the redshift. And it's as good a Hubble diagram as 122 00:08:33,127 --> 00:08:37,194 you'll ever Hope to get. Now the other kind of Supernovae type IIs 123 00:08:37,194 --> 00:08:40,189 can still be used using, with a different trick. 124 00:08:40,189 --> 00:08:43,177 This is so called Expanding Photosphere Method. 125 00:08:43,177 --> 00:08:48,176 An interesting thing about this method, it's based on physical reasoning and, in 126 00:08:48,176 --> 00:08:51,232 principle, does not require messy calibrations. 127 00:08:51,232 --> 00:08:55,857 However, it is model-dependent. And that more in compensates for the 128 00:08:55,857 --> 00:08:59,552 other benefits. It is very similar in principle to the 129 00:08:59,552 --> 00:09:03,172 Baade-Wesselink method we used for pulsating stars. 130 00:09:03,172 --> 00:09:08,588 This uses type II supernovae and it can be cross checked with Cepheids to see how 131 00:09:08,588 --> 00:09:12,359 well it works. The physical basis behind this method is 132 00:09:12,359 --> 00:09:16,862 that supernova photospheres Will emit light in a way that's not too different 133 00:09:16,862 --> 00:09:20,161 from the blackbody radiation, according to Stefan Boltzmann law. 134 00:09:20,161 --> 00:09:23,855 So if you can measure temperature, and if you can measure the radius of the 135 00:09:23,855 --> 00:09:26,780 photosphere, then you can immediately derive luminosity. 136 00:09:26,780 --> 00:09:30,902 From luminosity and observed apparent brightness, you can find the distance. 137 00:09:30,902 --> 00:09:34,892 So this is how it works. The angular diamater, of the expanding 138 00:09:34,892 --> 00:09:39,372 photosphere is the ratio of its physical diameter, and the distance. 139 00:09:39,372 --> 00:09:43,432 And that can be, folded through Stefan-Boltzmann formula, as shown, as 140 00:09:43,432 --> 00:09:48,522 shown here, except that there is an extra fudge factor, it's inserted to account 141 00:09:48,522 --> 00:09:52,832 for the deviations, of the, real supernova spectra from the black. 142 00:09:52,832 --> 00:09:55,845 Body. This is where, theory comes in, that's 143 00:09:55,845 --> 00:10:00,635 where the modeling comes in. Just like with [UNKNOWN] method, we can 144 00:10:00,635 --> 00:10:06,066 figure out the radius from observing the velocity of the expanding photo-sphere, 145 00:10:06,066 --> 00:10:09,795 from the moment of the explosion, as a function of time. 146 00:10:09,795 --> 00:10:15,153 It is probably as good approximation as any, to assume that the initial radius is 147 00:10:15,153 --> 00:10:18,735 about zero. Because it is certainly much smaller, 148 00:10:18,735 --> 00:10:21,994 than, radii of the expanding supernovae shells. 149 00:10:21,994 --> 00:10:26,587 Now we have everything we need. We can simply solve for the distance. 150 00:10:26,587 --> 00:10:31,427 But again, there is model dependance. An expanding, shell, of a stellar 151 00:10:31,427 --> 00:10:36,859 explosion, is not exactly in equilibrium, and spectrum is not exactly that one of 152 00:10:36,859 --> 00:10:40,062 the black body. So modeling has to be done to, 153 00:10:40,062 --> 00:10:43,587 to connect the two. Next we will talk about what's really the 154 00:10:43,587 --> 00:10:48,086 first definitive measurement of the Hubble's constant, using Hubble's Space 155 00:10:48,086 --> 00:10:48,355 Tell.