1 00:00:03,240 --> 00:00:08,710 So let's now find out how do black holes generate these amazing luminosities? 2 00:00:08,710 --> 00:00:13,556 After all, black holes are black because nothing can escape them, not even 3 00:00:13,556 --> 00:00:16,987 radiation. The answer is, the material around them 4 00:00:16,987 --> 00:00:20,339 can still be shining and be observed from far away. 5 00:00:22,000 --> 00:00:27,162 Now, we do know that black holes, or something like them, does exist in 6 00:00:27,162 --> 00:00:32,036 galactic nuclei. We know that because of the kinematical 7 00:00:32,036 --> 00:00:37,000 tracers, either stars or gas. We know that there is some depth to the 8 00:00:37,000 --> 00:00:40,978 potential well. But then, right in the middle, there is an 9 00:00:40,978 --> 00:00:44,637 extra mass that requires gas or stars to move faster. 10 00:00:44,637 --> 00:00:50,064 And so, if it is not the black hole, then it's something really similar to it, a lot 11 00:00:50,064 --> 00:00:55,701 of mass packed into a very small radius. So for all practical purposes it is like 12 00:00:55,701 --> 00:01:01,704 just like black hole, regardless of the details of its physics, very compact, very 13 00:01:01,704 --> 00:01:09,545 large masses near the centers of galaxies. We've seen evidence for it from variety of 14 00:01:09,545 --> 00:01:13,464 reasons, like the motions of water masers in the Seyfert galaxy. 15 00:01:13,464 --> 00:01:17,247 Now, there are about 20 of these that have been studied by now. 16 00:01:17,248 --> 00:01:21,748 And are like point masses, that are like solar system, except they're round giant 17 00:01:21,748 --> 00:01:24,795 blank hole. And the kinematics indeed indicates that 18 00:01:24,795 --> 00:01:27,979 this black hole is some tens of millions of solar masses. 19 00:01:29,000 --> 00:01:34,658 In the Milky Way itself, the motions of star in the intergalactic center indicates 20 00:01:34,658 --> 00:01:39,932 there is an extra point mass there of the order of 3 or 4 million solar masses. 21 00:01:39,932 --> 00:01:44,812 And even though it doesn't do much in terms of activity, we know it's there 22 00:01:44,812 --> 00:01:50,578 because of its gravitational influence. So something like black holes, or indeed 23 00:01:50,578 --> 00:01:54,422 black holes, exist in centers of the galaxies, but how do we get energy from 24 00:01:54,422 --> 00:01:57,365 them? The key to those is dissipation of binding 25 00:01:57,365 --> 00:02:01,850 energy. The fuel, gas comes from kiloparsec type 26 00:02:01,850 --> 00:02:07,392 radiis because of galaxy mergers. The size of the black hole is given by so 27 00:02:07,392 --> 00:02:10,924 called Schwarzschild radius. The formula is given here. 28 00:02:10,925 --> 00:02:15,052 For solar mass, that's about three kilometers. 29 00:02:15,052 --> 00:02:20,195 For a typical large black hole that might power a quasar, which has 100 million 30 00:02:20,195 --> 00:02:23,120 solar masses. It would be 300 million kilometers. 31 00:02:23,120 --> 00:02:26,280 Or about twice the distance of Earth from the sun. 32 00:02:26,280 --> 00:02:29,919 So these really are regions about the size of a solar system. 33 00:02:32,830 --> 00:02:36,521 That happens to be also about 10 microparsecs. 34 00:02:36,521 --> 00:02:42,506 And therefore, the material crosses approximately eight or nine orders of 35 00:02:42,506 --> 00:02:46,389 magnitude in radius to get to the center energy. 36 00:02:47,730 --> 00:02:52,326 Well, that means it will be coming in on roughly radial orbits. 37 00:02:52,326 --> 00:02:57,489 But however, it does get there. That net amount of energy lost will be a 38 00:02:57,489 --> 00:03:00,947 substantial fraction of it's rest mass energy. 39 00:03:00,948 --> 00:03:05,997 If it could get directly to Schwarzschild radius, then it could radiate away all of 40 00:03:05,997 --> 00:03:09,202 it's m c squared. But it doesn't. 41 00:03:09,202 --> 00:03:15,056 There is a smallest orbit which is stable. Remember that you can dissipate energy, 42 00:03:15,056 --> 00:03:18,985 but not the angular momentum. So the material that falls in has to 43 00:03:18,985 --> 00:03:23,047 settle into a small accretion disk. The inner edge of that is the smallest 44 00:03:23,047 --> 00:03:26,290 stable orbit. Now this is very much a general relativity 45 00:03:26,290 --> 00:03:28,407 concept. There is no such thing in Newtonian 46 00:03:28,407 --> 00:03:31,459 gravity. A Newtonian gravity of two point masses, 47 00:03:31,459 --> 00:03:35,702 you can get as close as you want. In general relativity, no, there is a 48 00:03:35,702 --> 00:03:39,996 smallest stable orbit. And so that is how deep the material has 49 00:03:39,996 --> 00:03:45,804 to get, and so therefore it will dissipate less than its full mc squared but a 50 00:03:45,804 --> 00:03:49,300 fraction thereof. Typically, we think that on average, it's 51 00:03:49,300 --> 00:03:53,878 about 10%. So it doesn't matter what you make black 52 00:03:53,878 --> 00:03:57,106 hole from, the regular matter, dark matter. 53 00:03:57,106 --> 00:04:02,060 It's just a mass that you know. But there are also a couple other things. 54 00:04:02,060 --> 00:04:07,097 In principle, you can also have electric or charge or magnetic field going through 55 00:04:07,097 --> 00:04:10,589 a black hole because of electromagnetic radiation. 56 00:04:10,590 --> 00:04:16,796 So electromagnetic interaction and gravity are the only two infinite range 57 00:04:16,796 --> 00:04:20,454 interactions. And black hole can be spinning, so three 58 00:04:20,454 --> 00:04:23,060 numbers really characterize the black hole. 59 00:04:23,060 --> 00:04:27,940 It's mass, it's angular momentum. And its electric charge. 60 00:04:27,940 --> 00:04:32,612 Now, charges are well mixed in the universe, protons and electrons, so black 61 00:04:32,612 --> 00:04:36,578 holes are not likely to have a significant net electric charge. 62 00:04:36,578 --> 00:04:40,377 And that leaves mass and the angular momentum. 63 00:04:40,378 --> 00:04:46,022 For a Schwarzchild black hole, classical black hole so to speak, the angular 64 00:04:46,022 --> 00:04:51,886 momentum is zero. And its radius is given by Schwarzschild 65 00:04:51,886 --> 00:04:54,984 formula. The smallest stable orbit around 66 00:04:54,984 --> 00:04:59,557 stationary black hole is three times the Schwarzschild radius. 67 00:04:59,558 --> 00:05:04,669 And this is how close material has to come in order to be eventually absorbed. 68 00:05:04,670 --> 00:05:07,720 But how do we know there really is black holes? 69 00:05:07,720 --> 00:05:12,584 Well it turns out there is another way to probe this, and this is from the X-ray 70 00:05:12,584 --> 00:05:15,693 emission. The material that's so close to black hole 71 00:05:15,693 --> 00:05:18,650 is very hot. It's plasma and millions of degrees of 72 00:05:18,650 --> 00:05:21,507 kelvin. And therefore, x-rays are a good way to 73 00:05:21,507 --> 00:05:25,169 probe it. There are emission lines in x-rays, which 74 00:05:25,169 --> 00:05:31,172 we can use to probe kinematics of the gas just as we did with non-relativistic cases 75 00:05:31,172 --> 00:05:35,140 earlier. And if you have a Newtonian case, there is 76 00:05:35,140 --> 00:05:41,185 just a big mass and the stuff is going round even at relativistic speeds, if you 77 00:05:41,185 --> 00:05:45,080 will. Then there'll be a two horn profile, one 78 00:05:45,080 --> 00:05:50,157 for gas coming towards you, the other one going away from you. 79 00:05:50,158 --> 00:05:53,623 But once we throw in relativity new things happen. 80 00:05:53,623 --> 00:05:58,780 First there is so called a transverse doppler effect. 81 00:05:58,780 --> 00:06:03,893 Moving clocks run slower. And then the, also the beaming, boosts of 82 00:06:03,893 --> 00:06:09,483 radiation is coming, when material's coming towards you, and the emission is 83 00:06:09,483 --> 00:06:14,485 the one going away from you. Those two would create asymetric profile, 84 00:06:14,485 --> 00:06:20,505 one form would be larger than the other. Then there is also gravitational redshift, 85 00:06:20,505 --> 00:06:24,501 that's the general altruistic effect. The photons would lose energy getting out 86 00:06:24,501 --> 00:06:28,899 of potential role. So the whole thing would be moved toward 87 00:06:28,899 --> 00:06:34,924 lower energies. And therefore you expect broad, asymmetric 88 00:06:34,924 --> 00:06:40,820 shifted line to come up. And that's exactly what's observed. 89 00:06:40,820 --> 00:06:46,834 Here is a profile of the x-ray emission line of iron seen in one of the active 90 00:06:46,834 --> 00:06:50,684 nuclei. You can see it's very asymmetric and also 91 00:06:50,684 --> 00:06:54,957 hapeens to be redshifted compared systemic velocity. 92 00:06:54,958 --> 00:06:58,972 And so this is exactly the prediction of what. 93 00:06:58,972 --> 00:07:04,780 Things should happen in case of point mass or something close enough to black hole 94 00:07:04,780 --> 00:07:09,755 and the material orbiting around it. So that's probably the most direct 95 00:07:09,755 --> 00:07:15,365 evidence that yes, really close in what we see are black holes or compact masses 96 00:07:15,365 --> 00:07:20,975 compressed to such small sizes that for all practical purposes, they're black 97 00:07:20,975 --> 00:07:25,439 holes. All right, now what in black hole is 98 00:07:25,439 --> 00:07:30,796 spinning? We introduced the spin parameter, given by 99 00:07:30,796 --> 00:07:35,735 this formula, little a. Which is ratio of angular momentum to mass 100 00:07:35,735 --> 00:07:41,584 squared, a couple constants thrown in. This was studied by physicist named Kerr, 101 00:07:41,584 --> 00:07:47,548 and those are called Kerr black holes, as opposed to Schwarzschild black holes which 102 00:07:47,548 --> 00:07:51,183 are stationary. And maximum amount of angular momentum 103 00:07:51,183 --> 00:07:56,011 that you can put in a black hole, spinning black hole, corresponds to the value of a 104 00:07:56,011 --> 00:07:58,892 parameter of 1. For no rotation, it is zero. 105 00:07:58,892 --> 00:08:04,560 It now turns out that the smallest radius of a smallest stable orbit around the 106 00:08:04,560 --> 00:08:10,389 rotating black holes is closer in than it would be for stationery Schwarzschild 107 00:08:10,389 --> 00:08:15,096 black hole. Therefore, you can extract more energy 108 00:08:15,096 --> 00:08:22,150 from the spinning black hole and. And thats just from stuff falling in. 109 00:08:22,150 --> 00:08:28,498 Now if you can somehow extract rotational kinetic energy from the black hole, then 110 00:08:28,498 --> 00:08:32,226 you can get some more. There is a mechanism to do this. 111 00:08:32,226 --> 00:08:38,958 And that is if there is a magnetic field threaded through black hole, and so the 112 00:08:38,958 --> 00:08:43,914 mechanism called Blandford-Znajek effect that does this. 113 00:08:43,914 --> 00:08:48,904 Alright, so this is how you can extract energy but how much. 114 00:08:48,904 --> 00:08:52,864 And we have to now turn to a concept of Eddington limit which was really 115 00:08:52,864 --> 00:08:56,539 introduced in stellar astrophysics and that's what limits the. 116 00:08:57,670 --> 00:09:02,300 Largest mass stars and most luminous stars and it works as follows. 117 00:09:02,300 --> 00:09:07,060 There is ionized gas, plasma, near the surface of a star. 118 00:09:07,060 --> 00:09:13,330 In this case, in the region around the black hole and electrons can be 119 00:09:13,330 --> 00:09:19,546 susceptible to radiaion pressure, absorb photons and so there is. 120 00:09:20,710 --> 00:09:25,976 Essentially radiation driven wind. On the other hand, the gravitational field 121 00:09:25,976 --> 00:09:30,021 pulls them back. So, for a given mass, there is certain 122 00:09:30,021 --> 00:09:36,456 critical luminosity above which the stuff will be blown away by the radiation 123 00:09:36,456 --> 00:09:40,590 pressure. And you can compute that using cross 124 00:09:40,590 --> 00:09:45,241 section for absorption, so called Thompson cross-section for free electrons. 125 00:09:45,241 --> 00:09:51,422 And it can put in now the, so they have outward force due to the photon wind 126 00:09:51,422 --> 00:09:58,431 that's pushing the material that's directly proportional to luminosity. 127 00:09:58,431 --> 00:10:03,252 And that has to be balanced exactlty with the gravitational force pulling back on 128 00:10:03,252 --> 00:10:07,349 our protons and electrons together. It's a problem because that's where all 129 00:10:07,349 --> 00:10:10,059 the mass is. They just latch to the electrons as 130 00:10:10,059 --> 00:10:14,402 they're well mixed. So, the equation of these gives you the 131 00:10:14,402 --> 00:10:20,901 limiting luminosity If luminosity is larger then that, radiaion pressure wins 132 00:10:20,901 --> 00:10:26,633 and thing blows itself apart. If it's less then that, it can still be 133 00:10:26,633 --> 00:10:30,946 sort of, of equilbrium. So the largest luminosity you can have 134 00:10:30,946 --> 00:10:35,552 around any given mass is given by this formula, the Eddington luminosity. 135 00:10:35,552 --> 00:10:39,502 And that turns out to be of the order of 10 to the 38 ergs. 136 00:10:39,502 --> 00:10:45,207 Times the mass of the object in solar mass units. 137 00:10:45,208 --> 00:10:50,947 So for something like 10 to the 8th solar mass black hole, Eddington luminosity 138 00:10:50,947 --> 00:10:53,732 would be of the order of 10 to the 46 ergs. 139 00:10:53,732 --> 00:10:58,192 Remember that solar luminosity is few times 10 to the 33 ergs. 140 00:10:58,193 --> 00:11:04,141 So that will be on the order of 10 to the 13 solar luminosities and that's about as 141 00:11:04,141 --> 00:11:07,828 much as the most luminous quasars that we do see. 142 00:11:07,828 --> 00:11:15,140 Next, we will consider qualimated emissions from black holes in the form of 143 00:11:15,140 --> 00:11:20,363 radio jets and other phenomena associated with them.