1 00:00:00,060 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT OpenCourseWare 4 00:00:06,030 --> 00:00:10,120 continue to offer high quality educational resources for free. 5 00:00:10,120 --> 00:00:12,660 To make a donation or to view additional materials 6 00:00:12,660 --> 00:00:16,620 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,620 --> 00:00:17,650 at ocw.mit.edu. 8 00:00:20,430 --> 00:00:27,840 MARK HARTMAN: Light production models, right? 9 00:00:27,840 --> 00:00:34,860 And before, we said in general, bouncing 10 00:00:34,860 --> 00:00:40,745 charged particles produce-- 11 00:00:43,320 --> 00:00:44,680 oops, I can't spell produce. 12 00:00:50,950 --> 00:00:54,520 And I'm going to do this so you can all see me. 13 00:00:54,520 --> 00:00:56,970 Produce photons. 14 00:01:02,495 --> 00:01:04,170 Hi, Juan. 15 00:01:04,170 --> 00:01:04,670 OK. 16 00:01:04,670 --> 00:01:05,900 So this is our general model. 17 00:01:05,900 --> 00:01:09,740 Bouncing charged particles produce photons. 18 00:01:09,740 --> 00:01:15,290 This idea, one particular model of thermal light production 19 00:01:15,290 --> 00:01:18,690 is this idea of bouncing charged particles. 20 00:01:18,690 --> 00:01:21,530 But there's a particular model that we're going to look at, 21 00:01:21,530 --> 00:01:23,795 and it's called the black body model. 22 00:01:26,510 --> 00:01:31,250 Black body model of light production. 23 00:01:35,980 --> 00:01:38,830 OK? 24 00:01:38,830 --> 00:01:41,080 And this black body model, it's actually 25 00:01:41,080 --> 00:01:42,376 a pretty complicated idea. 26 00:01:42,376 --> 00:01:43,750 It's got lots of different parts. 27 00:01:43,750 --> 00:01:45,790 It has to do with quantum mechanics. 28 00:01:45,790 --> 00:01:48,370 It's called a black body because it talks about 29 00:01:48,370 --> 00:01:52,510 that this object absorbs all radiation or absorbs all light 30 00:01:52,510 --> 00:01:54,832 and doesn't give any other light back. 31 00:01:54,832 --> 00:01:56,540 There's a lot of different parts to this, 32 00:01:56,540 --> 00:01:58,000 but we're going to simplify it so 33 00:01:58,000 --> 00:02:01,270 that we can think about it in terms of our objects. 34 00:02:01,270 --> 00:02:08,464 So we are going to say the black model applies-- 35 00:02:08,464 --> 00:02:14,170 oops, a-p-p-l-i-e-s to an opaque object. 36 00:02:18,400 --> 00:02:23,480 Has anybody heard this word, opaque? 37 00:02:23,480 --> 00:02:24,920 Bianca, what does opaque mean? 38 00:02:24,920 --> 00:02:26,490 Nice and loud. 39 00:02:26,490 --> 00:02:29,960 AUDIENCE: It's, like, semi-transparent. 40 00:02:29,960 --> 00:02:30,860 MARK HARTMAN: OK. 41 00:02:30,860 --> 00:02:32,969 Semi-transparent. 42 00:02:32,969 --> 00:02:34,010 What do you think, Steve? 43 00:02:34,010 --> 00:02:36,190 AUDIENCE: Doesn't allow light to pass through. 44 00:02:36,190 --> 00:02:36,898 MARK HARTMAN: OK. 45 00:02:36,898 --> 00:02:38,700 It doesn't allow light to pass through. 46 00:02:38,700 --> 00:02:40,880 So we've got transparent, which means light 47 00:02:40,880 --> 00:02:42,130 can go all the way through. 48 00:02:42,130 --> 00:02:46,610 Translucent is this idea that some light can go through, 49 00:02:46,610 --> 00:02:49,430 and I think that might be what you're thinking about, Bianca. 50 00:02:49,430 --> 00:02:52,850 But opaque means that you can't see light 51 00:02:52,850 --> 00:02:54,890 from an object on the other side. 52 00:02:54,890 --> 00:02:56,510 Like, a shirt is opaque. 53 00:02:56,510 --> 00:02:58,220 A person is opaque. 54 00:02:58,220 --> 00:02:59,750 A window is transparent. 55 00:02:59,750 --> 00:03:01,957 You can have light pass through that. 56 00:03:01,957 --> 00:03:04,040 So we're going to say applies to an opaque object. 57 00:03:04,040 --> 00:03:11,650 Opaque means you can't see-- 58 00:03:11,650 --> 00:03:17,600 well, let's just say light does not pass through. 59 00:03:27,640 --> 00:03:28,140 OK. 60 00:03:28,140 --> 00:03:29,640 So let's think about it. 61 00:03:29,640 --> 00:03:31,760 Is the sun an opaque object? 62 00:03:35,080 --> 00:03:37,600 What do you think? 63 00:03:37,600 --> 00:03:39,280 Why is the sun an opaque object? 64 00:03:39,280 --> 00:03:41,459 AUDIENCE: Because light can't go through it. 65 00:03:41,459 --> 00:03:43,000 MARK HARTMAN: Light can't go through. 66 00:03:43,000 --> 00:03:45,700 We can't see stuff on the other side of the sun. 67 00:03:45,700 --> 00:03:47,890 The sun does produce its own light, 68 00:03:47,890 --> 00:03:50,530 so it produces the light from the surface. 69 00:03:50,530 --> 00:03:52,750 So the sun is an opaque object. 70 00:03:52,750 --> 00:03:54,250 We can't see through it. 71 00:03:54,250 --> 00:03:56,380 Light doesn't pass through it. 72 00:03:56,380 --> 00:03:58,420 Light is produced at its surface. 73 00:03:58,420 --> 00:04:00,550 What about a supernova remnant? 74 00:04:00,550 --> 00:04:02,450 How about a supernova remnant group? 75 00:04:02,450 --> 00:04:05,740 Have you guys seen pictures of supernova remnants? 76 00:04:05,740 --> 00:04:08,320 Can you see stuff on the other side of the supernova remnant? 77 00:04:11,380 --> 00:04:12,239 Say it again? 78 00:04:12,239 --> 00:04:13,530 AUDIENCE: Some of them you can. 79 00:04:13,530 --> 00:04:15,210 MARK HARTMAN: Some of them you can. 80 00:04:15,210 --> 00:04:15,960 What do you think? 81 00:04:15,960 --> 00:04:17,430 Do you agree, Lauren? 82 00:04:17,430 --> 00:04:18,014 Yeah. 83 00:04:18,014 --> 00:04:20,430 So if you take a look at a picture of a supernova remnant, 84 00:04:20,430 --> 00:04:23,160 sometimes you can see stars on the other side. 85 00:04:23,160 --> 00:04:25,980 So supernova remnant is not an opaque object. 86 00:04:25,980 --> 00:04:27,660 What about a galaxy cluster? 87 00:04:27,660 --> 00:04:28,673 Clusters group? 88 00:04:28,673 --> 00:04:30,339 AUDIENCE: Well, the space in between you 89 00:04:30,339 --> 00:04:35,610 would be able to see from more distant objects. 90 00:04:35,610 --> 00:04:36,580 MARK HARTMAN: OK. 91 00:04:36,580 --> 00:04:37,350 OK. 92 00:04:37,350 --> 00:04:39,120 So you can kind of see there's light 93 00:04:39,120 --> 00:04:41,320 coming from the other side. 94 00:04:41,320 --> 00:04:44,170 So this is an important idea, this opaque object, 95 00:04:44,170 --> 00:04:48,160 which means it has a surface that produces light. 96 00:04:48,160 --> 00:04:48,660 OK? 97 00:04:48,660 --> 00:04:51,400 So we're going to say it applies to an opaque object. 98 00:04:51,400 --> 00:05:02,630 It has a surface that produces light. 99 00:05:06,020 --> 00:05:09,080 The sun's surface produces light, 100 00:05:09,080 --> 00:05:13,100 and it produces light because it has this thermal motion. 101 00:05:13,100 --> 00:05:14,630 This is the simplification here. 102 00:05:14,630 --> 00:05:32,150 We're going to say charged particles bounce around 103 00:05:32,150 --> 00:05:42,680 inside the object and when-- 104 00:05:42,680 --> 00:05:49,210 let's say and by the time the photons 105 00:05:49,210 --> 00:06:09,160 reach the surface that bouncing has created 106 00:06:09,160 --> 00:06:10,510 a distribution of light. 107 00:06:20,982 --> 00:06:22,440 Now, we're going to say has created 108 00:06:22,440 --> 00:06:25,150 a distribution of light. 109 00:06:25,150 --> 00:06:27,300 We had a special word for that last Friday. 110 00:06:27,300 --> 00:06:29,340 What did we call the distribution of light 111 00:06:29,340 --> 00:06:31,280 or the composition of light? 112 00:06:31,280 --> 00:06:32,450 AUDIENCE: Spectrum. 113 00:06:32,450 --> 00:06:33,610 MARK HARTMAN: A spectrum. 114 00:06:33,610 --> 00:06:34,110 Right? 115 00:06:34,110 --> 00:06:38,100 We said a spectrum was how many of each different energy 116 00:06:38,100 --> 00:06:39,630 of photon are we receiving? 117 00:06:39,630 --> 00:06:55,190 So that bouncing has created a spectrum 118 00:06:55,190 --> 00:07:07,410 that depends only on temperature, 119 00:07:07,410 --> 00:07:12,270 not what the material is made of. 120 00:07:12,270 --> 00:07:18,960 Not what the object is made of. 121 00:07:18,960 --> 00:07:20,720 It's not the world's greatest sentence, 122 00:07:20,720 --> 00:07:23,130 but I think it gets across the point. 123 00:07:23,130 --> 00:07:25,350 It's a very long sentence. 124 00:07:25,350 --> 00:07:28,180 So let's look at each part in turn. 125 00:07:28,180 --> 00:07:29,180 OK? 126 00:07:29,180 --> 00:07:32,370 Charged particles bounce around inside the object. 127 00:07:32,370 --> 00:07:37,860 So if we look at our model of sodium chloride, 128 00:07:37,860 --> 00:07:41,690 we are seeing these bounces happen. 129 00:07:41,690 --> 00:07:44,600 Photons are produced from each one of those bounces. 130 00:07:44,600 --> 00:07:46,640 A hard bounce produces a high energy 131 00:07:46,640 --> 00:07:52,130 photon, a not so hard bounce produces a low energy photon. 132 00:07:52,130 --> 00:07:56,430 Those photons then bounce around inside too. 133 00:07:56,430 --> 00:07:59,960 And by the time that those photons have bounced around 134 00:07:59,960 --> 00:08:03,140 to reach the surface, the bouncing 135 00:08:03,140 --> 00:08:07,110 creates a spectrum that depends only on temperature. 136 00:08:07,110 --> 00:08:13,080 So if we were to take an iron, say, a piece of iron and say, 137 00:08:13,080 --> 00:08:16,400 a piece of aluminum and we heated them up 138 00:08:16,400 --> 00:08:19,180 to a really high temperature. 139 00:08:19,180 --> 00:08:22,940 The spectrum that we would get from the iron and the aluminum 140 00:08:22,940 --> 00:08:24,470 would be the same. 141 00:08:24,470 --> 00:08:27,620 It wouldn't matter that it was iron versus aluminum, 142 00:08:27,620 --> 00:08:30,630 at least not for this kind of spectrum. 143 00:08:30,630 --> 00:08:33,289 Now, we'll see later on that some spectra have 144 00:08:33,289 --> 00:08:36,770 to do with what objects or what elements are making up 145 00:08:36,770 --> 00:08:38,309 that object. 146 00:08:38,309 --> 00:08:41,105 But here, we're just saying anything that's really hot, 147 00:08:41,105 --> 00:08:42,650 it doesn't matter. 148 00:08:42,650 --> 00:08:44,870 It gives off the same amount of light 149 00:08:44,870 --> 00:08:49,167 if it behaves like a black body. 150 00:08:49,167 --> 00:08:50,750 Now, let's think for a minute, though, 151 00:08:50,750 --> 00:08:53,330 because here we've got a solid object. 152 00:08:53,330 --> 00:08:54,960 But is the sun a solid? 153 00:08:57,600 --> 00:08:59,550 Is the sun a solid, a liquid, or a gas? 154 00:08:59,550 --> 00:09:00,480 AUDIENCE: It's a gas. 155 00:09:00,480 --> 00:09:02,060 MARK HARTMAN: It's a gas? 156 00:09:02,060 --> 00:09:03,060 It's actually not a gas. 157 00:09:03,060 --> 00:09:08,040 It's a plasma, which is a gas of ions. 158 00:09:08,040 --> 00:09:10,710 So even though here we're talking about a solid thing, 159 00:09:10,710 --> 00:09:14,730 we can have a black body that is made of gas. 160 00:09:14,730 --> 00:09:18,120 But the gases is dense enough that the light still doesn't 161 00:09:18,120 --> 00:09:19,230 pass all the way through. 162 00:09:19,230 --> 00:09:21,630 It still has a surface. 163 00:09:21,630 --> 00:09:22,500 OK? 164 00:09:22,500 --> 00:09:26,130 So when I think about this black body model of light. 165 00:09:26,130 --> 00:09:28,110 That's one way or one of our models 166 00:09:28,110 --> 00:09:29,970 that we're gonna think about. 167 00:09:29,970 --> 00:09:35,800 Shakib, can you bring up our other, our non-thermal model? 168 00:09:35,800 --> 00:09:38,125 Let's take a look, so scroll down a little bit. 169 00:09:38,125 --> 00:09:41,580 And let's play this animation again. 170 00:09:41,580 --> 00:09:44,130 So click to animate. 171 00:09:44,130 --> 00:09:47,910 So we were saying before that if we had charged particles 172 00:09:47,910 --> 00:09:51,450 that were spiraling around a magnetic field, 173 00:09:51,450 --> 00:09:55,620 that they would produce photons as they bounce, right? 174 00:09:55,620 --> 00:09:58,440 And just as a quick little review, 175 00:09:58,440 --> 00:09:59,820 I want to show us again. 176 00:09:59,820 --> 00:10:04,650 So can we change-- 177 00:10:04,650 --> 00:10:09,720 let's do group A to video. 178 00:10:09,720 --> 00:10:15,540 So again, let's take a look at this demonstration 179 00:10:15,540 --> 00:10:21,290 where we have charged particles that are being produced. 180 00:10:21,290 --> 00:10:23,760 Actually, let's turn the lights down a little bit more. 181 00:10:23,760 --> 00:10:33,447 And we saw that if we change-- 182 00:10:33,447 --> 00:10:34,530 see if we can get it here. 183 00:10:39,180 --> 00:10:39,850 Right. 184 00:10:39,850 --> 00:10:41,200 There we can see that if-- 185 00:10:41,200 --> 00:10:43,780 what I'm doing right now is I'm changing the strength 186 00:10:43,780 --> 00:10:46,010 of the magnetic field. 187 00:10:46,010 --> 00:10:49,380 If I turn the magnetic field so that it's very strong, 188 00:10:49,380 --> 00:10:51,880 I'm causing these charged particles 189 00:10:51,880 --> 00:10:55,900 to move in a smaller and smaller circle. 190 00:10:55,900 --> 00:11:00,160 If I make the magnetic field less strong, 191 00:11:00,160 --> 00:11:01,990 I can make those charged particles move 192 00:11:01,990 --> 00:11:03,910 in a larger circle. 193 00:11:03,910 --> 00:11:09,950 But they're moving in a circle, and if we look from up above-- 194 00:11:09,950 --> 00:11:14,490 let's open up iris a little bit more. 195 00:11:14,490 --> 00:11:19,480 Here, we see-- let's turn it to the side. 196 00:11:19,480 --> 00:11:23,740 There, we can kind of see this helix shape. 197 00:11:23,740 --> 00:11:28,330 Can we all see that it's making kind of a two-- 198 00:11:28,330 --> 00:11:30,760 a spiral shape? 199 00:11:30,760 --> 00:11:33,454 Because if our magnetic field isn't perfectly in line 200 00:11:33,454 --> 00:11:35,620 with that circle, it's not just going to make things 201 00:11:35,620 --> 00:11:36,730 do a circle. 202 00:11:36,730 --> 00:11:39,430 It's going to make things do this spiral shape. 203 00:11:39,430 --> 00:11:44,010 There, the spiral shape is on one side, and then if I-- 204 00:11:44,010 --> 00:11:49,090 I'm tilting my bulb here, and now, you 205 00:11:49,090 --> 00:11:52,970 can see the spiral shape on the other side. 206 00:11:52,970 --> 00:11:57,430 So now, the spiral shape is back on the first side. 207 00:11:57,430 --> 00:11:59,440 So if you have a strong magnetic field, 208 00:11:59,440 --> 00:12:04,390 you're not causing objects to bounce because they 209 00:12:04,390 --> 00:12:05,890 have a certain temperature. 210 00:12:05,890 --> 00:12:07,480 But you've got some outside force 211 00:12:07,480 --> 00:12:09,912 that's causing them to bounce in another way. 212 00:12:09,912 --> 00:12:11,870 Hey, Shakib, could you turn the lights back up? 213 00:12:15,940 --> 00:12:18,400 And we saw that these charged particles 214 00:12:18,400 --> 00:12:22,210 are being moved or being caused to spiral 215 00:12:22,210 --> 00:12:24,650 by that magnetic field. 216 00:12:24,650 --> 00:12:30,620 Now, we're going to introduce another model for a spectrum. 217 00:12:30,620 --> 00:12:35,300 So this is going to be a model that's called 218 00:12:35,300 --> 00:12:37,750 model two, that was model one. 219 00:12:37,750 --> 00:12:46,721 Model two, we're going to introduce a power law spectrum 220 00:12:46,721 --> 00:12:47,220 model. 221 00:12:50,850 --> 00:12:53,080 Now, this is really, really important. 222 00:12:53,080 --> 00:12:55,060 The power loss spectrum-- 223 00:12:55,060 --> 00:12:56,460 thank you, Shakib. 224 00:12:56,460 --> 00:12:59,520 It's just a mathematical model. 225 00:12:59,520 --> 00:13:02,040 It actually is related to a bunch 226 00:13:02,040 --> 00:13:05,250 of different physical ideas, like this idea 227 00:13:05,250 --> 00:13:09,810 of a particle spiraling around a magnetic field. 228 00:13:09,810 --> 00:13:19,170 But this is just a mathematical model, 229 00:13:19,170 --> 00:13:23,210 and the mathematical model is actually it's the intensity. 230 00:13:23,210 --> 00:13:33,010 Remember, we said intensity is equal to the energy 231 00:13:33,010 --> 00:13:37,495 to some power, to the power of x, OK? 232 00:13:41,770 --> 00:13:44,540 In a very simple way. 233 00:13:44,540 --> 00:13:48,490 So what that means is if I had intensity 234 00:13:48,490 --> 00:13:53,050 as a function of energy, if I wanted my power 235 00:13:53,050 --> 00:14:00,310 law to be intensity equals energy to the power of two, 236 00:14:00,310 --> 00:14:01,300 I could just say, OK. 237 00:14:01,300 --> 00:14:03,760 Well, that's just a quadratic graph. 238 00:14:03,760 --> 00:14:06,580 So my intensity is a function energy would go up like that. 239 00:14:09,470 --> 00:14:15,580 If I wanted to say that my intensity was maybe 240 00:14:15,580 --> 00:14:19,732 just equal to energy to the power of one, 241 00:14:19,732 --> 00:14:21,190 what kind of a graph would that be? 242 00:14:23,760 --> 00:14:24,260 Bianca? 243 00:14:24,260 --> 00:14:25,747 I saw you draw it in the air. 244 00:14:29,016 --> 00:14:30,492 AUDIENCE: Where x equals y. 245 00:14:30,492 --> 00:14:31,200 MARK HARTMAN: OK. 246 00:14:31,200 --> 00:14:33,660 This is just y equals x. 247 00:14:33,660 --> 00:14:36,460 Anything raised to the one power is still that same number. 248 00:14:36,460 --> 00:14:41,910 So in this case, it would just be a line, right? 249 00:14:41,910 --> 00:14:47,220 Has anybody ever seen intensity equals energy or y equals 250 00:14:47,220 --> 00:14:49,120 x to the power of minus one? 251 00:14:53,064 --> 00:14:56,510 It-- would it be negative? 252 00:14:56,510 --> 00:14:57,612 So let's think about this. 253 00:14:57,612 --> 00:14:59,320 Intensity equals energy to the minus one. 254 00:14:59,320 --> 00:15:03,760 That's the same as saying one over the energy, right? 255 00:15:03,760 --> 00:15:06,246 Let's say-- oops I didn't want to do that. 256 00:15:06,246 --> 00:15:07,370 I wanted a different color. 257 00:15:10,597 --> 00:15:12,980 Let me make it a little bit clearer. 258 00:15:12,980 --> 00:15:17,010 The intensity equals energy to the minus one, 259 00:15:17,010 --> 00:15:20,150 which is equal to one over the energy. 260 00:15:20,150 --> 00:15:25,440 Say that we had an energy of one electron volt, two electron 261 00:15:25,440 --> 00:15:29,010 volts, and then out here would be four. 262 00:15:29,010 --> 00:15:32,010 And there's three, right? 263 00:15:32,010 --> 00:15:34,530 If our intensity is equal to one over the energy, 264 00:15:34,530 --> 00:15:38,760 if the energy is one, what would be the intensity? 265 00:15:38,760 --> 00:15:42,038 1/1, so one. 266 00:15:42,038 --> 00:15:43,320 Right. 267 00:15:43,320 --> 00:15:46,140 What about if the energy is two electron volts? 268 00:15:46,140 --> 00:15:49,500 What happens to the intensity? 269 00:15:49,500 --> 00:15:50,340 It's one half. 270 00:15:50,340 --> 00:15:51,300 1/2. 271 00:15:51,300 --> 00:15:55,020 So here, we've got one half. 272 00:15:55,020 --> 00:15:57,210 What about three? 273 00:15:57,210 --> 00:15:59,610 If the energy is three, what happens to the intensity? 274 00:15:59,610 --> 00:16:01,860 Does it get bigger or smaller? 275 00:16:01,860 --> 00:16:02,360 Smaller. 276 00:16:02,360 --> 00:16:04,680 You get 1/3. 277 00:16:04,680 --> 00:16:06,870 What happens if it's four? 278 00:16:06,870 --> 00:16:07,470 1/4. 279 00:16:07,470 --> 00:16:08,850 It gets smaller. 280 00:16:08,850 --> 00:16:12,210 Will the intensity ever go to zero? 281 00:16:12,210 --> 00:16:14,460 It would just get smaller, and smaller, and smaller. 282 00:16:14,460 --> 00:16:19,140 As this number energy gets bigger, the shape of the graph, 283 00:16:19,140 --> 00:16:22,020 what happens if we went to an intensity where-- 284 00:16:22,020 --> 00:16:26,930 I'm sorry, if we go into an energy of 1/2, 285 00:16:26,930 --> 00:16:34,580 we'd have one over 1/2, which is the same as one times 286 00:16:34,580 --> 00:16:36,830 the reciprocal of 1/2. 287 00:16:36,830 --> 00:16:41,940 So one times 2/1, which equals 2. 288 00:16:41,940 --> 00:16:46,910 So at an energy of 1/2, I've actually gone up. 289 00:16:46,910 --> 00:16:49,960 So if anybody's has ever seen an inverse graph, 290 00:16:49,960 --> 00:16:50,840 it looks like this. 291 00:16:54,410 --> 00:16:55,320 OK? 292 00:16:55,320 --> 00:16:59,670 So if we have intensity is equal to energy to the minus 1 power, 293 00:16:59,670 --> 00:17:01,550 we get a graph that looks like that. 294 00:17:01,550 --> 00:17:02,430 Now, you guys are going to have a chance 295 00:17:02,430 --> 00:17:04,304 to play around with this in just a little bit 296 00:17:04,304 --> 00:17:06,480 and actually try to fit this model, 297 00:17:06,480 --> 00:17:09,306 but I wanted to point out one or two other things. 298 00:17:09,306 --> 00:17:10,680 When we have this model intensity 299 00:17:10,680 --> 00:17:14,310 equals energy to some power, to the power of x, that's 300 00:17:14,310 --> 00:17:17,020 why it's called a power law. 301 00:17:17,020 --> 00:17:18,690 Remember, a law, we said, was just 302 00:17:18,690 --> 00:17:23,050 something that said this is what always happens. 303 00:17:23,050 --> 00:17:26,190 So in this case, we're not explaining 304 00:17:26,190 --> 00:17:27,810 why it looks like this. 305 00:17:27,810 --> 00:17:30,330 We're just saying the mathematical form looks 306 00:17:30,330 --> 00:17:32,850 like that. 307 00:17:32,850 --> 00:17:37,560 So we're also going to say that this number, x, we're 308 00:17:37,560 --> 00:17:47,370 going to say x is the power law index. 309 00:17:47,370 --> 00:17:49,380 What does an index, like, if you just 310 00:17:49,380 --> 00:17:51,340 hear that word in normal everyday language. 311 00:17:54,050 --> 00:17:55,630 What do you, Chris, what's an index? 312 00:17:59,161 --> 00:17:59,660 OK. 313 00:17:59,660 --> 00:18:01,604 Like a little index card. 314 00:18:01,604 --> 00:18:03,020 If you've ever gone to the library 315 00:18:03,020 --> 00:18:04,770 and actually used the card catalog, 316 00:18:04,770 --> 00:18:08,040 they have lots of index cards there. 317 00:18:08,040 --> 00:18:11,950 AUDIENCE: It's just like a listing. 318 00:18:11,950 --> 00:18:13,750 It's like a listing. 319 00:18:13,750 --> 00:18:17,500 Not meanings, but, like, information. 320 00:18:17,500 --> 00:18:19,839 So, like, topics or something. 321 00:18:19,839 --> 00:18:20,630 MARK HARTMAN: Yeah. 322 00:18:20,630 --> 00:18:21,963 Like that in the back of a book. 323 00:18:21,963 --> 00:18:25,100 An index is where are all the topics in the book. 324 00:18:25,100 --> 00:18:28,310 It tells you what's important in the book and where is it. 325 00:18:28,310 --> 00:18:31,760 Well, the power law index here tells us what's 326 00:18:31,760 --> 00:18:33,589 important about this equation. 327 00:18:33,589 --> 00:18:35,630 We know the general form, intensity equals energy 328 00:18:35,630 --> 00:18:39,560 to some power, but this is what's telling us well, 329 00:18:39,560 --> 00:18:40,760 does it look like that? 330 00:18:40,760 --> 00:18:42,176 Does it look like a straight line? 331 00:18:42,176 --> 00:18:43,400 Does it go up? 332 00:18:43,400 --> 00:18:45,570 You know, something like that. 333 00:18:45,570 --> 00:18:48,680 So x is the power law index. 334 00:18:48,680 --> 00:18:51,560 And even though I said this is a mathematical model, 335 00:18:51,560 --> 00:18:54,890 we're going to say one interpretation-- 336 00:19:00,070 --> 00:19:02,230 because there's a bunch of different processes 337 00:19:02,230 --> 00:19:06,030 in astronomy that could lead to a power law model. 338 00:19:06,030 --> 00:19:08,530 And sometimes, you know, perhaps they can be very different. 339 00:19:08,530 --> 00:19:10,930 You know, this one right here, this line 340 00:19:10,930 --> 00:19:13,760 looks very different from this line over here. 341 00:19:13,760 --> 00:19:15,790 So there's different processes. 342 00:19:15,790 --> 00:19:23,330 One possible interpretation of a power law 343 00:19:23,330 --> 00:19:26,390 is, and this is a model of light production. 344 00:19:26,390 --> 00:19:32,192 We're going to say synchrotron radiation. 345 00:19:36,790 --> 00:19:38,877 Has anybody heard of this? 346 00:19:38,877 --> 00:19:40,710 A couple of people may have heard about that 347 00:19:40,710 --> 00:19:42,540 in their expert projects. 348 00:19:47,070 --> 00:19:48,440 Maybe not. 349 00:19:48,440 --> 00:19:53,967 So synchrotron radiation is a light production model. 350 00:19:53,967 --> 00:19:55,800 You know, this is just a mathematical model, 351 00:19:55,800 --> 00:20:04,350 but synchrotron radiation is an actual light production model, 352 00:20:04,350 --> 00:20:07,680 just like the black body model was a light production model. 353 00:20:07,680 --> 00:20:10,530 The black body model also has a mathematical form, 354 00:20:10,530 --> 00:20:16,650 but it's a little bit tough to understand or to interpret 355 00:20:16,650 --> 00:20:18,150 in the same way. 356 00:20:18,150 --> 00:20:20,160 So it's a light production model, 357 00:20:20,160 --> 00:20:24,540 and the synchrotron is this idea of particles 358 00:20:24,540 --> 00:20:27,540 bouncing up and down around a magnetic field. 359 00:20:46,274 --> 00:20:48,750 All right. 360 00:20:48,750 --> 00:20:51,920 So you would expect this model to fit. 361 00:20:51,920 --> 00:20:54,470 I mean, we are going to change this parameter. 362 00:20:54,470 --> 00:20:58,610 We're going to change the power law index so that it fits well, 363 00:20:58,610 --> 00:21:02,330 but if you had an object like a supernova remnant 364 00:21:02,330 --> 00:21:06,380 that did have strong magnetic fields, 365 00:21:06,380 --> 00:21:09,470 you would expect well, maybe there was some synchrotron 366 00:21:09,470 --> 00:21:11,430 radiation there. 367 00:21:11,430 --> 00:21:12,860 OK? 368 00:21:12,860 --> 00:21:16,440 So this is the basics of these two models. 369 00:21:16,440 --> 00:21:20,270 We've got a thermal model, which is the black body spectrum. 370 00:21:20,270 --> 00:21:22,670 We've also got this idea, this mathematical idea, 371 00:21:22,670 --> 00:21:25,640 of a power law spectrum, which is much more generic. 372 00:21:25,640 --> 00:21:27,590 And when people do astronomy, sometimes they 373 00:21:27,590 --> 00:21:30,380 want to fit things to mathematical models first, 374 00:21:30,380 --> 00:21:32,030 and then they'll think about, OK. 375 00:21:32,030 --> 00:21:35,967 Well, let's just describe the spectrum first. 376 00:21:35,967 --> 00:21:38,300 Then, we'll think about, well, what's actually going on? 377 00:21:38,300 --> 00:21:40,400 Because you could get a power law model 378 00:21:40,400 --> 00:21:43,340 but not have synchrotron radiation. 379 00:21:43,340 --> 00:21:45,530 In our case though, in some cases here, 380 00:21:45,530 --> 00:21:47,340 we're going to see synchrotron radiation. 381 00:21:47,340 --> 00:21:50,390 And that's what we're going to use this power law model. 382 00:21:50,390 --> 00:21:50,995 All right. 383 00:21:50,995 --> 00:21:54,290 I wanna show you guys one instance of how you're going 384 00:21:54,290 --> 00:21:57,515 to try and fit data to models. 385 00:22:04,270 --> 00:22:07,750 So you are going to, on your screen-- 386 00:22:07,750 --> 00:22:10,740 actually, are there any questions first? 387 00:22:10,740 --> 00:22:11,565 Go ahead, Lauren. 388 00:22:11,565 --> 00:22:15,445 AUDIENCE: In the equation, intensity 389 00:22:15,445 --> 00:22:20,682 equals energy to the x power, can x equal zero? 390 00:22:20,682 --> 00:22:21,390 MARK HARTMAN: OK. 391 00:22:21,390 --> 00:22:24,360 If x equaled zero, what is anything 392 00:22:24,360 --> 00:22:27,420 raised to the zero power? 393 00:22:27,420 --> 00:22:28,295 OK. 394 00:22:28,295 --> 00:22:29,670 It can, and you're actually going 395 00:22:29,670 --> 00:22:30,970 to play with that in just a minute. 396 00:22:30,970 --> 00:22:32,386 So I want you to keep that in mind 397 00:22:32,386 --> 00:22:33,990 when you're looking at this. 398 00:22:33,990 --> 00:22:34,851 Any other questions? 399 00:22:34,851 --> 00:22:35,850 That's a great question. 400 00:22:38,500 --> 00:22:39,040 OK. 401 00:22:39,040 --> 00:22:40,170 So here's what you're going to do. 402 00:22:40,170 --> 00:22:42,040 I'm going to do the first example for you, 403 00:22:42,040 --> 00:22:44,206 and then we're going to have our fellows come around 404 00:22:44,206 --> 00:22:46,240 and work with you for just a few minutes. 405 00:22:46,240 --> 00:22:48,360 So you're gonna open up Spectrum Explorer. 406 00:22:48,360 --> 00:22:50,610 So I need everybody-- well, don't open it up just yet. 407 00:22:50,610 --> 00:22:52,360 I want you to just watch what I'm doing. 408 00:22:58,220 --> 00:22:59,930 And I am, just like we did last week, 409 00:22:59,930 --> 00:23:01,880 going to look at the spectrum of the sun. 410 00:23:01,880 --> 00:23:06,170 But first, I'm going to change my x-axis dimension to energy, 411 00:23:06,170 --> 00:23:09,680 and then I'm gonna change my range to-- 412 00:23:09,680 --> 00:23:11,390 what did we say-- 413 00:23:11,390 --> 00:23:14,360 0.1 to 6.2. 414 00:23:14,360 --> 00:23:23,254 I'm going to pull up, under astronomy data file, 415 00:23:23,254 --> 00:23:25,170 and of course, it's going to take a long time. 416 00:23:25,170 --> 00:23:25,860 There we go. 417 00:23:25,860 --> 00:23:29,680 And I pull up my data about the sun, and I say, OK. 418 00:23:29,680 --> 00:23:34,060 So this is what our spectrum of the sun looked like. 419 00:23:34,060 --> 00:23:37,660 The sun has a certain way that it produces light. 420 00:23:37,660 --> 00:23:40,360 We don't know exactly what it is right now, 421 00:23:40,360 --> 00:23:45,189 but let's try our two different models. 422 00:23:45,189 --> 00:23:46,480 We are going to say, all right. 423 00:23:46,480 --> 00:23:48,250 You'll see here at the bottom it says add. 424 00:23:48,250 --> 00:23:52,590 It gonna say black body, power law, data file, drawing. 425 00:23:52,590 --> 00:23:53,682 We did a drawing. 426 00:23:53,682 --> 00:23:55,640 Element, we're going to worry about that later. 427 00:23:55,640 --> 00:23:58,910 So let's add a black body. 428 00:23:58,910 --> 00:24:00,805 So this is a black body model. 429 00:24:03,970 --> 00:24:07,060 And what we see here-- 430 00:24:07,060 --> 00:24:09,920 yeah, don't worry about this information 431 00:24:09,920 --> 00:24:11,240 down at the bottom just yet. 432 00:24:11,240 --> 00:24:14,060 What we see here is a temperature gauge, 433 00:24:14,060 --> 00:24:19,430 and it goes from 0 Kelvin all the way up to 15,000 Kelvin. 434 00:24:19,430 --> 00:24:22,130 We said that the black body model depended only 435 00:24:22,130 --> 00:24:23,030 on the temperature. 436 00:24:23,030 --> 00:24:25,400 Doesn't matter what the object's made out of. 437 00:24:25,400 --> 00:24:29,780 So what I want to do is, if I looked at the black body 438 00:24:29,780 --> 00:24:34,730 at a very low temperature, why do I get this shape? 439 00:24:34,730 --> 00:24:35,930 Why do we get-- 440 00:24:35,930 --> 00:24:38,570 why do I get intensity at low energies 441 00:24:38,570 --> 00:24:41,970 if I'm looking at a low temperature object? 442 00:24:41,970 --> 00:24:42,901 What do you think? 443 00:24:42,901 --> 00:24:43,400 Juan? 444 00:24:43,400 --> 00:24:45,992 AUDIENCE: Because red's a low energy. 445 00:24:45,992 --> 00:24:46,700 MARK HARTMAN: OK. 446 00:24:46,700 --> 00:24:51,150 Red is a low energy, so I'm getting more red photons. 447 00:24:51,150 --> 00:24:51,650 Right. 448 00:24:51,650 --> 00:24:54,770 There you can see up at the top. 449 00:24:54,770 --> 00:24:56,270 You know, I've got only red, and I 450 00:24:56,270 --> 00:24:59,420 don't have a lot of any of the other colors. 451 00:24:59,420 --> 00:25:01,130 Where does each one of these photons 452 00:25:01,130 --> 00:25:03,290 come from in the black body model? 453 00:25:10,234 --> 00:25:13,320 Let's take a look back at atoms in motion. 454 00:25:13,320 --> 00:25:16,610 If we have a low temperature, we say 455 00:25:16,610 --> 00:25:21,290 go down 10, what did we say about the number of collisions 456 00:25:21,290 --> 00:25:22,880 and how hard the collisions are? 457 00:25:25,654 --> 00:25:26,320 Go ahead, Nikki. 458 00:25:26,320 --> 00:25:31,886 AUDIENCE: Less collision and less [INAUDIBLE] 459 00:25:31,886 --> 00:25:34,260 MARK HARTMAN: So what happens in the number of collisions 460 00:25:34,260 --> 00:25:35,700 and how hard the collisions are? 461 00:25:35,700 --> 00:25:40,650 AUDIENCE: Like, they don't collide as much, 462 00:25:40,650 --> 00:25:43,730 and they don't bounce that far. 463 00:25:43,730 --> 00:25:44,480 MARK HARTMAN: Yes. 464 00:25:44,480 --> 00:25:47,720 So if you have low temperature, the bouncing isn't as hard. 465 00:25:47,720 --> 00:25:49,550 And if the bounces aren't as hard, 466 00:25:49,550 --> 00:25:51,230 then each photon that you produce 467 00:25:51,230 --> 00:25:54,060 is not going to be very high energy. 468 00:25:54,060 --> 00:25:56,960 So if we look just generically here, 469 00:25:56,960 --> 00:25:59,240 we look at a low temperature object. 470 00:25:59,240 --> 00:26:01,730 We're getting a lot of low energy photons 471 00:26:01,730 --> 00:26:04,640 down here at one electron volt, but not a whole lot 472 00:26:04,640 --> 00:26:07,670 out here at four electron volts. 473 00:26:07,670 --> 00:26:10,610 We're still getting a range because the bounces that 474 00:26:10,610 --> 00:26:13,100 happen inside the object, not all of them 475 00:26:13,100 --> 00:26:14,480 are the same, you know, strength. 476 00:26:14,480 --> 00:26:18,650 You're not bouncing as hard with every atom. 477 00:26:18,650 --> 00:26:22,510 So-- but if I turn the temperature way up, 478 00:26:22,510 --> 00:26:23,890 what happens, you know? 479 00:26:23,890 --> 00:26:26,830 If I'm all the way out here, why do I 480 00:26:26,830 --> 00:26:33,049 have so much purple, but not so much red? 481 00:26:33,049 --> 00:26:34,090 What do you think, Chris? 482 00:26:34,090 --> 00:26:36,475 AUDIENCE: Because all the bounces 483 00:26:36,475 --> 00:26:38,860 you can get the really hard mass, 484 00:26:38,860 --> 00:26:43,931 so it's going to get higher energy than soft bounces. 485 00:26:43,931 --> 00:26:44,930 MARK HARTMAN: All right. 486 00:26:44,930 --> 00:26:46,420 So if we have a higher temperature, 487 00:26:46,420 --> 00:26:48,290 obviously there's going to be more bounces. 488 00:26:48,290 --> 00:26:51,140 There's going to be harder bounces, 489 00:26:51,140 --> 00:26:54,500 so you're going to get higher energy photons. 490 00:26:54,500 --> 00:27:00,980 So what we mean by fitting a data or fitting a model to data 491 00:27:00,980 --> 00:27:02,570 is this process. 492 00:27:02,570 --> 00:27:05,280 Here we have our data from the sun. 493 00:27:05,280 --> 00:27:07,710 Now, this model is applicable. 494 00:27:07,710 --> 00:27:09,830 You know, the model is shown in red. 495 00:27:09,830 --> 00:27:12,410 We can-- I mean, it's still a black body over here. 496 00:27:12,410 --> 00:27:13,880 It's still a black body over there, 497 00:27:13,880 --> 00:27:16,970 but the black body has a different temperature. 498 00:27:16,970 --> 00:27:22,400 Let's adjust the temperature until it fits or goes 499 00:27:22,400 --> 00:27:26,480 near most of those data points. 500 00:27:26,480 --> 00:27:27,140 Right? 501 00:27:27,140 --> 00:27:29,510 Because right here, I'm pretty close, 502 00:27:29,510 --> 00:27:32,170 you know, my model is pretty close to the data. 503 00:27:32,170 --> 00:27:33,230 And over here, yeah. 504 00:27:33,230 --> 00:27:34,410 Maybe it's not so good. 505 00:27:34,410 --> 00:27:36,290 So maybe I could, you know, maybe that 506 00:27:36,290 --> 00:27:37,680 fits a little bit better. 507 00:27:37,680 --> 00:27:42,080 So that's at a temperature 5,000 or turn it up. 508 00:27:42,080 --> 00:27:45,630 You know, if I fit the one on the left there, 509 00:27:45,630 --> 00:27:47,210 we're at a temperature of 6,000. 510 00:27:47,210 --> 00:27:50,420 6,400. 511 00:27:50,420 --> 00:27:52,620 Excuse me. 512 00:27:52,620 --> 00:27:57,770 So if I'm right here, somewhere in the middle, 513 00:27:57,770 --> 00:28:01,220 that is a pretty good fit to my data. 514 00:28:01,220 --> 00:28:05,250 My model is pretty close to most of my data points. 515 00:28:05,250 --> 00:28:07,700 So this model fits pretty well. 516 00:28:07,700 --> 00:28:10,900 Now, let me take a look at a power law model.