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 00:00:21,430 --> 00:00:32,740 MARK HARTMAN: --of, let's say, detector and interstellar dust. 9 00:00:32,740 --> 00:00:33,410 Oops. 10 00:00:33,410 --> 00:00:35,925 Let's draw a line in between there. 11 00:00:35,925 --> 00:00:36,425 Response. 12 00:00:41,730 --> 00:00:45,410 And let me put myself back up there. 13 00:00:45,410 --> 00:00:46,900 Is that going to work? 14 00:00:46,900 --> 00:00:50,430 Can you guys put board one up? 15 00:00:50,430 --> 00:00:54,710 Again, we have-- here's our source. 16 00:00:54,710 --> 00:00:56,040 It's putting out photons. 17 00:00:56,040 --> 00:00:59,900 In this case, we're talking about X-ray photons. 18 00:00:59,900 --> 00:01:02,460 X-ray photons are going out in all directions. 19 00:01:05,110 --> 00:01:09,600 We also have interstellar material. 20 00:01:09,600 --> 00:01:11,835 Some of these photons go through. 21 00:01:16,080 --> 00:01:20,110 Some of the photons go here and stop. 22 00:01:20,110 --> 00:01:22,300 Maybe the photon makes it a little bit further 23 00:01:22,300 --> 00:01:26,020 into the cloud, but still stops. 24 00:01:26,020 --> 00:01:29,294 What we're interested in is, what is this-- 25 00:01:29,294 --> 00:01:31,210 we really want to know, what does the spectrum 26 00:01:31,210 --> 00:01:33,940 look like just after it's been put out of the source? 27 00:01:33,940 --> 00:01:35,830 Because that's going to tell us what's 28 00:01:35,830 --> 00:01:38,020 really going on at the source. 29 00:01:38,020 --> 00:01:39,070 But there's our source. 30 00:01:39,070 --> 00:01:40,645 There's our interstellar dust. 31 00:01:46,580 --> 00:01:50,900 And then over here, we have Chandra, our detector. 32 00:01:54,410 --> 00:01:58,620 And some of the photons continue to go through. 33 00:01:58,620 --> 00:02:03,050 Some of the photons here are not collected by the detector. 34 00:02:03,050 --> 00:02:06,710 Some of the photons are. 35 00:02:06,710 --> 00:02:08,330 So this is our detector. 36 00:02:14,940 --> 00:02:19,310 That diagram should look somewhat familiar. 37 00:02:19,310 --> 00:02:21,750 I want you to leave a little space below it. 38 00:02:21,750 --> 00:02:22,490 AUDIENCE: Mark. 39 00:02:22,490 --> 00:02:23,281 MARK HARTMAN: Yeah? 40 00:02:23,281 --> 00:02:25,940 AUDIENCE: Why is there one circle particle there? 41 00:02:25,940 --> 00:02:28,240 MARK HARTMAN: Oh, because I didn't change it. 42 00:02:28,240 --> 00:02:30,570 Let's just all talk about x-rays for right now. 43 00:02:35,560 --> 00:02:45,550 So the detector puts out intensity versus energy. 44 00:02:45,550 --> 00:02:48,010 This is your actual observation. 45 00:02:48,010 --> 00:02:53,530 So this is your observation, and it looks like this. 46 00:02:53,530 --> 00:02:56,410 Or at least in the case of the neutron star, 47 00:02:56,410 --> 00:02:57,820 it kind of looked like that. 48 00:02:57,820 --> 00:02:59,980 This is what we observe-- 49 00:02:59,980 --> 00:03:03,629 our observation. 50 00:03:08,030 --> 00:03:14,250 The computer has a model for what's going on at the source. 51 00:03:14,250 --> 00:03:17,720 It also has a model for what's going on in the dust. 52 00:03:17,720 --> 00:03:20,870 And can we switch, Shekib, to the other image? 53 00:03:29,840 --> 00:03:33,380 This is our model of what's going on in the dust. 54 00:03:33,380 --> 00:03:37,160 This model also has a parameter that the computer 55 00:03:37,160 --> 00:03:38,840 tries to change. 56 00:03:38,840 --> 00:03:44,180 It tries to change the amount of dust between us and the object. 57 00:03:44,180 --> 00:03:46,490 Remember, we said that these high values 58 00:03:46,490 --> 00:03:48,290 were for very thin clouds, if there's not 59 00:03:48,290 --> 00:03:50,840 a whole lot of particles between us and the source. 60 00:03:50,840 --> 00:03:53,570 This one is for an average number of particles, 61 00:03:53,570 --> 00:03:57,500 and we see that we get much fewer low-energy particles. 62 00:03:57,500 --> 00:04:00,910 And this line is a prediction from the model, 63 00:04:00,910 --> 00:04:02,650 because you guys are actually fitting-- 64 00:04:02,650 --> 00:04:06,680 you're fitting a power law model and a dust model 65 00:04:06,680 --> 00:04:08,060 at the same time. 66 00:04:08,060 --> 00:04:10,130 Since there's always dust in the way, 67 00:04:10,130 --> 00:04:14,390 that model is always tacked on to whatever you guys fit. 68 00:04:14,390 --> 00:04:16,399 So you'll see if we have more dust, 69 00:04:16,399 --> 00:04:21,140 well, there's even fewer red photons that get through. 70 00:04:21,140 --> 00:04:26,000 So the computer has a model for what the dust does. 71 00:04:26,000 --> 00:04:28,880 We have a model of the source, and we're going to say that was 72 00:04:28,880 --> 00:04:34,202 our black-body, or-- 73 00:04:34,202 --> 00:04:36,410 so we're going to have the model, black-body or power 74 00:04:36,410 --> 00:04:40,460 law, that we looked at there. 75 00:04:40,460 --> 00:04:48,040 Our dust also has an absorption model. 76 00:04:55,660 --> 00:05:00,680 And that tells us how much light and what energies of light 77 00:05:00,680 --> 00:05:04,040 are absorbed by that interstellar dust. 78 00:05:04,040 --> 00:05:07,425 And we also have a model over here for the detector response. 79 00:05:15,882 --> 00:05:17,590 So the computer is actually taking, well, 80 00:05:17,590 --> 00:05:21,430 let's look at this actual model of the object that we want. 81 00:05:21,430 --> 00:05:24,250 I'll also throw in this model of the interstellar 82 00:05:24,250 --> 00:05:27,130 dust in between, and I also need to know 83 00:05:27,130 --> 00:05:29,140 how my detector responds, because I'm not 84 00:05:29,140 --> 00:05:31,520 going to collect everything. 85 00:05:31,520 --> 00:05:35,860 That's why we have the computer twiddle all the knobs, 86 00:05:35,860 --> 00:05:37,720 so that it can get a model that's 87 00:05:37,720 --> 00:05:39,875 close to what you observe. 88 00:05:39,875 --> 00:05:41,500 This morning, when we were just looking 89 00:05:41,500 --> 00:05:44,250 at very simple models with visible light, 90 00:05:44,250 --> 00:05:47,440 we were able to change the parameters, and it made sense. 91 00:05:47,440 --> 00:05:49,420 We could do it pretty easily. 92 00:05:49,420 --> 00:05:51,100 Well, in this case, you've got to have 93 00:05:51,100 --> 00:05:54,200 several different parameters. 94 00:05:54,200 --> 00:05:57,529 So from this model, the black-body or power law, 95 00:05:57,529 --> 00:05:58,320 what do we predict? 96 00:06:03,070 --> 00:06:08,200 For the black-body or power law, we predict the temperature. 97 00:06:08,200 --> 00:06:10,490 We could also predict the power law index. 98 00:06:13,940 --> 00:06:19,100 From the absorption model, we can predict-- 99 00:06:19,100 --> 00:06:20,030 and you'll see this. 100 00:06:20,030 --> 00:06:23,110 I know some of you guys had clicked on the Show Sherpa 101 00:06:23,110 --> 00:06:24,390 Fitting Logs. 102 00:06:24,390 --> 00:06:26,390 If you click on that option when you do the fit, 103 00:06:26,390 --> 00:06:29,090 you get a little bit more information. 104 00:06:29,090 --> 00:06:34,360 And there's a parameter called N sub h. 105 00:06:34,360 --> 00:06:38,630 You say that N sub h. 106 00:06:38,630 --> 00:06:40,332 That's how you say it. 107 00:06:40,332 --> 00:06:42,050 AUDIENCE: What's that? 108 00:06:42,050 --> 00:06:45,320 MARK HARTMAN: It's the letter N with a little h down below it. 109 00:06:45,320 --> 00:06:47,730 And what that is is-- we're going 110 00:06:47,730 --> 00:06:51,320 to call this column density. 111 00:06:53,940 --> 00:06:57,330 It's essentially related to the number of particles 112 00:06:57,330 --> 00:07:00,405 that are in the dust cloud between you and that object. 113 00:07:05,150 --> 00:07:09,630 So column density is related to-- 114 00:07:09,630 --> 00:07:19,110 let's say related to amount of dust. 115 00:07:19,110 --> 00:07:22,540 Now some of you, for your projects, 116 00:07:22,540 --> 00:07:24,930 will learn a little bit more about column density, 117 00:07:24,930 --> 00:07:26,432 but not everybody has to. 118 00:07:26,432 --> 00:07:28,140 So we're going to leave that out for now. 119 00:07:28,140 --> 00:07:30,240 OK? 120 00:07:30,240 --> 00:07:33,570 And from the detector, we don't need to predict anything 121 00:07:33,570 --> 00:07:35,847 about the detector, because we're always 122 00:07:35,847 --> 00:07:36,930 using the same instrument. 123 00:07:36,930 --> 00:07:38,790 We're always using Chandra. 124 00:07:38,790 --> 00:07:43,380 But we need to know what the detector response is. 125 00:07:43,380 --> 00:07:47,830 So what the computer does is, it puts this model and this model 126 00:07:47,830 --> 00:07:53,730 and this model all together, and it allows us to fit-- 127 00:07:53,730 --> 00:07:55,950 maybe it doesn't fit perfectly, but it 128 00:07:55,950 --> 00:07:59,610 allows us to fit our observation, 129 00:07:59,610 --> 00:08:01,290 because we only observe the light that 130 00:08:01,290 --> 00:08:02,310 came through the cloud. 131 00:08:02,310 --> 00:08:05,670 We only observe the light that got detected by Chandra. 132 00:08:05,670 --> 00:08:08,340 So we need to know all this other stuff in between. 133 00:08:11,000 --> 00:08:15,170 However, if we want to measure real stuff, 134 00:08:15,170 --> 00:08:18,440 we-- don't it's not that great to have 135 00:08:18,440 --> 00:08:19,730 just what we measure there. 136 00:08:19,730 --> 00:08:22,820 We actually want to know what is the light that 137 00:08:22,820 --> 00:08:26,520 was given out by the source. 138 00:08:26,520 --> 00:08:29,780 So that's why you have two separate lines that 139 00:08:29,780 --> 00:08:35,674 give you the flux in your output for your model. 140 00:08:39,559 --> 00:08:43,610 This temperature and power law index is for the source. 141 00:08:43,610 --> 00:08:47,820 This N sub h, or column density, is for the dust. 142 00:08:47,820 --> 00:08:50,620 But what we're interested in-- let me get another color here. 143 00:08:56,860 --> 00:09:06,105 So this light-- the flux from this, that is-- 144 00:09:11,190 --> 00:09:16,800 the flux is what gets to Chandra. 145 00:09:19,580 --> 00:09:22,860 That's right, Dean. 146 00:09:22,860 --> 00:09:28,470 After the cloud. 147 00:09:28,470 --> 00:09:29,880 So it's what gets there. 148 00:09:29,880 --> 00:09:32,510 It hasn't had a detector response just yet. 149 00:09:36,570 --> 00:09:44,210 But we took out the detector response. 150 00:09:49,921 --> 00:09:51,920 That's probably kind of hard to read down there. 151 00:09:54,780 --> 00:09:57,935 And this is the flux on the first two lines. 152 00:10:02,790 --> 00:10:04,800 This is important. 153 00:10:04,800 --> 00:10:08,760 The flux on the first two lines is the flux 154 00:10:08,760 --> 00:10:11,168 that is getting to Chandra. 155 00:10:11,168 --> 00:10:13,590 AUDIENCE: After what did it say? 156 00:10:13,590 --> 00:10:17,730 MARK HARTMAN: After the cloud, because it's 157 00:10:17,730 --> 00:10:22,460 the light that came out after the cloud, or after the dust. 158 00:10:25,070 --> 00:10:30,310 But if we are fitting our model correctly, 159 00:10:30,310 --> 00:10:38,010 the flux from the second two lines 160 00:10:38,010 --> 00:10:41,940 is what was emitted by the source. 161 00:10:41,940 --> 00:10:44,730 And this is this flux over here. 162 00:10:44,730 --> 00:10:47,100 It's out of the source, but it hadn't yet 163 00:10:47,100 --> 00:10:50,100 gone through the dust. 164 00:10:50,100 --> 00:10:53,820 Because if we know what model we're using for this source 165 00:10:53,820 --> 00:10:54,720 and we know-- 166 00:10:54,720 --> 00:10:58,484 and we measure or we predict how much dust is in the way, 167 00:10:58,484 --> 00:11:00,150 well, we know how this works, so then we 168 00:11:00,150 --> 00:11:01,816 can work backwards and figure out, well, 169 00:11:01,816 --> 00:11:04,830 what's the flux that was actually put out by the source? 170 00:11:04,830 --> 00:11:05,820 That's interesting. 171 00:11:05,820 --> 00:11:08,220 That's what we really want to know. 172 00:11:08,220 --> 00:11:15,470 So the second two lines is a prediction-- again, 173 00:11:15,470 --> 00:11:19,590 all of these things down here are predictions. 174 00:11:19,590 --> 00:11:24,935 That's the prediction of the flux emitted by the source. 175 00:11:28,601 --> 00:11:30,680 The flux on the second two lines. 176 00:11:30,680 --> 00:11:33,110 That's the flux emitted by the source 177 00:11:33,110 --> 00:11:34,850 before it went through the cloud. 178 00:11:43,150 --> 00:11:47,710 It's not what gets to Chandra after the cloud. 179 00:11:47,710 --> 00:11:48,250 Oops. 180 00:11:48,250 --> 00:11:49,290 I wrote emitted twice. 181 00:11:53,490 --> 00:11:55,500 Emitted by the source before the cloud. 182 00:11:58,240 --> 00:12:02,180 And in that case, we took out just the detector response. 183 00:12:02,180 --> 00:12:04,000 Here, we took out-- 184 00:12:08,960 --> 00:12:14,470 took out the detector and the cloud response.