1 00:00:00,012 --> 00:00:05,322 Let us now turn to the internal motions inside elliptical galaxies. 2 00:00:05,322 --> 00:00:11,002 This turns out to be really the key to their nature and understanding. 3 00:00:11,002 --> 00:00:16,117 So the stars in elliptical galaxies have largely random motions. 4 00:00:16,117 --> 00:00:23,263 And so therefore, their kinetic energy can be characterized by a velocity dispersion. 5 00:00:23,263 --> 00:00:29,680 You can think of the distribution as being pretty close to Gaussian, because they're 6 00:00:29,680 --> 00:00:35,248 supported by random motions rather than rotation, they're called pressure 7 00:00:35,248 --> 00:00:39,703 supported systems. And the way we usually measure this is 8 00:00:39,703 --> 00:00:45,436 through Doppler broadening of their absorption lines as I'm sure you know, 9 00:00:45,436 --> 00:00:51,806 spectra of galaxies composed of stars, have many different absorption lines those 10 00:00:51,806 --> 00:00:56,875 are different elements. And, each of these lines is pretty sharp 11 00:00:56,875 --> 00:01:01,093 when it originates. But, because there are many, many 12 00:01:01,093 --> 00:01:07,267 different stars moving at random velocities, the total observed Line will 13 00:01:07,267 --> 00:01:13,245 be a weighted sum of those and it's shape will reflect the overall Doppler 14 00:01:13,245 --> 00:01:20,453 broadening by the velocity distribution. So by deconvolving an unmeasured line, say 15 00:01:20,453 --> 00:01:24,684 from templates. Spectral stars that are like those that 16 00:01:24,684 --> 00:01:30,269 make elliptical convolved with say Gaussian distribution of Doppler shifts. 17 00:01:30,269 --> 00:01:35,545 We can infer what is the underlying velocity dispersion of the elliptical 18 00:01:35,545 --> 00:01:39,547 galaxy. Note that whereas, we measure rotation by 19 00:01:39,547 --> 00:01:45,716 simple shift of the line, the red or blue. Here, the line is not shifted it's just 20 00:01:45,716 --> 00:01:49,623 broadened. And here are some velocity profiles of 21 00:01:49,623 --> 00:01:54,858 elliptical galaxies. The velocity dispersion up top, rotational 22 00:01:54,858 --> 00:01:58,864 speed on the bottom. In some cases, there is actually a 23 00:01:58,864 --> 00:02:04,492 rotational component, those tend to be this elliptical, because in other cases 24 00:02:04,492 --> 00:02:10,239 there is no net overall rotation, but there is a lot of velocity dispersion. 25 00:02:10,240 --> 00:02:16,039 Generally speaking, velocity dispersions tend to be higher near the center of the 26 00:02:16,039 --> 00:02:21,434 galaxy but, by and large they remain nearly flat by analogy with flat rotation 27 00:02:21,434 --> 00:02:25,897 curves of spiral galaxies. A nice new way to measure this is so 28 00:02:25,897 --> 00:02:31,544 called integral field spectroscopy. Here a spectrograph is composed of many 29 00:02:31,544 --> 00:02:37,749 different entrance aperture, usually it's done with optical fibers and then spectrum 30 00:02:37,749 --> 00:02:42,423 taken of each one of those. So you're getting a spectroscopically 31 00:02:42,423 --> 00:02:47,300 resolved picture in the sky. And from that you can reconstruct what 32 00:02:47,300 --> 00:02:52,516 Doppler shifts and broadening are anywhere across the face of the galaxy. 33 00:02:52,516 --> 00:02:58,298 It can also add up all the light and then you have surface brightness distribution. 34 00:02:58,298 --> 00:03:03,999 So here are some examples from group, an instrument called Sauron of several 35 00:03:03,999 --> 00:03:09,568 elliptical galaxies as indicated here. The top row shows their surface brightness 36 00:03:09,568 --> 00:03:14,265 distribution, just adding up the light. The middle row shows the rotational 37 00:03:14,265 --> 00:03:19,448 velocity component and it's coded into two fashion, red ones going away from us, blue 38 00:03:19,448 --> 00:03:23,251 ones approaching us. And you can see that there is definitely 39 00:03:23,251 --> 00:03:28,347 some rotation present in some cases. Actually, in all cases in this particular 40 00:03:28,347 --> 00:03:32,924 set, which is not chosen randomly. And the bottom shows the distribution of 41 00:03:32,924 --> 00:03:37,204 velocity dispersion. There, you can see there is generally a 42 00:03:37,204 --> 00:03:43,210 tendency to be a little higher in the middle, but otherwise, it doesn't not seem 43 00:03:43,210 --> 00:03:49,627 to show have much of a shape distribution. So when velocity dispersions and 44 00:03:49,627 --> 00:03:57,131 rotational speeds were measured for elliptical, to everybody's surprise back 45 00:03:57,131 --> 00:04:04,074 then, it was found out that shapes are not due to the rotational velocity. 46 00:04:04,074 --> 00:04:10,566 And you can compute from simple dynamical models that for a given ellipsoid that's 47 00:04:10,566 --> 00:04:16,864 supported largely by rotation and has a commensurate amount of random motions, 48 00:04:16,864 --> 00:04:23,444 viewed from different angles, what should be the ratio between maximum rotational 49 00:04:23,444 --> 00:04:28,546 speed and velocity dispersion. And you can divide the two and so for 50 00:04:28,546 --> 00:04:33,906 purely rotationally supported oblate ellipsoids, that's a line in the diagram 51 00:04:33,906 --> 00:04:39,666 that shows the ratio of velocity to the rotational speed to velocity dispersion as 52 00:04:39,666 --> 00:04:44,520 a function of [unknown]. As it turns out, the elliptical do go up 53 00:04:44,520 --> 00:04:49,885 to that line, but most of them are below. Meaning that they have too little 54 00:04:49,885 --> 00:04:55,576 rotational speed for their ellipticity and their radial velocity component. 55 00:04:55,576 --> 00:05:01,076 And so, that also means that they cannot be supported entirely by rotation, that 56 00:05:01,076 --> 00:05:06,228 could be that sort of the upper envelope. There can be none of the rotation that 57 00:05:06,228 --> 00:05:11,128 will be the zero point on this diagram. But they're somewhere in between and so a 58 00:05:11,128 --> 00:05:16,075 great majority of elliptical galaxies are supported by velocity anisotropy. 59 00:05:16,075 --> 00:05:21,323 And it can take that the ratio of maximum rotational speed to velocity dispersion. 60 00:05:21,324 --> 00:05:28,085 And align for perfect oblate rotationally supported ellipsoid and normalized by that 61 00:05:28,085 --> 00:05:31,482 line. So that rotationally supported oblate 62 00:05:31,482 --> 00:05:37,466 ellipsoid will have the normalized value of exactly one and lower than one, means 63 00:05:37,466 --> 00:05:41,473 more anisotropy. So now we can plot this normalized 64 00:05:41,473 --> 00:05:45,163 quantity. The relative importance of velocity 65 00:05:45,163 --> 00:05:49,124 anisotropy as a function of say galaxy luminosity. 66 00:05:49,124 --> 00:05:54,296 And it was found that more luminous galaxies are more anisotropic. 67 00:05:54,296 --> 00:05:58,905 This can be understood as a consequence of random merging. 68 00:05:58,905 --> 00:06:03,541 You may remember that disks have to involve dissipative formation. 69 00:06:03,541 --> 00:06:08,650 You have to dissipate energy, not the angular momentum get a disk, then make 70 00:06:08,650 --> 00:06:12,078 stars. Whereas, random merging does not preserve 71 00:06:12,078 --> 00:06:15,372 rotation. It scrambles up any rotation and just 72 00:06:15,372 --> 00:06:20,814 creates pressure supported systems. So if you indeed you build up ellipticals 73 00:06:20,814 --> 00:06:25,884 through random merging then you would expect the more luminous ones to be more 74 00:06:25,884 --> 00:06:28,826 anisotropic and that's exactly what we see. 75 00:06:28,826 --> 00:06:33,782 As we measure spectra we can tell about chemical composition of stars, not just 76 00:06:33,782 --> 00:06:37,486 their velocities. And so we can measure strengths of 77 00:06:37,486 --> 00:06:43,646 absorption lines of elements such as iron or magnesium, which are fairly common and 78 00:06:43,646 --> 00:06:49,138 use that as an indicator of the chemical evolution history of the galaxy. 79 00:06:49,138 --> 00:06:55,224 So the, it was found that elliptical galaxies are more metal rich near the 80 00:06:55,224 --> 00:07:00,836 middle than on the outside skirts. There is, there was a more recycling of 81 00:07:00,836 --> 00:07:07,172 interstellar material through subsequent actions of star formations in the central 82 00:07:07,172 --> 00:07:11,028 portions. Now you cannot do this through merging. 83 00:07:11,028 --> 00:07:14,949 In fact, merging will scramble any such arrangement. 84 00:07:14,949 --> 00:07:20,203 So there has to be a dissipative self-enrichment component to the formation 85 00:07:20,203 --> 00:07:25,533 of ellipticals that then reflects itself through this dependence of stellar 86 00:07:25,533 --> 00:07:28,639 population as in the function of red shift. 87 00:07:28,639 --> 00:07:33,752 Now spectra are hard to obtin because they require long observation times. 88 00:07:33,752 --> 00:07:39,722 A much easier thing to measure are colors, which are ratios of [unknown] to different 89 00:07:39,722 --> 00:07:42,927 filter. Now it turns out that more metal rich 90 00:07:42,927 --> 00:07:48,707 stellar populations have more absorption lines in the blue part of the spectrum, 91 00:07:48,707 --> 00:07:53,457 removing some blue light. So the more metal rich populations will 92 00:07:53,457 --> 00:07:58,277 have a redder color. And you can measure colors fairly easily, 93 00:07:58,277 --> 00:08:02,672 you use them as a proxy for the metallicity of galaxies. 94 00:08:02,672 --> 00:08:09,402 And it turns out that more luminous ones are redder, they're more metal rich. 95 00:08:09,402 --> 00:08:16,752 And you may recall that there's a picture whereby supernova ejecta, which is where 96 00:08:16,752 --> 00:08:23,076 metals come from into the new generation of stars, can escape from low mass 97 00:08:23,076 --> 00:08:26,622 galaxies. But are still bound to the higher mass 98 00:08:26,622 --> 00:08:30,235 host galaxies where it can be recycled into new stars. 99 00:08:30,235 --> 00:08:35,545 So it makes sense that subsequent episodes of star formation in deeper potential 100 00:08:35,545 --> 00:08:40,615 levels in more luminous galaxies, more massive galaxies would result after a 101 00:08:40,615 --> 00:08:44,411 little while in a more metal rich stellar population. 102 00:08:44,412 --> 00:08:50,632 So we see that both within individual galaxies, more metal rich stuff near the 103 00:08:50,632 --> 00:08:56,836 middle and between different galaxies, the more luminous or more massive ones 104 00:08:56,836 --> 00:09:02,638 retaining more of their metals. Likewise, you can use velocity dispersion 105 00:09:02,638 --> 00:09:08,067 instead of luminosity and find out that those which have higher velocity 106 00:09:08,067 --> 00:09:14,297 dispersions, which are really kinetic energy per unit mass, therefore reflecting 107 00:09:14,297 --> 00:09:17,963 in a very equilibrium the depth of potential oil. 108 00:09:17,963 --> 00:09:23,513 Also have higher metallicities deeper potential wells, more recycling of the 109 00:09:23,513 --> 00:09:26,986 metals. We already talked about gas in elliptical 110 00:09:26,986 --> 00:09:32,726 galaxies so whereas spiral galaxies have plenty of interstellar medium, cold one, 111 00:09:32,726 --> 00:09:37,314 hydrogen mostly. In elliptical galaxies there is hardly any 112 00:09:37,314 --> 00:09:40,895 cold gas. Only if its been recently secreted, but 113 00:09:40,895 --> 00:09:46,571 there is plenty of gas all cold and that gas comes largely as a product of stellar 114 00:09:46,571 --> 00:09:50,076 evolution. But somehow it's secreted from the 115 00:09:50,076 --> 00:09:55,324 outside, and it's heated to millions of degrees, which is a very equilibrium 116 00:09:55,324 --> 00:10:00,771 temperature for the corresponding potential wells in elliptical galaxies. 117 00:10:00,771 --> 00:10:06,472 Now that we can measure kinematics of ellipticals, reflecting their potential 118 00:10:06,472 --> 00:10:12,337 wells, we can fit dynamical models and find what their masses are so here is from 119 00:10:12,337 --> 00:10:17,734 a large survey of gal-, of particular galaxies by a group called Spider 120 00:10:17,735 --> 00:10:21,714 [unknown] and Carvalho [unknown] collaborators. 121 00:10:21,714 --> 00:10:27,636 Plot of stellar masses and directly from integration of visible light versus the 122 00:10:27,636 --> 00:10:33,934 nominal masses, which are now inferred. From kinematics velocities of stars 123 00:10:33,934 --> 00:10:38,662 reflecting total mass not just the visible component. 124 00:10:38,662 --> 00:10:44,705 And they're proportional, right? But there is trend the more massive 125 00:10:44,705 --> 00:10:51,320 galaxies tend to have a larger component of dark matter, or I should say more 126 00:10:51,320 --> 00:10:58,437 masses in form of the dark component. So the moss galaxy is on this band where 127 00:10:58,437 --> 00:11:04,128 one envelope is that there is no dark matter, there is just stars. 128 00:11:04,128 --> 00:11:10,722 The other envelope is that the anomical mass is about 6 times the amount of 129 00:11:10,722 --> 00:11:17,027 visible mass in stars. Interestingly enough, that corresponds to 130 00:11:17,027 --> 00:11:23,804 the riot of omega matter to the omega of variance in [unknown] at large. 131 00:11:23,804 --> 00:11:30,530 If you can think of stellar masses for luminosity then that means that mass to 132 00:11:30,530 --> 00:11:35,693 light ratios will be higher for the more massive galaxies. 133 00:11:35,693 --> 00:11:41,020 And that's indeed what's seen through a number of other pieces of evidence. 134 00:11:41,020 --> 00:11:46,788 So fitting dynamical models in detail to galaxies we can figure out exactly what 135 00:11:46,788 --> 00:11:52,292 their masses are, and you can plot masses to light ratio versus luminosity or 136 00:11:52,292 --> 00:11:58,239 reduced mass, and here they are. The more massive or more luminous galaxies 137 00:11:58,239 --> 00:12:04,738 have higher mass to light ratios, which [unknown] need not specify the amount of 138 00:12:04,738 --> 00:12:08,731 dark matter. It could be the invisible variance, but 139 00:12:08,731 --> 00:12:14,473 there are good reasons to believe that in fact most of this is due to the relative 140 00:12:14,473 --> 00:12:20,302 abundance or relative amounts of dark luminous matter within the regions where 141 00:12:20,302 --> 00:12:23,559 we measure this. Now, notice that qualifier. 142 00:12:23,559 --> 00:12:30,734 We, remember that we already talked how in galaxies baryionic component is more 143 00:12:30,734 --> 00:12:35,676 condensate than dark matter. Dark matter halos are fluffier and 144 00:12:35,676 --> 00:12:39,947 dominate more at large radii. This is certainly true in elliptical 145 00:12:39,947 --> 00:12:43,225 galaxies as well. So if you're measuring velocity 146 00:12:43,225 --> 00:12:48,676 dispersions and what not in the luminous parts of the galaxies, you're liable to be 147 00:12:48,676 --> 00:12:54,532 finding mostly luminous bariartic mass. In the ratio of distribution of dark and 148 00:12:54,532 --> 00:12:57,945 luminous matter changes is a function of mass. 149 00:12:57,945 --> 00:13:03,561 So that halo distributions are more extended but the light distributions tend 150 00:13:03,561 --> 00:13:09,341 to be more condensed for smaller galaxies as is indeed the case if you remember how 151 00:13:09,341 --> 00:13:13,263 surface brightness profiles the pen in luminosity. 152 00:13:13,263 --> 00:13:16,430 Well, then you would expect to see just this. 153 00:13:16,430 --> 00:13:21,246 So it's not 100% clear at this point how much of this effect is due to a different 154 00:13:21,246 --> 00:13:26,411 distribution of luminous and dark matter. Or is this different amounts of luminous 155 00:13:26,411 --> 00:13:29,855 and dark matter? It's probably a combination of both a 156 00:13:29,855 --> 00:13:34,629 gravitational lensing provides a completely different way of measuring 157 00:13:34,629 --> 00:13:40,134 masses, independent of all the schematics and so this was done, for sample galaxies 158 00:13:40,135 --> 00:13:46,130 using galaxies themselves as, as lenses. And what's plotted here, confusingly in 159 00:13:46,130 --> 00:13:52,018 the same diagram, is the mass to light ratios for the total mass that's sort of 160 00:13:52,018 --> 00:13:57,814 the tilted component and for the luminous mass alone, which is a kind of flat 161 00:13:57,814 --> 00:14:01,376 component. And we find out that for the luminous mass 162 00:14:01,376 --> 00:14:06,034 alone, mass to light ratio doesn't change through the function of mass. 163 00:14:06,034 --> 00:14:10,775 Meaning, ellipticals of all different masses have the same stellar populations. 164 00:14:10,775 --> 00:14:14,630 And, consistent from what we expect from stellar evolution laws. 165 00:14:14,631 --> 00:14:20,166 But there is always total mass, so higher total mass the light ration and more so t 166 00:14:20,166 --> 00:14:25,496 higher mass end which is exactly what you've seen in for previous diagrams but 167 00:14:25,496 --> 00:14:29,089 this time measured in a completely different way. 168 00:14:29,089 --> 00:14:33,359 Thus, giving us some confidence that this is in fact correct. 169 00:14:33,359 --> 00:14:37,463 Yet another independent way of assessing this is through. 170 00:14:37,464 --> 00:14:43,277 Their X-ray profiles just like we use X-ray measurements to constrain masses 171 00:14:43,277 --> 00:14:49,685 inside clusters of galaxies you can do the same thing inside elliptical galaxies, and 172 00:14:49,685 --> 00:14:55,915 there again you find out using X-ray gases dust particles that the ratio of total, or 173 00:14:55,915 --> 00:15:01,476 non luminous mass to the luminous ones, increases as a function of radius. 174 00:15:01,476 --> 00:15:07,638 And next time we'll talk about supermassive black holes in galactic 175 00:15:07,638 --> 00:15:13,943 centers and something that's completely unrelated dwarf galaxies.