Let us now look in a little more detail what the properties, quantifiable physical properties of galaxies are. The first question is, what can we measure, and we can use photometry or imaging, and quantify in some way how much light is there as a, say, function of radius in different filters, say. We can also measure their metallicity or stellar population as a function of special distribution, we can determine kinematics through doppler shifts of rotational motions or just random motions, but puff up the absorption lines. And those have to be put into some context. It's impossible to invert these measurements and derive a model directly from them. There's just not enough information. Instead of that, we make reasonably conceived models, so galaxy evolution, both dynamical and stellar evolution, see what they would predict in terms of observable properties and then compare that with what's actually observed. And that seems to work actually very well. Now the distribution of light is the simplest thing to answer. And since they're all centrally symmetric, it's the radial distribution of light. And for spiral galaxies well there are two components. There is a bulge in the middle and then there is a disk. The disks themselves are exponential. Just like in milky way there is semi-log that plots the straight line is exponential and you can see in the outer parts its is just that and then you have an extra component in the middle which is bulge is like a little elliptical. Now if you look in gas, you see some similarities and some differences. This is contours of the density of neutral hydrogen superimposed in a visible light picture of this galaxy and you can see galaxy 16 is much further out. Then stars. And this is generally the case. So we think what happens is the galaxies get built up in terms of starts from inside out. Most of early start formation happens with a bulge, and the disk. And the disk keeps growing and there is still plenty of hydrogen left in the outer radii to provide for star formation. On the other hand, if you look at dense gas like molecular gas, you find out that it follows up spiral arms very nicely and this is again not a great surprise because spiral arms by compressing gases, what stimulates a lot of star formation in the disks. But these are just images taken in the lines of molecular hydrogen or carbon dioxide, carbon monoxide. Now what about the elliptical galaxies [INAUDIBLE]? Well they're not exponential, they're fit with this funny formula which is exponential of radius to one quarter power. And that is due to an astronomer names Gerard DeVoceuler and I think he came up upon this purely by experimenting to see what'll work. Now there is a more general formula that reduces to this one, but this tends to be the one that fits a lot of elliptical galaxies, fairly well. The two plots, the one is the log log diagram, so parallel will be straight line. The one on the right is log brightness versus radius to the one-quarter power. And that gives you a straight line. This is where this came from. Why this particular profile? Nobody knows. For that matter we don't really know why the disc galaxy are exponential. They just are. These are standard dynamical forms that the galaxy assume, and they don't come in any other flavors, ad understanding why this is the case is going to be one of the very interesting things to figure out in the future. But what about their shapes? The shapes will clearly depend from what side you look at them. So, the observed distribution of peaks around 0.2, 0.3. So, it's just lightly flattened. But, you don't know whether you're looking at a oblate ellipsoid that's tilted. Or pro light one, sound gated, or something in between. And it turns out that actually elliptical galaxies are triaxial. They have different flattening in the axis, or it could be spherical. Now the reason for this is interesting it's not that they are flattened by rotation which is what you mainly assume and which is what people assumed early on. That elliptical galaxies are flattened by rotation, by centrifugal force. Now, their shapes are given by anisotropic velocity dispersion. This may look a little strange. Now, like pressure of gas in this room. You don't feel it different when you look North vs West. And yet this is exactly what happens with gaseous stars in an elliptical galaxy. So there is nothing to prevent this from happening. You have independent dynamics, if you will, in each of the orthogonal directions. And so you could, and you do, get different amounts of random motion in the three orthogonal directions. So in the direction we have the highest velocity of the dispersion of stars, they'll go further South and those would be the longest axis. The one we have the least amount of motion would be the shortest axis, and they'll be one in between. And so they're not grossly triaxial but they're just slightly triaxial and dynamical measurements confirm this. One interesting thing is that those that are bigger tend to be more anisotropic, and our understanding of this is that a lot of ellipticals form or grow by creeping out of galaxies. So if you, say, have to begin spherical elliptical galaxy and you drop another galaxy in it from some direction, it gets eventually absorbed. But that has brought kinetic energy that kinda prefers the particular direction of the impact. And so you'll end up with a stellar system that's a little elongated because because you'll have a little extra random motion along that particular axis. All right, do this a million times, and they incoming galaxies come from any odd direction and depending from which direction you get more impacts, that's the one you're going to develop the largest velocity of dispersion. So it makes sense, that the biggest ones, have eaten most galaxies, would have the largest anisotropic. And what about masses? We talked about masses, spirals, and flat rotation curves. For elliptical curves, we don't have rotation curves. It doesn't matter, really. But use random motions of stars or the rotational lancing. And if you plot mass of stars on y-axis versus total mass, dynamical mass infrared measurements, so velocities. They correlate, all right, but in tilted fashion in the sense that more massive galaxies have a larger fraction of the dark matter. And that means the smaller ones were more efficient in converting gas into stars while they could. And finally dwarf galaxies. I mentioned that they're really very different kind of beast. And most notably, they're very different in their densities. So these two thoughts show three different families of what we call hot start systems, globular star clusters which are here really just for symmetry's sake, regular ellipticals and those and you can see in these correlations of radius versus projected or rather they're set in a very different part of the perimeter of space. And they have even correlations of some sort, which are products of their physics. So that tells us right away that these are really very different kinds of objects. Now, for so-called dwarf elliptical galaxies you can look at, say, some common luminosity and compare their mean densities. And it turns out the mean density between your typical dwarf elliptical and regular elliptical is roughly like between air and uranium, something like four orders of magnitude. And so, calling them dwarf ellipticals is like using cotton puffs and calling them dwarf cannonballs. And so they really are very different kind of object.
