 Greetings and welcome to the introduction to astronomy. In this video we are going to talk about a couple of things, including different properties of galaxies, and especially distances. How do we determine distances to galaxies, and how far away they are? Previously we've looked at methods of determining distances to stars, but they only work to the very nearest galaxies, so we're going to need some other methods to be able to figure out distances to the further galaxies. So let's go ahead and get started here. And first thing we want to look at is how do we determine the masses of galaxies? And that's a good question. How can we determine the mass? How much does a galaxy weigh? Well, one way that we can do this is by using Kepler's third law. And Kepler's third law, as modified by Newton, told us that the mass is equal to the cube of the semi-major axis divided by the square of the period. So we can measure the orbits, for example, of a star around the edge of a galaxy and figure out how long it takes to get around that galaxy, and that would allow us to determine the mass. Another way to do it would be for spiral galaxies. We can look at the rotation of objects and look at the velocities as we see in the graph here, velocity in velocity as a function of distance. That means that we can then look at what we would see in terms of the velocities, and that is a way of telling us about the mass as well. And we can also look at the broadening of spectral lines, because elliptical galaxies don't have a disc in the same type of regular rotation that a spiral galaxy has. We can't look at their rotation, but we can look at the broadening of the spectral lines, and that can help us to determine the mass of an elliptical galaxy. And the thing is what we find in each case is a problem, and that problem is that there seems to be far more mass in galaxies than we see. So the graph here for this galaxy shows the rotation curve that we expect here. That's expected based on what we see, based on the galaxy that we see. What we actually observe is that the rotation curve continues to rise. And what that means is that there must be a lot of matter that is not visible to us. Not just part of the luminous matter, the stars and the nebulae and all of the gas and materials that we see, but there has to be a lot of dark matter as well. So let's take a look at what we have here. In terms of ranges, what kind of galaxies do we find? Well, we find that galaxies, here we're looking at spiral galaxies, ellipticals, and irregulars, and we find that there's a range in masses, and we look at the ellipticals having the largest range in mass, going from 10 to the 5th to 10 to the 13th solar masses. So that means ellipticals have the smallest and largest galaxies. Ellipticals tend to be smaller than the spirals, but you can actually have a smaller spiral. You can have an irregular that's actually larger than a spiral. In terms of sizes, again, the ellipticals have the widest range of those that they can range from 3,000 light years for a very small elliptical to greater than 700,000 light years for the very largest ones. Maybe again, we're going to find the same pattern here for the different types of galaxies, but really what we're looking at right now is the mass of the galaxies, and we see that spirals and irregulars are roughly similar, but ellipticals have the much largest ones and the very smallest. Now if you recall, when we looked at stars, we talked about what we call the mass to light ratio, and the mass to light ratio, just to review, was to compare the mass of an object in solar masses and the luminosity of an object in solar luminosities. If we divide those, we get what we call the mass to light ratio, and that is a way to compare. Now just to go back and review this, if we use the sun as an example, the sun has a mass of one solar mass, it has a luminosity of one solar luminosity, that's by definition, and if we divide one by one for the sun, we get a one for the mass to light ratio. So that's a way to compare how much mass and how much light things are giving out. Now if we look at this for other objects, which we can do, we can look at stars and galaxies, what it means is that if we look at low mass stars, they contribute a lot of mass, but very little light. So low mass stars have a very large mass to light ratio. High mass stars have a very small mass to light ratio. They are giving off a lot of light relative to their mass, so even though they may be 20 times the mass of the sun, they don't give off 20 times the light, they might give off thousands of times the amount of light or even more. So when we look at a galaxy's mass to light ratio, we add up the mass to light ratio of all of the objects that is composed of. And what we find is that for things like young galaxies, like spirals and irregular galaxies, we find mass to light ratios in the range of 1 to 10. For older galaxies, we find that the mass to light ratio is much higher going up to 20 to 30. So that depends on the types of stars that are there. Young galaxies have lots of these high mass stars, so high mass stars associated with young galaxies here, and low mass stars associated with older galaxies, meaning that we get a difference in the mass to light ratios between the two. So how does this tie into the masses of galaxies and what we look at as dark matter? Well, what we find is that dark matter also applies to this mass to light ratio. What we see is we're looking at the inner parts of the galaxy. Most of the matter in galaxies is what we call this invisible dark matter. Dark matter has lots of mass and no light. That means it really helps to raise the mass to light ratio. It has an extremely high mass to light ratio because you're taking a big number and dividing it by a really little number, and that makes something really large. All galaxies that we look at have some amount of dark matter. So it's not just present in one galaxy, but it's present in almost all galaxies. And galaxies with significant amounts of dark matter can have a mass to light ratio in excess of 100. Remember what we looked at previously for some galaxies? We were looking at things in the teens into the 20s. Here we have galaxies with mass to light ratios in excess of 100. So really, we need to be able to understand dark matter to understand galaxies and the universe overall. So that's looking a little bit at the mass. Let's look a little at the distances as well in terms of how do we determine the distance to a galaxy? In order to determine the distance to a galaxy, we need to use, need to find ways to determine those distances. And what we know we cannot use is parallax. Parallax only works for things within our galaxy. And while we've been extending that with things like Gaia, it still is only doing a part of our galaxy because the shifts are so small. So we cannot use that even though we can see individual stars in some nearby galaxies. They are way too far away to be able to use parallax. Variable stars and cepheids that we used, this helps a little bit more and this was actually done for the Andromeda galaxy in the 1920s and determined that it was not a part of our galaxy. But still, it only works for the very nearest galaxies. Anything more than, you know, tens of light years away is not going to work for this method. So what we need to find is another method, another way of being able to determine distances. And that is where we use what we call standard bulbs. And a standard bulb or standard candle is a way to determine the distance to more distant galaxies. A standard bulb, what we mean by that is objects that have the same luminosity. So if we have a standard light bulb, it has the same luminosity as any other light bulb of that wattage. So we can examine it and if it's at different distances, the brightness, the apparent brightness depends only on the distance and the distance is what we are trying to find. What that means is if we find a standard bulb, we know the luminosity once the object is identified. And things like our Lyrae stars were one example of this. Our Lyrae stars all had about the same luminosity. So once we identified one in our galaxy, or in a globular cluster around our galaxy, we knew its luminosity, we could measure its apparent brightness, and we could immediately get the distance to it. So it gave us a way to be able to determine distances. Now these do not work for distant galaxies because the Lyrae stars are too faint. However, they will work for others. There are other types of things that we can use. And let's take a look at some of those. And one of those, one of the prominent ones, is what we call the Type 1A supernova. Now a Type 1A supernova, if you recall, was an object that formed when a white dwarf star exceeded the 1.4 solar mass limit and became unstable and ripped itself apart. The key thing is that every single one of these supernovae forms from a 1.4 solar mass white dwarf star. There are none that are 1.3, there are none that are 1.8. They are all exactly the same type of object. And what that means is that, theoretically then, all of these should have the same peak luminosity. They should all get just as bright. The other thing is that they are incredibly bright so that they can be seen not just in nearby galaxies but out to 8 billion light years. Our galaxy, our universe, stretches out 14 billion years old so that stretches us a good way to the edge of our universe. And these are very important for determining distances and understanding the evolution of the universe as we will see in coming lessons. So what are some other methods of using distances? Type 1A supernovae are one very important one that we use. But some other methods that we use are, for spiral galaxies, we can use what we call the Tully-Fisher relationship. And what was found is that there was a relationship between the luminosity of a spiral galaxy and its rotation rate. So we could look at the luminosity, we know the rotation rate, that's something we can measure, and we can then find that there's a relationship between that and the luminosity, and we find the more luminosity spirals spin faster. So a more luminous spiral galaxy would be spinning faster than a less luminous one. In a way, it's very similar to the period luminosity relationship for Cepheid variables. And that was a way to be able to determine distances in our galaxy. Well, this gives us a way to be able to determine the distances to spiral galaxies as long as we're able to measure this, as long as we're able to measure their rotation. And we do that using that 21 centimeter hydrogen line. And once we do that, we can then figure out the rotation speed from the spreading of that line. Use that to get the luminosity and use the luminosity to get the distance. The limitation here is that this is limited to spiral galaxies, so this will not help unless the galaxy has a distinct disk and has hydrogen gas in it to be able to detect the 21 centimeter line. So let's finish up here as we've looked at a few distances, and let's finish up with our summary as we like to. And what we found in this lesson is that the masses of galaxies can be determined by a number of ways, including Newton's form of Kepler's third law. We use the mass to light ratio to compare... compares the amount of mass it contains to the amount of light it emits. The mass to light ratio for the sun as an example is one, so we compare everything relative to the sun. And we can use distances to galaxies using Cepheid variables if they're nearby or standard bulbs like the Type 1A supernovae going out towards the edge of the universe. So that concludes this lecture on galaxy properties and distances. We'll be back again next time for another topic in astronomy. So until then, have a great day, everyone, and I will see you in class.