 Greetings and welcome to the Introduction to Astronomy. In this video we are going to still talk about the distances to the stars, but are going to look specifically at using variable stars to determine the distances. And this is one of the first steps that is used in the distance ladder to determine distances out in the universe. Parallax and radar work very close to us, radar only within our solar system and very close to us. Parallax working out to some of the nearest stars but in order to determine distances further across our galaxy and to other galaxies we are going to need stars that could actually be seen there that we can use to calibrate our distance scale. And we're going to start that out by looking at variable stars today. So what we find is for variable stars, first of all what is a variable star? Well there are several different types and we have eclipsing variable stars where one star passes in front of another and causes it to dim. Algal is an example of this. This is the demon star in the constellation of Perseus and it is an eclipsing binary star and you can actually look up when the eclipses will occur and notice if you identify the star you can actually see it get fainter when it is in eclipse. It is actually visible to the naked eye and one of the reasons that it was called the demon star because it was something in the heavens that was changing which was not expected to occur. Now so there are eclipsing variables. There are also intrinsic variables. Now these are the ones that we're going to start looking at a little bit more because the star itself varies in brightness with a regular period and we can see an example of the Cepheid variable shown here that they will vary in brightness so they will actually go down fainter fainter fainter and then will quickly rise up and get brighter again and then continue to do this with a regular very regular period. They will continually do this and this is going to be very important. These are the ones that we want to look at for being able to determine distances. There are also what we call cataclysmic variables which do not occur on such a regular scale. You can see the Cepheids have periods of maybe a couple of or sorry the Cepheids will have periods of running a few days to months and the change in magnitude can be a whole magnitude a factor of two and a half times in brightness. Cataclysmic variables can change much more quickly. These are sometimes what we call the Novi and a Nova can change its brightness very rapidly but then will sit for a long long period of time so it's not a regular change here and we can never know precisely when a Nova will go off. We can have a pretty good idea because some of them do recur from time to time but that might take decades or even centuries for them to build up to that again. Now what we look at here is what we call the light curve of the star how the brightness varies over time. Each of the dots on here is a single observation of the brightness of the star and over time over days weeks and months we can then see how that pattern changes and we're gonna find that to be very important for determining the distances. So let's look a little bit more at the Cepheid variables that we have and when we look at the Cepheids first of all they've got their name from the first one that was seen which was Delta Cephi the fourth brightest star essentially in the constellation of Cepheus in the Northern sky and they can vary in brightness with periods of between about three and fifty days. So they will get brighter and fainter as we saw on the previous slide. Why this makes them so important is because in 1908 Henrietta Leavitt found that there was a period luminosity relationship which is shown in the first graph here and what that means is that the period how long it takes to vary something that we can easily see so this is easy to view is related to the luminosity. Well this is what we want because if we know the luminosity and the apparent brightness we can get the distances so this is why it is so important we can easily measure the period by watching the light curve and watching how long it takes it to vary from peak to peak again and we can then measure that time in days that time in days if that happens to be you know 20 some days then we go up here and find out where that fits and that will give us the luminosity of the star. We can then use that to determine the distance the luminosity and the apparent magnitude the apparent brightness in the sky will give us the distance. So what we find is that the longer period the ones that take longer to vary means they have a higher overall luminosity. Now let's look a little bit more detail about how this works. For the sephiids why is this so important as I've mentioned the period is very easy to measure that is something that we can get very quickly and then we can use as I showed on the graph on the previous page we can use this to determine the luminosity of the star. If we know the luminosity and the apparent brightness and apparent brightness we just have to observe how bright the star appears to be we can then determine the distance using the inverse square law of brightness. So once we've done this we can then use that to determine the brightness and that gives us the distance which is what we are really looking for is trying to be able to determine this distance. However before it can be used we need to calibrate this luminosity relationship. We need to know the luminosity for one sephiid to be able to determine that. And so for one of these this is difficult because none of them were close enough to have a measurable parallax and we will look in other lectures at other ways to be able to kind of bridge the gap between these two because sephiids are quite important. So we could not use parallax which we have already talked about but we need some other method to determine the distance to just one sephiid and that would calibrate this scale. Now this was important because once it was done back in the 1920s Edwin Hubble did find sephiids on images taken of the Andromeda Galaxy and this was the first time that we learned that it was another galaxy and not part of our own. Up until that time it was still a great debate as to whether galaxies were actual other galaxies other island universes as they were called or if they were a part of our own galaxy and it was not until this time that we were actually able to figure that out and the sephiid variables that we're looking at here played a key part in this once we could use them and use their period luminosity relationship we could then get the distance again that's the all important thing that we are looking for right now is to get these distances and that allowed us to say that it was the distance was so large that it could not possibly be a part of our own galaxy. Now sephiids are not the only variable star that can be used there's another related type of star that we look at as well and these are called the RR Lyrae stars. They are named again after their primary one which was RR Lyrae the first one discovered in the constellation of Lyra and RR just means is the designation for variable stars. There's a way to catalog and name variable stars. Now these are interesting because these are like sephiids but they all have periods that are very short in less than one day and what that means is that if we look at them on the period luminosity relationship we looked at sephiids variables well they are all way down here at the bottom so all of the RR Lyrae stars are down here and that means that roughly they have all about the same period of about half a day and therefore all very close to the same luminosity about fifty times the luminosity of the Sun which means that as soon as we identify a star as an RR Lyrae star we immediately know its luminosity so we know what its luminosity is and can therefore determine its distance that makes them very important immediately we know that luminosity and we can use that to determine the distance and these have been used to map the size of the Milky Way these are very common stars in globular clusters and we can use those to then map out the extent of our Milky Way and learn something about the sizes of it so these are two ways to be able to determine distances using these different types of variable stars using the RR Lyrae stars using the sephiid variables we can map distances not only within our galaxy but also to other nearby galaxies however we are going to need more methods these are not visible across the universe when we start to think of things that are hundreds of millions of light years away or billions of light years away even though sephiid and RR Lyrae stars would be present there they're not going to be bright enough to be seen across those immense distances and we are going to need other methods to be able to determine those distances so let's finish up here as we do with our summary and here we look at first of all we talked about the number of different types of variable stars there were the eclipsing variables and the cataclysmic variables as well but the ones that we need to measure the distance are the intrinsic variables and the ones that are periodic so that we can observe a period observe how they vary in brightness and we use that to measure the important distance that we are trying to figure out the sephiids have a period luminosity relationship that allows us to measure the distance based on their period and as you recall the period gives us the luminosity and the luminosity and the apparent brightness give us the distance so we can use that to go back and get the distances and determine them the other type we looked at where the RR Lyrae stars these similar to the sephiids except we don't need a period luminosity relationship they are all the same luminosity so once one has been identified the distance can be easily determined so that concludes our lecture on determining distances using variable stars 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