 Greetings and welcome to the Introduction to Astronomy. In this lecture we are talking about distances of the stars, and this time we will focus on variable stars and using variable stars to be able to measure distances. So what is a variable star? Well, we have different types of them and some of them are more helpful for distances than others. We have, for example, eclipsing variables where one star passes in front of another which causes it to dim. So that will change the brightness. We also have intrinsic variables with a star itself. All by itself varies in brightness with the regular period. It will get brighter and it will get fainter. And we have cataclysmic variables where there is a sudden change in brightness. ANOVA is one example of these where there is a very sudden change in brightness. Now we will look at cataclysmic variables later on and eclipsing variables. But really what we want to talk about are the intrinsic variables here. Intrinsic variables will give us a light curve which will show how the star varies. Of course any of the stars will give us this. But we can look at how that varies, how the star varies in brightness over time. And when there is a regular pattern for certain types of stars we can actually use that to determine distances. So let's look at one type of these stars which are called the Cepheid variables named after delta Cphii which was the first of these to be discovered. And the Cphiids vary in brightness with periods of about three days to fifty days. So we can go down to very low periods down in here and we can go up to pushing towards over fifty days and those are what we classify as Cphiids in the green and the blue here. The period luminosity relationship between them, now remember when we graph things we tend to graph here a graphing period and luminosity we find that it's not scattered all over the place but there is definitely a relationship between period and luminosity. Those variables with very long periods are much brighter. Those with very short periods are fainter. And we can use that to be able to help us determine distances. This was discovered in 1908 by Henrietta Levitt and used by Edwin Hubble in the 1920s to determine the distance to the Andromeda galaxy. So let's look at how we can use this for distances. So why is the period luminosity of the Cepheid so important? Well first of all the period is very easy to measure. All we have to do is be able to have a star that's bright enough to be visible as long as we can see the star and measure its brightness and how it changes over time we can measure the period. We can then use the period luminosity relationship to tell us the luminosity. That is how bright the star actually is. Remember luminosity is the true brightness, how much energy that star is putting out every single second. Now we know the luminosity and we can measure the apparent brightness that's just how bright it appears in the sky. We can then put these two together to get the distance from the inverse square law of brightness. So we can use those to then determine the distance of the star. However, we first need to calibrate this. We need to know the distance and the intrinsic brightness of one Cepheid. That allows us to calibrate the period luminosity relationship. This was a problem. None of these are close enough to have a measurable parallax. So we need other methods to determine the distances and we will look at other methods coming up. But it is a good way to be able to measure stars and works out even to the Andromeda Galaxy. And in the 1920s Edwin Hubble found Cepheids in the Andromeda Galaxy measuring their distances and found out that the Andromeda Galaxy was actually another galaxy and not a part of our own. Now another type of star similar to the Cepheids are the RR Lyrae stars. These are another type of intrinsic variable. They are stars that are pulsating and varying. So here we have the Cepheids up here and the longer periods are RR Lyrae stars all about the same. And they all have periods of less than one day and they all have approximately the same luminosity about 50 times the luminosity of the Sun. Now that's great because if you identify a star as an RR Lyrae star, you know the luminosity. If you know the luminosity and you measure the apparent magnitude, you can get the distance. As soon as you can again calibrate this you need to calibrate and know the distance to one of these stars so that you can make a calibration and say that okay this is where the actual luminosity is. Otherwise until you know that this can be adjusted up and down a little bit. So we were able to use this once we could get the luminosity of one RR Lyrae star now anywhere we can see them we were able to measure distances and this is important because these are very bright. Some of these Cepheids 10,000 times brighter than the Sun they can be seen over vast distances. RR Lyrae stars about 50 times the brightness of the Sun we have used them to map the Milky Way the size and distribution of the Milky Way. So this is one of the important methods and one of the links in our distance ladder to be able to measure distances to the stars and galaxies. So let's finish up here with our summary and we looked at some briefly at a couple different types of variable stars but as these intrinsic periodic variables that can be used to measure distances. We looked at the Cepheids which have a period luminosity relationship which means we can get the distance based on their period. RR Lyrae stars have the same luminosity so once they are identified the distance can be determined. So that concludes this lecture on distances to the stars, 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.