 Greetings and welcome to the introduction to astronomy. In this video we are going to look at another way of determining distances, what is called the spectroscopic parallax. Even though it has the word parallax in its name, it has nothing to do with parallax as has been discussed in another video. Parallax was measuring the apparent shift of a star compared to more distant stars. Spectroscopic parallax just means it is a spectroscopic way, using the spectra of the stars, to be able to determine distances. So let's take a look at how this works and why it is so important. And what we want to look at first is the fact that, you know, can we use the spectral class? The O, the B, the A, the F, the G, the K, or the M, and can we use that to determine distances? This would be a great thing since it is very easy to measure the spectral class. All we need to do is have a star that is bright enough to be able to get a spectrum and to be able to classify it. Now some of the difficulties with it are, first of all, that they have various, there are different luminosity, so that a star can have one spectral class, but there can be a variety of possible luminosity classes for it as seen here. So for example, a K-type star, as we work our way up, could be a main sequence or class five star here with a certain luminosity, or it might be a giant star up here in the red giant region, which has a different luminosity, or it could be a super giant star way up here that has an even different luminosity. So not only do we have to determine the spectral class here, but we also have to determine the luminosity class as well. We need to know if it is a main sequence star, a main sequence star, if it's a giant star, a super giant star, because that will make a difference in determining the distance. So not only do we need to classify a star as, say, for the sun as a G star, and in fact the sun very specifically is a G2 star, a subclassification, but it is a luminosity class five given by the Roman numeral V, and that classifies it very specifically and tells us where it falls on the HR diagram, and in that case if we can get a complete classification, a two-dimensional classification using the G2 and the luminosity class, that could determine where the star would be. So that G2 star might be here for something like the sun, so for the sun it would be somewhere around here, but a giant star, a G2 luminosity class three star, might be instead up here. And if we misclassify it, that can make a significant difference in the determination of the distance. So let's look at how this works, how we can use this to determine distances. And as I've said at the beginning, it has nothing to do with parallax, even though we call it spectroscopic parallax, it still has nothing to do with parallax, except for the fact that it is being used to determine distances. What we do is we have to measure two things. We need to get the spectral class of a star and the luminosity of a class of the star. Once we do that, we can just find its position on the HR diagram and use that to determine the luminosity. So where it is located here, once we find a star and determine that it is a certain class and luminosity class, we can then say we know what its luminosity will be. And once we know the luminosity, we can then use the inverse square law to determine the distance to the star. Now, as with other methods, this does need to be calibrated. We need stars of known distance, perhaps through regular parallax, that could be used to calibrate, to determine where the luminosity scales fit in on here, and allows us to calibrate the scale and tell us where these stars fit in. Once we find this for several stars, we can then use this to determine other stars of unknown distance and be able to determine the distances to them just by determining their spectral classification. So this leads us to what we call the cosmic distance ladder, and that is the fact that no distance measurement can work for all stars because they only work over various ranges. So some stars are close enough that we can determine their distances directly through parallax. Some stars are specific types like Cepheids or our Lyrae stars that can have other methods that we can use for the variable stars to determine their distances. If a star is close enough for us to get a good spectrum of it, we can use spectroscopic parallax. But what I want to point out is that these two methods, the variable stars and the spectroscopic parallax methods are both indirect methods. They are not direct ways of getting the distance. They depend on the parallax measurements. So you have to go back to having stars with measured parallax in order to be able to use them, and that's what we mean by calibration. We can use the parallax measurements to calibrate the spectroscopic parallax. We can then use spectroscopic parallax measurements of distance to calibrate variable stars. And we build on this over time. We can build on this as we get stars that are further and further away, and start to use it for galaxies. We use this calibration in order to build and to determine distances that are further away. Now, if we look at some of these examples for the nearby stars, for the relatively close stars that we look at, that we can use trigonometric parallax, we'll work out to about 30,000 light years once the Gaia mission is complete. We'll be able to measure distances out to 30,000 light years. Our Lyrae stars can be seen out to 300,000 light years, 10 times the distance that the Gaia mission will be able to do with trigonometric parallax. The HR diagram and spectroscopic parallax can get four times larger than this, out to 1.2 million light years. And Cepheid variables can get out very far, though some of the brightest Cepheid variables can be seen to 60 million light years away. However, we are still going to need other methods as we get to talk about galaxies. This certainly gets us well outside our galaxy. However, stars like these could not even be seen in the Andromeda galaxy. Our Lyrae and spectroscopic parallax could not even be used in the Andromeda galaxy, which is about 2 to 2 and 1 half million light years away. Cepheid variable stars could and could be used for other galaxies out there. But there are still many galaxies that are hundreds of millions or even billions of light years away. And we are going to need other methods. Now one of the problems here is when we measure something, any measurement that we make has an error associated with it. So if we measure, for example, a star to be 100 light years, there might be an error associated with it of 10%, which is a decent error for determining distances. In many cases, it can be much larger than that. But that would mean that the star would be between 90 and 110 light years away. So we know roughly where it is. But remember, if this is determined by trigonometric parallax, that we are then using that. And we now have an error associated with that that we are using to calibrate to use the Our Lyrae stars, to use the spectroscopic parallax, to use the Cepheid variable stars. And any small errors here will lead to errors in distances determined by these other methods. And we'll continue on because we have to use those methods to calibrate other methods as we go outward. So each errors will build up on the distance ladder because each step depends on the previous step. So we need to get as accurate, and that's why Gaia is so important here, is because it is going to help us nail down those distances using trigonometric parallax out to far further than we possibly could before. So that is going to help us stabilize that first step on the distance ladder, which will hopefully give us better values for these later steps as well. So let's finish this up with our summary. And what we found is, in this case, we've learned that we can use the HR diagram to determine the luminosities. And therefore, we can get distances using just the HR diagram. To get these distances, we need to know the spectral class of the star and the luminosity class of the star. So we can't do it with just one. We can't get just spectral class. We need to know what spectral classification it is. For example, the sun would be a G2, but we also need its luminosity class, which for the sun would be a Roman numeral 5. So that we need both of those, and then that gives us the luminosity, which allows us to get the distance. Then we wanted to look at the cosmic distance ladder itself, and that is a series of steps to determine distances. And one of the problems, because of the way it has to be done, is that each step builds on the previous step. And that means that small errors in determining distances to nearby stars can become very large errors as we head further out into the universe and start determining distances to distant galaxies. So that completes our lecture on determining distances using a spectroscopic parallax. 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.