Okay, gang let's roll. In the early decades of the 20th century two momentous discoveries were made that would change the face of astronomy forever. The first was Henrietta Leavitt's discovery of the cepheid variable stars' period-luminosity relationship. As we have seen, this gave astronomers at long last a means to probe the distances to many more objects than were accessible Via parallax measurements, and hence now we could determine the intrinsic luminosity for a sizable number of stars. In addition another woman, Cecilia Payne, discovered that the spectral types of stars that were classified using atomic spectra, were actually representative of a temperature sequence of the surface layers of stars. But even before this latter understanding, Ejnar Hertzsprung, working in Denmark, and Henry Norris Russell, working at Princeton, began graphing the correlation between spectral types of stars and their intrinsic luminosity. The results were breathtaking and led to far-reaching understanding of not only the characteristics of stars as they appear today but also the nature of stellar evolution. How the stars change over vast periods of time. Let's see how this came about. First, notice what happens if you just take a bunch of stars and do a scatter plot of their apparent magnitudes and colors, or spectral types. You will get a random useless mess, such as shown here. The reason for this is that the stars can be at any apparent magnitude because their distances are all different. But now we can see what happens when we know the stars distance and hence intrinsic luminosity. Here you see Henry Norris Russel's first plot Using about 200 stars with known absolute magnitudes. It's crude, but you can see the pattern emerging. And here is a refined version incorporating the ideas spawned by Henrietta Leavitt Cecilia Payne and Ejnar Hertzsprung as well. We see 23,000 stars whose spectral classifications and luminosities are known. The first thing that immediately strikes you is that the stars are not randomly distributed. There's a line running diagonally across the graph that contains the vast majority of all the stars. It's called the main sequence. And this non random pattern, is a very powerful indicator for astronomy. It means that when you observe, say a cluster of stars. Whose members are more or less at the same distance from the earth. You can look at their HR diagram, fit their main sequence to this calibrated one, and thereby immediately find out how far the cluster is from the earth. All you need to do is compare the cluster members' observed magnitudes. And compare them to the absolute or intrinsic magnitudes shown here. And voila, you have their distance via the Inverse Square law. Pretty neat. But before we explore this further let's look at how many ways we have to express both the spectral type of the stars and their associated luminosity. First you can see that the spectral classification scheme we talked about last week is associated with the star's temperature. This was Cecilia Payne's work. Also at the bottom is another often-used indicator called the star's B minus V color. This number refers to the measurement of the brightness of the star Through two color filters. In this case, the B filter, which emphasizes the blue portion of the star's light and the V filter, which emphasizes the visual or more yellow part of the output. It turns out that comparing these two measurements, by subtracting the V magnitude from the B magnitude, gives a quick and reliable way to compute the spectral type, and hence temperature, as well. Now, let's look at the 'y' axis. At the left we see the value of the luminosity is compared with that of the Sun. Corresponding to that at the right is the value of the stars absolute magnitude which is defined as the magnitude that the star would have At a distance of 10 parsecs. A moment's thought will show you that in order to know that number, the absolute magnitude, you must know the star's distance, so you can convert the observed apparent magnitude To the value it would have at 10 parsecs. But now look what you can do. You can stand the problem on its head. Imagine you observed the spectrum of a star that looks identical to, say, one whose B minus V color is 1.5 and whose luminosity is 0.01 times that of the sun. You know then, that your star has an absolute magnitude of plus ten. Now, by comparing your observed apparent magnitude, to the value of plus ten, you immediately know the distance. You have derived what is called a spectroscopic parallax. It is not really a parallax at all, but a way to get the distance to stars for which the parallax might be unmeasurable because it is too far away. So you can see how powerful the HR diagram can be. But now we can go beyond this and using some theoretical results of stellar structure understand how stars evolve in time. This, in turn, will lead us to a basic understanding Of how some of our x ray sources come into being. The first thing that guides us is the rather surprising fact, that stars have a fairly restricted range of masses, again the name of Henry Norris Russell pops up, and it turns out that by the middle of the 20th century. We had a fairly accurate appraisal that the very low luminosity stars had masses of about 1/10th of a solar mass, while the upper end of the scale was populated with stars of about 50 solar masses. That range, a factor of about 500, stands in stark contrast to the range in luminosity, which you can see is a factor of 10 billion. How is that possible? Well, clearly, one way out is if the high mass stars exhaust their fuel much more rapidly than the low mass objects. In other words, they burn a tremendous amount of fuel, hence providing a high luminosity, but they must burn out very rapidly since they aren't billions of times more massive than there are low luminosity counter parts and in deed our model show that stars at the very low end of the main sequence have enough fuel to last for over 10 billion years, whereas at the high end objects exhaust their supply in a mere 1 million years or so So we ought to be able to use observations of various clusters of stars to see this effect if indeed some are older than others. Here are two clusters, one an open cluster called the Pleiades, And the other, a globular cluster called M15. These are truly beautiful sights in a telescope. Now, let's look at their HR diagrams. These diagrams for clusters are sometimes called cluster magnitude diagrams as well. You can see that the main sequence of M15 is much shorter. In fact, the arrow that you see in the plot of the Pleiades stars marks the so-called turnoff point of the main sequence that you see for M15. Evidently, M15 is much older than the Pleiades, since all the high-mass high-luminosity stars are simply not there, at least not on the main sequence. There are other clues that point in this direction as well. So now let's combine many clusters into one diagram. What you get is shown here. You can clearly see the trend off the main sequence as you go further down towards the low mass positions. If our ideas about this are correct, we should be able to model these various clusters and see how they evolved with time, and indeed, we can do this quite well. But where do all those evolved stars go? Well, their paths are torturous and complicated. But, it appears that when stars like the sun exhaust their fuel, they end up in the stellar graveyard indicated by the white dwarf area of our diagram. These objects, for the most part incredibly hot, are astonishingly small, and turn out to be about the size of the Earth. How do we know this? Well, we, remember our old friend, luminosity equals the surface area of a star Times a constant, times the temperature of the star to the fourth power. The Stefan Boltzmann Law. T is very very high, but we know the luminosity is very very low. The only way that this can come about is if the size is extremely small. Let's see how unusual these objects really are. Imagine a typical white dwarf, then. The size, its radius, is about equal to the size of the Earth, 6 times 10 to the 8 centimeters, and the mass is about that of the Sun, 2 times 10 to the 33 grams. Let's compute its average density. The average density is given by the mass divided by the volume. And for this object, it turns out to be 2 times 10 to the 33 grams. Divided by 4 3rds pi r cubed where r is given by 6 times 10 to the 8th centimeters. You can do this calculation and you find. That, that density is equal to two times ten to the six grams per cubic centimeter. Now this is just a number. Okay, let's see if we can. Put this in real perspective. Here we have a teaspoon. It has a volume in the spoon part of about 5 cubic centimeters. So let's scoop up One teaspoon of material. From a typical white dwarf. How much will that material weigh? Or what will its mass be? Well, we know that. It's just going to be 5 times this amount. And it turns out that that is approximately for 5 cubic centimeters about 10,000 kilograms. This mass is about the same as a typical 53 foot semi tractor trailer, and it turns out that these astonishing objects play a prominent role in the x ray universe. In our next lectures we will see one of these objects in action. So stay tuned for GKPer. Also known as the fireworks nebula.
