H-R Diagram for StarsA Most Important DiagramClassifying starsaccording to their spectrum is a very powerful way to begin to understandhow they work. As we said last time, the spectral sequence O, B,A, F, G, K, M is a temperature sequence, with the hottest stars being oftype O (surface temperatures 30,000-40,000 K), and the coolest stars beingof type M (surface temperatures around 3,000 K). Because hot starsare blue, and cool stars are red, the temperaturesequence is also a color sequence. It is sometimes helpful,though, to classify objects according to two different properties.Let"s say we try to classify stars according to their apparent brightness,also. We could make a plot with color on one axis, and apparent brightnesson the other axis, like this:Figure 1: H-R Diagram of apparent brightness versus star color (ortemperature). You can see that thisclassification scheme is not helpful -- the stars are randomly scatteredon the plot.Obviously, plotting apparentbrightness against color is not helpful, because there are no patternsin the placement of the dots representing stars. They are scatteredaround randomly. This is because the starsare at all different distances, so the nearby ones appear brighteven though they may be intrinsically not so bright.But what if we look at thissame plot, but somehow make sure that the stars are all at the same distance.You know that stars sometimes appear in clusters (because they were allformed out of the same giant cloud, parts of which collapsed to form alot of stars all around the same time). Here is a photograph of thePleiades star cluster:Figure 2.If we plot the apparent brightnessversus color for such a cluster, where all the stars are the same distance,you get a plot like this:Figure 3.Now you can see that thepoints representing the stars fall along a clear line in the plot.Such a plot was first made by two astronomers working independently: EjnarHertzsprung (Denmark) and Henry Norris Russell (Princeton, USA).This kind of diagram was named after them, as the Hertzsprung-RussellDiagram, or H-R Diagram.It is an extremely powerful diagram for classifying stars and understandinghow stars work. We are going to spend the rest of this lecture lookingin detail at this diagram. First, though, note the relationship betweenapparent brightness and absolute brightness that we talked about last time.We said that astronomers use absolute brightness, which is the apparentbrightness stars would have if they were all at the same distance of 10parsecs. The diagram above uses apparent brightness (apparent magnitudes),but for stars all at the same distance (the distance to the Pleiades starcluster), so it is really a plot of absolute brightness versus color.Or we could plot luminosity versus color, as below:Figure 4. When we know the distances to stars, we can determine theirabsolute brightness, or luminosity.When we then plot luminosity (or absolute brightness) versus color(or temperature), the stars allfall along a narrow strip in the diagram. This is the H-R Diagram.So the right way to thinkabout an H-R Diagram. It is telling us that a star"s color (or temperature)and its luminosity are related. Blue stars are more luminous thanred stars. To find this out, though, wehave to know the distances to the stars. Remember thestar catalog we showed one page of in the last lecture, from the NearbyStars catalog. We know the distances to these stars, by measuringtheir parallax. Here is the H-R diagram for that catalog:Figure 5.Now we see that there isa new region in the lower left, which correspond to faint-blue stars.If blue stars are so luminous, why are these so faint? These arefaint because they are very small! They are a class of stars calledWhiteDwarf stars. We can also look at the H-R diagram for otherclusters. Here is one for an old cluster of stars, M3, which is aglobular cluster:
Figure 6 a.

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Figure 6 b.
Now we see a newregion of luminous red stars in the upper-right! If red stars arefainter than blue stars, why are these red stars so luminous? Itis because they are giant stars, like the star Betelgeuse, which I mentionedlast time is so large that, if it were at the distance of the Sun, it wouldengulf the Earth"s orbit, and even the orbit of Mars. These are theRedGiant stars.Patterns in the H-R DiagramWe see that theH-R diagram can help us classify different kinds of stars, according tothe pattern of where the stars fall in the diagram. The diagonalline that we saw for the Pleiades star cluster represents what we would call normalstars. The White Dwarfs and Red Giants are different classes of starsthat the H-R diagram helps us to identify. So the H-R diagram cantell us something about the size (radius) of the stars. The factthat the H-R diagrams for the nearby stars, the Pleiades star cluster,and the M3 star cluster are all different leads us to look for other differencesin these groups of stars that might explain it. It turns out thatthe difference is the age of the stars.The H-R diagram is going to help us learn something about how stars changeas they get older. So you can already see that this is a very powerfuldiagram indeed. Let"s take a look at theoverall H-R diagram, including all the different types of stars that weknow of.

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Figure 7.The horizontal axis againshows the color of the stars, and the vertical axis shows the luminosity,in units of the solar luminosity. Note that the tick marks on thisvertical, luminosity axis are a factor of 10 apart! A factor of 10is called an order of magnitude.So the range of luminosity from bottom to top in this diagram is enormous.Each star in the sky can be placed in a unique place on this diagram.For example, the Sun is a yellow star of 1 solar luminosity (by definition!),so you can find it near the center of the diagram. It falls on the"normal star" line running diagonally from the lower right to the upperleft. This is called the Main Sequence.Most stars fall along this line.Radius:Remember that last lecturewe said that if we know the temperature and distance to a star we can determineits size. As it turns out, the red stars on the Main Sequence aresmaller than the Sun, and the stars get bigger as you go along the MainSequence toward the hotter (bluer) end. Stars on the Main Sequencethat are hotter than the Sun are also larger than the Sun. So hotblue stars are more luminous (and therefore appear higher in this diagram)for two reasons: they are hotter, and hot objects are more luminous thancool objects, but they are also larger. In fact, if a hot star wereto get cooler without changing its radius, its luminosity would drop andits color would become more red so that it would follow the diagonal linesin the above diagram. Notice that the White Dwarfs, in the lowerleft part of the diagram, are parallel with these constant radius lines.From this we might expect that White Dwarfs get cooler, but stay the samesize, as they get older, and we would be right! Other stars alsoget hotter or cooler during their lifetimes, but they also change sizeat the same time, so they do not follow these lines.The Red Giant andRed Supergiant parts of the diagram show that these stars are 30 to severalhundred times larger in radius than the Sun. We will learn next timethat such stars are old, and that the Sun, as it nears the end of its lifetime,will also swell up and become a red giant star.Lifetimes:Notice that there are timemarkers along the Main Sequence. These are the lifetimes of the starsthat are found there. At the spot where the Sun is located, with1 solar luminosity and a surface temperature of 6,000 K, stars live forabout 1010 years, or 10 billion years.Stars that are hotter and more luminous than the Sun live for shorter times,while stars that are cooler and less luminous live for longer times.This seems reasonable, since more luminous stars must be putting out energyat a higher rate, so they use up their hydrogen "fuel" faster. Thehottest stars, of type O and B, live only for 10 million years or less!It is a good thing for us that the Sun is not this kind of star, or elselife would never have had time to develop on Earth.Masses:There is a single parameterthat accounts for all of the patterns we see on the Main Sequence, andthat is the star"s mass. If a star develops out of a 10 solar masscloud, it will become a B star, its surface temperature will be about 20,000K, it will have a luminosity of about 10,000 Sun"s, and it will live foronly about 20 million years. All of these characteristics of thestar are determined by the initial mass of the cloud, with very littledependence on anything else! So this is the main point to keep inmind. The Main Sequence is a mass sequence. Higher mass starswill have surface temperatures and luminosities that place at the upper-leftend of the Main Sequence, and lower mass stars will have parameters thatplace them at the lower-right.Numbers of Stars vs. Mass:As it turns out, a giantcloud of gas of hundreds or thousands of solar masses will collapse notto form a single giant star, but will collapse in several places at once(several dense centers) to form many stars. Typically, only a fewhigh-mass stars are formed, and many more of the lower-mass variety areformed. Such a cloud will form a cluster of stars. Becauseof the lifetime difference, if we look at a young cluster we will see allmasses of stars but if we look at an old cluster we will see only the smallermass stars. Why? Because the high-mass stars have already livedtheir lives out and died (we will discuss how stars die later). Comparethe young Pleiades cluster (figures 2 and 3, above), with the much olderM3 cluster (figure 6 a and b). The Pleiades has a few very brightstars and lots of less luminous (lower-mass) stars. The M3 clusterhas only fainter stars on the main sequence. It also has lots ofRed Giants, but that is another story. If we look at the stars inour neighborhood (figure 5), we see far more low-mass stars. So moststars in the galaxy today are low-mass stars, for two reasons: 1) morelow-mass than high-mass stars are born in each cloud, and 2) low-massstars live much much longer than high-mass stars.Main Sequence Turn-off:If you look at the M3 clusterH-R diagram (figure 6b), you see that the main sequence only extends partway to the upper-left, and then the stars appear off the main sequenceto the upper right, in the Red Giant area of the H-R diagram. Thisis because when stars age, they get cooler (which makes them turn red)and larger (which makes them more luminous), so they actually become RedGiants. If we look at an H-R diagram for several clusters of differentages, here is what we see:Figure 8Really young clusters like theDouble Cluster h and chi Persei have high-mass O stars at the upper endof the Main Sequence. Older clusters like the Pleiades have B starsstarting to age off the Main Sequence. The Hyades, even holder, isstarting to have A stars leave the Main Sequence, and the much older NGC188 has F stars leaving the Main Sequence. This aging off the MainSequence is called the Main Sequence Turn-off, and we can use it to actuallytell how old clusters are. The oldest clusters in our galaxy areabout 14 billion years old, which is one way we know how old the Universeis.