The HR Diagram:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
knowing the distances of stars allows us to investigate whether the various intrinsic properties depend on one another. This kind of search for correlations is an everyday tool used by scientists of all kinds
we have to be careful to look at intrinsic properties, unaffected by irrelevant factors. So we have to compensate for the fact that remote stars look fainter in a way that tells you nothing about the stars themselves. The knowledge of distances allows us to do this, to metaphorically place the stars "side-by-side" to identify those which are truly brightest and faintest
perhaps the most obvious correlation to consider is that of seeing whether the brightness of a star depends in any way on its temperature
the star's temperature may be manifested by its colour (although interstellar material can make a star look redder [cooler] than it really is) or by its spectral type
historically, this important correlation was studied independently by Hertzsprung and Russell, so the resultant figure is known as the HR diagram. It is the single most important figure in all of astronomy
even the first HR diagrams revealed that there are significant correlations: there is some (moderately complex) relationship between the temperatures and brightnesses of the stars. Thanks to increased numbers of stars with known distances, we can now construct HR diagrams using the data for literally millions of stars
we notice the presence of several different broad groupings of points in the HR diagram, and assign some names
there is a broad band of stars ranging from bright blue [hot] ones to faint red [cool] ones; we call that diagonal distribution the main sequence
we notice a bunch of very bright red stars. Being cool, they emit rather little energy per square metre of surface area (remember the fundamental radiation laws). So the only way they can be bright is to be enormous in size, with a vast surface area. Such stars may be hundreds of times as big as the sun in diameter, and are called red giants
note that red giants may be much bigger than the sun but not necessarily more massive. (Compare a beach ball and a billiard ball. The beach ball is not massive, merely large. The billiard ball is the more massive object: it contains the most atoms. The mass is a measure of the total content, not how 'spread out' the material is)
we also see some very faint but rather hot stars. To explain their limited luminosity, we deduce that they must be quite small (comparable in size to the Earth). We give them the name 'white dwarfs'
investigations of binary star systems that contain white dwarfs reveal that they are as massive as the sun. To pack this much mass into such a small volume implies that the white dwarfs must be a million times as dense as water. This is a new state of matter, to be discussed later
Associated Readings from the Text.Please look at: Chapter 16, pages 532-535A Search for Correlations.Let us put things in the correct historical context, by asking about the state of our knowledge in the early 1900's, after half a century of parallax measurements. By that time, we knew fairly reliable distances for some thousands of stars, which meant that we could convert their apparent brightnesses to total (absolute) luminosities. Thanks to Annie Cannon's work, we also knew the spectral types (or equivalently the temperature or colour) of those stars, and could make moderately good estimates of their diameters. The important question, from the point of our physical understanding, is to ask whether we can combine these disparate data into a coherent picture of some sort, and perhaps learn more about the structure and evolution of the stars. A very common and fruitful approach in science is to search for correlations between various attributes and observed properties in the hope of determining causes and effects. For instance, do the tallest people in the class always get the best marks? (presumably not) Do heavy smokers run a greater risk of getting lung cancer? (yes, and this probably tells us that smoking causes cancer) Are heavy coffee drinkers more likely to have heart attacks? (apparently not, although this one is argued about by scientists) Likewise here we might ask pertinent questions: Are the hottest stars always the brightest? Are the biggest stars always the coolest? and so on. To discover and examine such dependences, we plot the various properties of the stars against one another. We begin with a simple example. Suppose you were to plot the measured colours of the stars versus their spectral types. What would you find? In general, this plot would provide no extra information. The O,B stars, being hotter, are blue, while the K,M stars, being cooler, are red. So the experiment adds no extra insight in general -- if you know the spectral type, you already know the colour. Or do you? It turns out that this exercise is not completely useless because. as we have seen, there are some stars which are exceptions to the general relationship. Occasionally, you find a star which has an `O-type' spectrum (displaying strong helium absorption lines, for instance) but which has a red colour. The spectral type tells you that the star must be hot, or else you would not see the helium absorption lines. Since the star is hot, it must be blue: that is a simple fact of physics. Why, then, does it look red? The answer, in most cases, is that the star is being observed through an intervening cloud of interstellar gas and dust which makes it look deceptively red. So you have learned something.A Second Correlation.What happens if we plot the colours of the stars versus their apparent brightnesses? A little thought suggests that there will probably be no correlation at all! Some of the cool (red) stars will be moderately close, so that they look bright; others will be far away, and will look faint. The same reasoning holds true for the hot (blue) stars. Consequently, whether you look at the fainter stars in the sky or the brighter ones, you expect to see a mix of red and blue objects, with no obvious correlation. But it is worth checking! It could be, for example, that stars of different kinds are not distributed at random in space. Perhaps the hottest stars are found only very near the sun, owing to some accident of birth; if so, all these blue stars will look fairly bright, owing to their proximity. In that case, if we focus our attention on the faintest observable stars, we will find only red ones -- and learn something to our advantage. (In fact, however, no such results are found.) To figure out what is really going on, you want to consider the intrinsic properties of the stars, which means that we have to compensate for the very different distances of the stars in the sample. Metaphorically, you have to imagine pushing them back and forth in space until they are all side-by-side, at some common distance. Only then can we figure out what the real differences and similarities are. Here's an analogy. Suppose you wanted to investigate whether the loudness of a person's voice was related to his or her weight. (You might be testing the proposition that bigger, heavier people have louder voices.) To test this general prediction, you would draw together some moderately large sample of people of a variety of body types, and ask them to say a few words. But in doing this experiment, you would want to be sure that each of them stood at the same distance from you! Someone with a booming voice might sound very faint if he stood at the other end of the block. You need to compensate for this irrelevant geometrical factor (their varied distances) to see if there is any real correlation at all.A Breakthrough in Understanding.Although we cannot move the stars, we can imagine reaching out to push and pull them around until they are all sitting out in space at some common distance away from us, side by side. (The calculations which are required are very straightforward, based on the inverse-square law of brightness.) After this simple calculation, we can address the question of which stars are truly the most luminous, and which are less so -- not because of mere accidents of their varied proximity to us. Done correctly, this yields the absolute brightness of each star of known distance. An obvious question, then, is to ask whether the absolute brightness is related to the temperature. To be historically true, however, let us plot the intrinsic brightnesses of the stars against their spectral types, rather than their temperatures. (As you know, these are intimately related.) This is the way in which the most famous diagram in astronomy was originally constructed, looking a little like the more modern version on page 533 of your text. This kind of plot quickly came to be known as an HR diagram, after the initials of Enjar H ertzsprung and Henry Norris R ussell, the two astronomers who did this independently early this century. What do such figures suggest? Before answering that question, let me point out that the stars to the left of the diagram are the hotter ones, and the cooler ones are to the right (look at the spectral types shown on the bottom of the plots). Stars near the bottom are fainter than the ones at the top, as shown by the quantitative scale on the left of the figure. We notice the following: The Non-Uniform Distribution of Points: The very first thing to notice is that the stars are not scattered all over the place: there are regions in which few stars appear. This tells us that there is some structural relationship which we need to consider: it seems that Nature does not build stars which have every imaginable combination of surface temperature and absolute brightness. It does not seem possible to build a star which is exactly as bright as the sun but which is twice as hot, for instance. The Main Sequence: Next, your eye may be struck by the long diagonal distribution of points running from upper left to lower right. This distribution quickly got named the ` main sequence. ' One of the stars on the main sequence is the sun, just about in the middle of the diagram - it is a star of spectral type G (middling temperature) and moderate luminosity. The Red Giants: We next notice that there are some stars to the upper right of the diagram. These stars are cool (which is why they are of K or M spectral type) but are much brighter than the sun. How can that be? As we saw before, the answer must be that they must have very large surfaces, so that there is a huge radiating area giving off lots of light in total. These are red giants; Betelgeuse is an example. Let me take a moment to quantify this. Suppose you discover that one of these stars has a surface temperature which is about two thirds that of the sun (4000 vs 6000 degrees). This means that every square metre of that star emits only 20 percent as much light as the sun does per square metre (because the emission depends on the fourth power of the temperature). If the star is, say, three thousand times as bright as the sun in total light output, it must have fifteen thousand times as much surface area as the sun. Since the area depends on the square of the radius, it must have a radius which is more than one hundred times that of the sun. In other words, if you put it where the sun is now, Venus and Mercury would be inside it - a giant indeed! And even bigger stars are known. An important reminder (yet again): the large sizes of such stars (that is, their diameters, radii, or surface areas) do not necessarily mean that they are massive. People often use this word in conversation simply to mean `big', but in physics an object's mass is technically a measure of how much matter it contains -- in effect, you add up all the protons and neutrons in all the atoms. Thus it may be possible for a star with the same mass as the sun to be as big as a red giant if it is simply `puffed up.' The atoms in the outer parts will then be quite far apart, and the density of the star in these outer regions will be very low. Indeed, we now know that this is what will happen to the sun billions of years from now: it will become a red giant, but its mass will be the same. The White Dwarfs: Finally, we notice that there are a few stars to the lower left of the figure. (Only one showed up in the original HR diagram, in fact.) What are these? Consider that they are hotter than the sun, but very much fainter. By the same arguments as in the discussion of the Red Giants, we must conclude that these stars are very small. Indeed, some of them have only the diameter of the Earth itself. One such example is the faint companion to the bright star Sirius, which is a binary. (On page 530 of your text you will find a photograph of Sirius and its companion, but the image has been adjusted to make the white dwarf show up - in reality it is a scarcely visible dot beside the extreme brightness of Sirius itself.) This may not seem surprising to you. Why shouldn't there be stars of this size? But there is a surprising implication that follows from this conclusion. As we will see, a detailed study of binary stars allows us to determine their masses. In this way, we discover that the white dwarf associated with Sirius has a mass about equal to that of the sun. So what? Well, remember that an object the size of the Earth has about one one-millionth of the volume of the sun -- in other words, we could pack one million Earth-sized bodies into the sun. If all the mass of a sun is packed into such a tiny object, it must be very dense, in fact about one million times the density of water. This means that a teaspoonful (5 cubic centimeters, say) of the material of a white dwarf would contain five million grams of matter (5000 kilograms, or 5 metric tonnes, about the mass of a African elephant). No known materials on Earth have anything like this density, and in fact white dwarfs represent a new state of matter, the so-called degenerate matter. We will explore this topic in some detail later. Naturally, discoveries of such strange objects were a source of great interest to astronomers early in this century. Previous chapter:Next chapter0: Physics 016: The Course Notes, spring 2005. 1: The Properties of the Sun: 2: What Is The Sun Doing? 3: An Introduction to Thermonuclear Fusion. 4: Probing the Deep Interior of the Sun. 5: The Sun in More Detail. 6: An Introduction to the Stars. 7: Stars and Their Distances: 8: The HR Diagram: 9: Questions Arising from the HR Diagram: 10: The Importance of Binary Stars: 11: Implications from Stellar Masses: 12: Late in the Life of the Sun: 13: The Importance of Star Clusters in Understanding Stellar Evolution: 14: The Chandrasekhar Limit: 15: Supernovae: The Deaths of Massive Stars, 16: Pulsars: 17: Novae: 18: An Introduction to Black Holes: 19: Gravity as Geometry: 20: Finishing Off Black Holes: 21: Star Formation: 22: Dust in the Interstellar Medium: 23: Gas in the ISM: 24: The Size and Shape of Our Galaxy: 25: The Discovery of External Galaxies: 26: Galaxies of All Kinds: 27: The Expanding Universe: 28: Quasars and Active Galaxies: 29: The Hot Big Bang: 30: The Geometry of the Universe: 31: Closing Thoughts: Part 1:Part 2:Part 3: |
(Wednesday, 22 April, 2026.)
