Hertzsprung Russell Diagram
And Stellar Evolution


Introduction

If this webpage looks different than it did the last time you saw it, that's because I changed it! I have removed all reference to the electric sun hypothesis, which I now take to task in great detail on another page: On the "Electric Sun" Hypothesis. I have also radically altered the text and descriptions, hopefully for the better.

What follows is not an exhaustive study of stellar evolution. But it is, I hope, an introduction to stellar evolution, through the intermediary services of the Hertzsprung-Russel (HR) diagram. Simply put, the HR diagram is a plot of brightness versus color, for as many stars as you want to plot. The fact that this simple plot is highly non-random is a hint that something is going on that we may want to know about. That something turns out to be stellar evolution. As it turns out, by building mathematical models of stars, based on straight forward physics, and allowing those models to evolve naturally in time as a star ages, we can recreate the HR diagram as it is observed. The fidelity of the agreement between theory & observation is far greater than I can communicate in this one webpage. Even small details are now the stuff of intense study in astrophysics. The ability of the theory of stellar evolution to explain the HR diagram in its finest details, singles out stellar evolution as one of the most successful and productive of scientific theories.

More details about stellar structure and evolution are available from my companion webpage, Solar Fusion and Neutrinos, including a much larger bibliography, and lists of books and webpages.


The HR Diagram in General

figure 1
A schematic Hertzsprung-Russell (HR) Diagram

All stars have two properties that are fairly easy to see: Brightness and color. Some stars look red (like Betelgeuse), some look more yellow (like the sun), and some look blue or blue-white (like Sirius). Color, as it turns out, is directly related to temperature; things that look red are relatively cool, compared to things that look yellow, which in their own turn are relatively cool compared to things that look blue or white.

Figure 1 above shows a schematic plot of temperature (X-axis) vs brightness (Y-axis) [temperature increases to the left for historical reasons; the HR diagrams were originally based on color, left to right being blue to red]. This plot is called a Hertzsprung-Russell (or HR) diagram, after the two astronomers who developed the concept in the late 1800's, Henry Norris Russell and Ejnar Hertzsprung.

The HR diagram is important because it is the graphical interface between observation and theory in stellar evolution. One can compute the surface temperature and brightness of a star, based on the physics of stellar structure, and from that derive an expected color based on the temperature. Or, one can observe the brightness and color, deriving the surface temperature from the observed color (we can now use spectroscopy to derive temperatures in a manner not readily available to Hertzsprung & Russell).

Figure 1 is of particular interest, because we can see at a glance that the diagram is not random. If you observe lots and lots of stars, and plot a point for each star observed, the points are not scattered freely around the page, as one might think. Instead, a specific pattern emerges. Stars tend to concentrate along a curve that angles down across the plot, from left to right, which is called the main sequence, because that's where Hertzsprung & Russell saw the most stars. There are clumps of bright red stars to the upper right, as well as the dim red stars along the bottom of the main sequence. The bright red stars are called red giants, because they must be very large to be simultaneously cool (red) and bright. Likewise, the dim blue stars that hang around the lower left are called white dwarfs, since they must be very small in order to be simultaneously hot (white) and dim.

figure 2
Schematic Stellar Evolution


A star is not a static thing, it changes with time. The process of aging in stars is called stellar evolution. As a star ages, it goes through changes reminiscent of the life cycles of living things, the details of which depend on the star's overall mass. Massive stars live short but exciting lives, whereas small stars live long, quiescent lives. We can build a model of a star using physics & mathematics, and then turn that model loose in time and watch it evolve. At any given time the star will always have a brightness and a temperature (both of which are as seen at the surface of the star). We can plot those points at lots of different times, and then connect the points together in order of time, and we get a curve (or trajectory across the HR diagram.

Figure 2 shows examples of stellar evolution curves for stars of 1.6 and 2.0 solar masses. The blue curves represent the track followed by the collapsing protostar, and are called Hayashi Tracks. The green line represents the main sequence, where the star spends most of its lifetime sitting around fusing hydrogen into helium. Once the star stops burning hydrogen in its core, it begins to expand, and moves off the main sequence towards the upper right (the giant region). The more massive stars sit on the hotter portion of the main sequence, live shorter lives than the less massive stars, and become larger giants. Less massive stars sit on the cooler portion of the main sequence, live much longer lives, and may never become giant stars at all. Our sun should remain essentially as we see it now, on the main sequence, for a total of about 8,000,000,000 years. A supermassive hot star, say in the 20,000 degree and hotter range, may sit on the main sequence for only 1,000,000 years or less. A cool red star, down in the 3000 degree and cooler range would be expected to sit on the main sequence for as long as an astounding 100,000,000,000,000 years.


The HR Diagram for a Specific Case

figure 3
HR Diagram for
Globular Cluster M5


In figure 3 above, we see an HR plot of the stars in globular cluster M5 (I shamelessly confess that I took this diagram from that page). The X-axis plots "B-V", which is the color index, and "B-V" means "B minus V", where B and V are the relative brightness of the B and V colors, in the system of magnitudes normally used in astronomy. This can be quite confusing, because astronomical magnitudes run "backwards", the smaller the magnitude, the brighter the object. So, if B-V is positive, then B is biffer than V, which means that B is dimmer than V, and the object is relatively red, compared to an object with a smaller value of B-V. So the scale is relative in color, or temperature. So red is to the right, and blue is to the left on this scale, just as it was in the previous figures. The color index and temperature are directly related, so it is a matter of convenience which one chooses to plot. In practice, this kind of plot, called a color-magnitude diagram, is more common, since the color index is derived directly from the photometer data.

Now, back up a paragraph or two, and remember the bit about stellar evolution curves, like those in figure 2. If you drew 100 curves at once, it would be pretty confusing. But, you could select a point from each of those 100 curves, all of them at the same time, and plot 100 points instead. If you do that, you get something that looks just like figure 3 above. The figure has several features labeled with letters, which can be identified by stellar evolution, and the assumption that all of the stars in the cluster are about the same age (i.e., the cluster formed together).

The main sequence is labeled A in figure 3. But it does not run all the way across the image, as the schematic in figure 1 shows it. That's because the massive, bright stars live shorter lives. So, as the cluster ages, the stars beginning with the upper right portion of the HR diagram, will peel off to the right, becoming red giants. The main sequence in figure 3 goes up a bit to the left, and then disappears, with a sharp turn to the right (that unlabeled point is called the main sequence turn off or the turn off point).

The red giant branch is labeled B in figure 3. Those are the stars which have evolved off of the main sequence, and are now becoming red giants. The stars that were bigger in the beginning, are already up at the tip of the red giant branch. The stars that form the line heading back towards the main sequence, are the smaller (less massive) stars. The ones that are still on the main sequence are even less massive. Stars that sit on the main sequence are fusing hydrogen into helium in the core of the star. But once the star runs out of hydrogen in the core, fusion moves away from the core, and into an expanding shell around the core. When that happens the star expands, and becomes a red giant.

The tip of the red giant branch is labeled C in figure 3. As time goes by on the red giant branch, the helium created in the shell around the core, drops onto the core, causing it to heat up. When that core gets hot enough (say about 100,000,000 Kelvins), it suddenly begins to fuse helium into carbon, which generates a lot of new energy flowing from the core. This sudden event is called the helium flash, and occurs about the point labeled C in the diagram. The new source of energy from the core pushes the hydrogen fusing shell outwards, forcing it to cool and shut off. Now that the star is generating new energy in the core instead of a shell, it shrinks back to a smaller size, and the star winds up on the horizontal branch.

The horizontal branch (HB) is labeled D in figure 3. Stars with a brightness and temperature that put them on the HB are fusing helium into carbon, in the core of the star. The HB has some structure of its own, the Schwarzschild space is labeled E in the diagram, and the red clump (not labeled), is immediately to the right of the Schwarzschild space. The horizontal extent of the HB is determined by metalicity. In the jargon of astronomers, everything heavier than helium is a metal by definition. The ratio of metal abundance to hydrogen abundance is called metalicity. Stars with a higher metalicity will look redder, because the metals absorb the bluer light. The red clump is formed by the higher metalicity stars, while the lower metalicity stars string out to the blue (left) end of the HB (which also turns down here, for reasons not yet fully understood). The Schwarzschild space (E) is peculiarly empty, because any star that winds up in that spot is unstable, and becomes an RR-Lyra type variable star. Since these variable brightness stars cannot be plotted with a single point, they are usually left off the diagram. So it's not that there aren't any stars, it's just that they are variable in brightness. This small detail is one of the many satisfying consistencies between theory (which predicts instability), and observation (which verifies instability).

The asymptotic giant branch (AGB) is not labeled, but lies along the left side of the red giant branch (B), essentially parallel to it. Stars on the HB will run out of helium in their cores eventually, just as they ran out of hydrogen before. And just as that sent the stars to the giant realm once before, it will do so again. Once an HB star runs out of core helium, it begins to fuse helium into carbon in a shell, and the star expands once again. The expansion takes the evolutionary track of the star asymptotically towards the red giant branch (hence the monicker asymptotic giant branch). Stars on the AGB that are smaller than maybe 8 solar masses will age more or less gracefully, into planetary nebulae, and eventually into white dwarf stars. Those that are heavier will not manage such a peaceful end, and terminate in supernova explosions.

The white dwarf branch is labeled F in figure 3. After making it to the asymptotic giant branch, the track for the further evolution of stars moves up and out of the diagram, way off to the left, and then swings around under the diagram to the white dwarf branch. Once the stars that are too small to blow up as supernova explosions have finished all the nuclear fusion they can do, they wind up as small intensely hot white dwarf stars. All they do after that is cool, which takes a long time. The disk of our Milky Way galaxy is only about 9 or 10 billion years old, still too young for any of its white dwarf stars to have cooled beyond visibility. That's how long it takes.

figure 4
HR Diagram #2 for
Globular Cluster M5


Figure 4 (shamelessly swiped from COSMOS Project on Globular Clusters) shows us yet another HR diagram for M5. This one is more complete than the one in figure 3, it has a lot more stars plotted (all those little dots). But it also has an isochrone on it, the dark curve through the main sequence and red giant branch. An isochrone is a line of constant age. It's a theoretical ideal, the line along which all of the little dots would sit, in a perfect universe, if M5 was 11 billion years old. In fact, the COSMOS folks decided that anything from 9 billion to 13 billion fit pretty well, so they set the age of the cluster at 11 2 billion years (uncertainty is a fact of life in science, you might as well get used to it now). That isochrone is created by allowing a mathematical model of the cluster and its stars to age, constrained as best we can by the laws of phsyics. It tells us that there is good reason to believe that the age of this cluster really is 11 2 billion years.

Figure 4 is just one example of an isochrone, the literature on stellar evolution is packed with isochrones (unfortunately, the WWW is not). The literature on stellar evolution is also packed with evolutionary tracks (another item missing from the WWW). An evolutionary track looks superficially like an isochrone, but tracks the "life history" of a single star, so it makes a pretty convoluted looking curve as it goes up & down & up the giant branch, loops through the HB, and so forth.

The connectikon to the HR diagram is by now obvious (I hope). As the star ages, the color-brightness point that identifies it moves around on the HR diagram, drawing out the evolutionary track. The real beauty of it all is that the tracks and isochrones, derived from the pure physics models of stars, can recreate the essential features for HR diagrams of real star clusters.


Appendix - Relevant Websites


Appendix - Relevant Books


Page last Modified on April 15, 2003
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