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## The Hertzprung-Russell diagram

Probably the most important diagram in stellar astrophysics is the Hertzprung-Russell diagram. It was arrived at independently by Danish astronomer Enjar Hertzsprung in 1911 and American astrophysicist Henry Norris Russell in 1913.

By the start of the 1910s, the Harvard College Observatory’s programme of obtaining the spectra of stars and classifying them (see my blog about that here) meant that the spectral type of a star was one of its measured properties. Another measured property was a star’s apparent magnitude, how bright it appears to be in the sky. As I’ve mentioned before, to calculate a star’s intrinsic brightness (its absolute magnitude>, we also need to know a star’s distance. But with the stellar parallax measured for about one hundred stars, and the period-luminosity relationship for Cepheid variables newly discovered by Henrietta Leavitt, in the early 1910s astronomers were beginning to have a way to convert from a star’s apparent magnitude to its absolute magnitude, and hence measure their intrinsic luminosities.

Henry Norris Russell was based at Princeton as an Assistant Professor when he came up with his version of the H-R diagram in 1913. He would spend the rest of his career at Princeton, and became one of the foremost astrophysicists in the early 20th Century.

Enjar Hertzsprung, who was based at Copenhagen when he came up with his version of the H-R diagram in 1911. He would spend most of his career at Leiden in the Netherlands.

Hertzsprung and Russell independently decided to plot the spectral type (or colour, or surface temperature; they are related) of a collection of stars against their absolute magnitudes (intrinsic luminosities). What they found was intriguing – rather than stars appearing all over the plot as they might have expected, most stars lay along a well defined band which stretched from the top left to the bottom right. Some stars were above this band, and a few were below it.

The Hertzsprung-Russell diagram is usually plotted with temperature (or spectral type, or colour) on the x-axis and absolute magnitude (intrinsic brightness) on the y-axis. Also, the x-axis is backwards with the temperature increasing going towards the left! The band which stretches from the top left to the bottom right is called the main sequence, and all stars on the main sequence are burning hydrogen in their cores.

Clearly the concentrations of stars in different places on the H-R diagram was telling us something, but it would be a number of decades before astronomers had got it all figured out. In fact, it is one of the great triumphs of 20th Century astronomy that we went from not understanding the H-R diagram when it was first presented by Hertzsprung and Russell to having an essentially complete understanding of it by the 1950s. In the early 1910s we didn’t now that stars were mainly hydrogen, we didn’t know from where they got their energy, and we didn’t know about the life-cycle of stars.

You can think of the H-R diagram as giving the history of stellar evolution. A star like our Sun will be in different parts of the H-R diagram at different stages of its life, it is currently on the main sequence as it is burning hydrogen in its core. It has been in this part of the H-R diagram for the last 4.6 billion years, and should remain on the main sequence happily burning hydrogen in its core for about another 5-6 billion years.

Clearly, with these kind of time scales, we cannot see the evolution of an individual star. But, luckily for us, with thousands of stars visible to even the naked eye, and millions visible through telescopes, we are able to see stars at each stage of stars’ evolution, from birth to death.

All of the stars which are on the band of points which stretches from the top left to the bottom right, which we call the Main Sequence, are burning hydrogen in their cores. They are the only stars on the H-R diagram which are burning hydrogen in their cores, if a star is not burning hydrogen in its core it will not be on the main sequence. Our Sun is a main sequence star, and this stage of a star’s life is the most stable period of its evolution, and it spends some 90% of its life on the main sequence.

When the Sun formed, it would have started off as a cool nebula (cloud of gas and dust) which would have started collapsing under gravity, and the gravitational collapse converts gravitational potential energy into kinetic energy of the gas, so the nebula gets warmer. As the nebula collapses more and more the central concentration forms a proto-star, and at this point the proto-Sun would have appeared to the right of the main sequence, at a temperature of some 2000-3000 Kelvin. Its luminosity would have been comparable to the Sun’s present luminosity, or at least not much less, but this is because of the proto-star’s size, it would have been hundreds of times larger than the current Sun.

As the proto-Sun contracted still further the density and temperature in the core would have become high enough for hydrogen fusion to start. In this process, which I will describe in more detail in another blog, hydrogen is converted into helium. The Sun then settled down to a long life on the main sequence; our Sun will spend some 10 billion years in this part of its evolution.

The stars above the main sequence are red giant stars, and these are stars which have finished burning hydrogen in their cores and have started burning it in a shell about a helium core. When a star does this it swells up, becoming cooler and much brighter. It moves away from the main sequence, in a process we call “ascending the red giant branch”. Eventually the helium in the core will start to fuse, with three helium nuclei combining to form carbon, and when a star is in this phase of its evolution it sits on a part of the diagram called the horizontal branch.

For low mass stars, less than about three times the mass of the Sun, converting helium to carbon is as far as they will get in their nuclosynthesis. After they have finished on the horizontal branch, these low mass stars will blow off their outer layers and form what we call a planetary nebula, leaving a dead carbon core behind which cools over time. The name for this dead carbon core is a white dwarf

Higher mass stars, more than about three times the mass of the Sun, are able to go beyond helium burning, and can burn carbon, and sometimes oxygen, silicon and other elements all the way up to iron. However, a star will never burn iron, as iron is the most tightly bound nucleus of all the elements in the periodic table, and so such high mass tars have a sudden energy crisis and explode in a supernova. I will blog about the details low mass and high mass stellar evolution in a pair of future blogs.

So, to summarise, the H-R diagram is in a visual illustration of stellar evolution, and now we understand how stars move about on the H-R diagram during their lives, a triumph of 20th Century astrophysics.

### 3 Responses

There is a twist to the story. Hertzsprung published the principles of a HR-diagram, in the form of a table, already in 1905 (and 1907). But in the journal “Zeitschrift für wissenschaftliche Photographie, Photophysik und Photochemie” , “Zur Strahlung der Sterne” 1 and 2. A journal not read by astronomers. Since Hertzsprung was a chemist and worked with photography it was natural for him to publish the results in that journal.

The first paper in a “astronomy journal” with a HR-diagram by Hertzsprung came 1911. But the first printed HR-diagram was in an article by Hans Rosenberg in 1910 in “Astronomische Nachrichten” (vol 186, p 71).
But Rosenberg worked with Karl Schwarzschild who knew of Hertzsprung work already in 1908.
Russel did the same as Hertzsprung and presented his results in tables, The first diagram of Russel were presented on the 13 June 1913 at a Royal Astronomical Society meeting in London.

There is also an interesting story about the naming but that is a different story…

• Thank you Jonas for that interesting additional information. Like most stories, there is more to it than is usually presented in textbooks 🙂

2. […] stars. A star like the Sun is what we call a “main sequence” star, (see my blog on the HR diagram here) and this means that it is burning hydrogen in its core. It is turning the hydrogen into helium via […]