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# 12.20 The Hertzsprung-Russell Diagram

When astronomers realized the variety of stars that exist, their first step was to devise a sensible way to arrange and study the data to find relationships among the various forms of stars. This could have been done in numerous ways, but one method has become traditional. Building on the work of Annie Cannon, the Danish astronomer Ejnar Hertzsprung and the American astronomer Henry Norris Russell independently conceived the idea of plotting the spectral class of stars according to their luminosity. They did this work from 1905 to 1915. The plot they produced is usually called the H-R diagram in honor of Hertzsprung and Russell.

Hertzsprung-Russell diagram showing color and size of stars. Click here for original source URL

Temperature is the principal factor that governs the differences among the spectra of stars. Remember that this is temperature of the outer layer or photosphere — the inner core where fusion occur is not visible. Spectra had originally been named based on the strength of the hydrogen Balmer lines (with A being strongest). When sorted by temperature, the spectral classes take on the order O, B, A, F, G, K, and M. Spectral classes directly correlate with stellar temperatures, and for this reason, most astrophysicists make H-R diagrams using a temperature scale instead of a scale showing spectral class. Following Russell's original version, and the tradition of astronomers ever since, the spectral classes are arranged with cooler stars to the right.

Different locations on the H-R diagram correspond to different types of stars. It is important to understand why this is true. First, remember from Wien’s law that stars of different temperature have different color. Redder stars are cooler and bluer stars are hotter. Similarly, the upper part corresponds to more luminous stars, and the lower part to less luminous stars.

The Sun is near the middle of the diagram (one solar luminosity, spectral type G). If we move upward from the Sun’s position, we encounter stars more luminous than the Sun, even though they have the same temperature. These stars must be bigger than the Sun, since the Stefan-Boltzmann law tells us that each square meter on a star at the same temperature as the Sun will radiate as much energy as a square meter on the Sun. Thus, to get more total luminosity, we must have more square meters of surface area and hence a larger size. Similarly, a star below the Sun on the diagram must be smaller than the Sun. To summarize, luminous stars are hot and big while less luminous stars are cool and small.

Do stars appear throughout the diagram? Or are there only certain combinations of temperature and luminosity? The answer is that only a few regions of the H-R diagram are crowded with stars. Stars that would fall in other parts of the diagram are rare or nonexistent. Even the earliest H-R diagram revealed an important discovery about stars: among most stars there is a smooth relation between surface temperature and luminosity. Hertzsprung called these stars main-sequence stars. They lie on the diagonal band from upper left to lower right in the H-R diagram. The main sequence runs from hot luminous blue stars (upper left) to cool faint red stars (lower right). It turns out that main sequence stars all have something in common — they all get their energy from the fusion of hydrogen into helium, just like the Sun.

The H-R diagram is extremely useful in studying the properties of stars, but it is not a pictorial representation of where stars lie in space. It is formed by graphing two measured properties of a star, with each point in the diagram representing the properties of a different star in the sky. The H-R diagram is a tool or method that can be applied to any sample of stars. Let’s take the 100 stars closest to the Sun. Stars at this range are near enough for us to measure accurate distances and to detect examples of very low luminosity. Stars in such a sample are believed to be representative of all stars in the neighborhood of the Sun. Over 90% of this representative sample of stars fall on the main sequence. The H-R diagram shows that most nearby stars are fainter and cooler than the Sun.

If astronomers try to expand this statistical sample of stars by tabulating more distant ones, they run into a problem. At great distances the less luminous stars are too faint to see. The only distant stars we see are unusual, luminous ones. In fact, the prominent stars in our night sky are mostly distant, unusually luminous stars. These stars are quite rare in any volume of space. In other words, even though giant stars are intrinsically rare, they are far more visible than dwarf stars. This means that we do not get a correctly representative sample of stars at further distances – we only see the bright ones.

Why is the visibility of stars an important issue? The simple answer is that we are trapped in space. We can only view the universe from our fixed location of the Earth. Some stars are so dim that they elude detection with our telescopes. Other stars are so bright that we can see them from very far away. When astronomers carry out surveys of stars, they are limited to the light they can capture with their telescopes. This type of census gives a very different answer from a count of stars throughout a volume. Imagine for example that you could jet through space and count every one. In general, stuck on Earth, we will over-count luminous or giant stars compared to their true space density and under-count dim or dwarf stars compared to their true space density. There may be a big difference between what we easily see and what is truly out there in space.

The 20 brightest stars in the sky are each more luminous than the Sun. All but three of them are farther away than all of the 20 nearest stellar systems. Sirius is the only star that is common to both lists, which means that the brightest stars and the nearest stars are quite different groups of objects. The brightest stars are luminous and distant, while the nearest stars are mostly less luminous than the Sun. In terms of their true distribution in space, hot and high luminosity stars are rare, and cool and low luminosity stars are ubiquitous.

Hertzsprung aptly called the luminous stars "whales among the fishes." Thus the statistics of prominent stars do not give us a sample of representative stars. Rather, they are biased toward the "whales." Nonetheless, a tabulation of such stars is important because it reveals that some of the "whales" do not occupy the main sequence of the H-R diagram.

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