## The Size of Stars

Since ancient times, people have known that not all stars are alike. But it was not until the 20th century that they began to discover why. In 1905, Ejnar Hertzsprung showed that the hottest stars are also the brightest stars. Differences in the brightness of stars of the same color or temperature were a result of distance. Using the parallax of stars (see figure on page 24), Hertzsprung found that both the brightest and faintest red stars had small parallaxes, meaning that they were equally distant.

Ejnar Hertzsprung studied the connection between stellar color and magnitude that led to the Hertzsprung-Russell diagram that shows the correlation between stellar luminosity and spectral class. (Yerkes Observatory Photographs)

PARALLAX

As the star moves farther away, the angle is smaller and the parallax is less September Proper motion

Diameter of Earth's orbit -Ji

As the star moves farther away, the angle is smaller and the parallax is less September Proper motion

> Parallax hParal lax

March

Because the angle of the triangle is measured, and the base is known (Earth's orbit), the distance to the star can be determined

March

Because the angle of the triangle is measured, and the base is known (Earth's orbit), the distance to the star can be determined

> Parallax hParal lax

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September

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March

September

September

Target star

Target star position in year 1

T _ Target star 5 position in year 5

Tm Target star position

1 in March, year 1

Tm Target star position

5 in March, year 5

Ts _ Target star position 1 in September, year 1

Ts _ Target star position 5 in September, year 5

 Ts N ^ V /

Years 1 and 5 compared show proper motion of the target star. The background stars are so far away that their proper motion is essentially zero.

Trigometric parallax is the most accurate way to find the distance to a star.

He correctly decided that the difference in brightness was because of physical size. Hertzsprung's mentor, Karl Schwarzschild (1873-1916), coined the term giant for these stars. The revolutionary idea that stars come in different sizes would lead to an understanding of how stars form and evolve.

Ejnar Hertzsprung discovered that red giant stars had different spectra from other red stars—a difference noted by Antonia Maury (1866-1952), the only woman trained in science who was working on E. C. Pickering's staff at Harvard. She had dubbed them "c-stars" and suggested that a subclass be created for them.

In 1906, Hertzsprung wrote to Pickering saying that he supported adding the "c" subclass. Pickering thought that Antonia Maury's sample was too small to warrant adding a subclass. He had only agreed to let Maury publish her paper on c-stars because she was the niece of Henry Draper (1837-82), Harvard's major patron.

Hertzsprung explained in Astronomishche Nachrichten in January 1909 that a new radiation formula developed by Max Planck (1858-1947) could be used to estimate the diameter of stars from their temperature. He proved mathematically that Arcturus, one of Maury's c-stars, had a diameter more than 100 times that of the Sun. Hertzsprung again urged Pickering to adopt the subclass, but again he refused. (Maury's subclass was finally adopted in 1922, three years after Pickering's death.)

Henry Norris Russell of Princeton was aware of Hertzsprung's work and quickly focused on discovering why only a rare few red stars were giants. He believed, as most astronomers do today, that stars form when gravity draws gas clouds together. The contraction of the cloud heats the gas until it glows hot enough to become a star.

Nuclear fusion was not yet understood, so most astronomers (incorrectly) assumed that starlight was produced by gravitational contraction. The resulting loss of energy through starlight caused the stars to cool and become fainter as they aged, so red stars were considered the oldest and smallest of stars. The idea of giant red stars contradicted this theory.

As a student, Henry Norris Russell had studied under George Darwin (1845-1912, son of Charles) at Cambridge in England. He had come to favor Darwin's fission theory that stated that at a certain spin rate, a condensing body would fly apart and form two or more bodies in orbit around each other. (The competing encounter theory said that closely passing stars pulled mass away to form binary stars and solar systems.) The fission theory predicted that as binary stars aged, they would continue to move apart. To test this theory, Russell examined 74 multiple-star systems. His analysis, "On the Origin of Binary Stars," appeared in the January 1910 issue of the Astrophysical Journal. It showed that binary systems with periods less than two days had blue and white stars. Long-period binaries contained yellow, orange, and red stars. Russell's work supported the fission theory and also the (incorrect) idea that blue stars were young and red stars old. (The real explanation is that blue stars have short lifetimes compared to red stars.)

In 1910, Dutch astronomer Jacobus Kapteyn (1851-1922) and Lick Observatory Director William Campbell (who both received Bruce

Medals—see page 249) announced that the hottest (blue) stars had the smallest proper motion, and that the coolest (red) stars had the largest proper motion. They speculated that space somehow resisted larger (blue) stars more than small dense (red) ones like objects moving through a fluid (though they knew that space was a vacuum). Because red stars were believed (incorrectly) to be the oldest and most contracted stars, the proper motion data seemed to prove that red stars could not be giants. (They found large proper motions because dim red stars must be close to Earth to be seen, whereas hotter stars are brighter and visible from great distances.)

Henry Norris Russell began to question the assumption that stars cool as they age. He was not alone. In 1902, English astronomer Norman Lockyer (1836-1920) published the meteoritic hypothesis that suggested that stars heated to a peak temperature before beginning to cool down. His theory was based on Lane's law that stated that temperature increased when radius decreased. Russell speculated (incorrectly) that stars began life as red giants. As the pressure of the gas resisted contraction, the stars would heat up and become orange, then yellow, white, and—if they had enough mass—blue. This would continue until the stars reached a critical density. After that, the stars could not contract further and would enter their cooling phase—slowly going from white to yellow to red again.

Henry Norris Russell believed (correctly) that the contraction phase was fairly quick and that not many stars had enough mass to heat up to blue. This explained the observation that both red giants and blue stars were rare. Russell then tested this theory of stellar evolution by measuring the density of binary stars. If the contraction/cooling theory were right, then blue stars would have the lowest densities, and both giant and dwarf red stars would have high densities.

Measuring stellar density was tricky and time consuming. The time it took one binary star to eclipse another was used to estimate the volume of stars. Then the total mass of a binary system was derived, using Kepler's third law that relates the sum of the masses to their separation and period of revolution about each other. Careful measurements of how much each star moved relative to the center of the system yielded how much mass belonged to each star in the system. The mass was then distributed among the stars and divided by the estimated volume to get the density. Because some binaries have periods of years, it takes a long time to gather the data to determine the density of stars.

Russell presented his initial density findings at a symposium in April 1912. He found that blue stars had higher densities than red stars and that red giants were less dense than red dwarfs. So red giants were not bigger because they had more mass. Blue giants could not evolve into red giants because the densities were the reverse of what the contraction theory predicted. "This is a revolutionary conclusion," Russell said, "but, so far as I can see, we are simply shut up to it with no reasonable escape."

Russell misinterpreted this data as support for his theory that red giants were the first stage of a star's life and that they evolved into red dwarfs. William Campbell objected to Russell's theory of stellar evolution because it did not explain the large proper motion of red stars. Russell needed more data to make his case and turned to his graduate student, Harlow Shapley, and his friend Pickering at Harvard for help.

Harvard had completed a sky survey in conjunction with other observatories. The enormous job of sorting all the spectra into classes fell to Annie Jump Cannon, who was appointed curator of the astronomical photographs there in 1911. Pickering asked her to sort all stars down to the ninth magnitude: a quarter million objects. Between 1911 and 1915, Cannon classified 5,000 stars per month.

Annie Jump Cannon's predecessor, Willamina Fleming, had created a classification system based on 15 categories named alphabetically from A to Q. Cannon dropped some empty categories and rearranged the rest from hottest to coolest stars rather than alphabetically. The new sequence became OBAFGKM, memorized by astronomy students ever since as "Oh Be A Fine Girl, Kiss Me." This classification system, called the Harvard Spectral Sequence, was adopted by the International Astronomical Union in December 1913.

Using the data provided by Harvard, Henry Norris Russell stunned the astronomical community in December 1913 with a plot of magnitude versus spectral type for more than 300 stars. He used radiation theory and lab tests to show the temperature sequence was reflected in the spectral classes. Hertzsprung had previously shown that temperature determined brightness (with the exception of the red giants). Russell showed with overwhelming observational data that spectral class (OBAFGKM) determined both temperature and brightness.

Russell's diagram was the first "family tree" of stars and was later called the Hertzsprung-Russell, or simply H-R, diagram (see figure on page 29). It clearly showed that 90 percent of stars fall into a band that was defined by brightness and class, later called the main sequence. Though the reasons would not be understood for another decade, it was clear that there were rules to how stars formed and evolved.

The diagram also provided astronomers with a powerful new way to find the distance to stars. Because Russell had correlated spectral class with brightness, just having a spectrum of a star was enough to determine its intrinsic or absolute brightness. By comparing this brightness with the observed or apparent brightness, the distance was found.

In December 1920, giant stars were proven to exist beyond doubt by the spectacular measurement of the angular diameter of Betelgeuse. Albert A. Michelson (1852-1931) and Francis Pease (1881-1938) mounted an interferometer on the new 100-inch (2.5-m) Hooker telescope that had gone into operation on Mount Wilson in November 1917. The diameter of Betelgeuse was found to be 240 million miles (386 million km), compared to the Sun's 870,000 miles (1.4 million km).

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