# Case Study: Friedrich Bessel and the Companion of Sirius

Part of the Cosmic Horizons Curriculum Collection.

Important advances in astronomy often come from increased precision of observations. The work of the German astronomer and mathematician Friedrich Wilhelm Bessel (1784 –1846) provides a good illustration. Among his many other accomplishments, Bessel developed techniques to measure the positions of stars with far greater accuracy than previously possible. For example, he made the first precise measurements of refraction of light by the Earth’s atmosphere. Refraction is the bending of light rays as they pass at an angle through different substances, like glass, water, or air. When a star is near the horizon, its apparent position can differ from its true position by as much as the diameter of the Moon. This effect was poorly-quantified until Bessel studied it in 1811. His tables of refraction allowed observers to measure star positions to an unprecedented accuracy of less than a tenth of a second of arc (the size of a small coin as seen from a mile away).

This kind of precision in astrometry (the branch of astronomy that measures stellar positions) allowed Bessel in 1838 to find the first reliable distance to another star. He discovered the long-sought stellar parallax—the extremely tiny shift in the apparent position of a star when observed from opposite sides of the Earth’s orbit. Since the size of the Earth’s orbit was known, the observed parallax angle allowed Bessel to calculate the distance to the star 61 Cygni by triangulation. This discovery also provided the most convincing proof that the Earth really moves around the Sun.

Bessel went on to obtain precise positional measurements of Sirius, the brightest star in the sky. His observations revealed that Sirius was slowly changing its position as if it were being pulled around in orbit by the gravity of another star. In 1844, Bessel had a sufficient number of precise observations to announce that Sirius must have an unseen companion. The orbital period of the two stars around each other turned out to be about fifty years.

Astronomers searched for the companion star but couldn’t find it. Finally, in 1862, after Bessel died, the American telescope maker Alvan Clark, while testing a new telescope on the bright star Sirius, actually discovered the companion. It was indeed a star, but so very faint that it was almost lost in the glare of Sirius. Because the companion was about twice as far as Sirius from their common center of mass, it had to weigh about half as much (like a child twice as far from the center of a see-saw balancing an adult). Why then was the companion almost a thousand times fainter?

Around 1915, Walter Adams at Mt. Wilson Observatory obtained the spectrum of the companion and was astonished to find that the faint star was nearly three times hotter than Sirius. Using the laws of physics, astronomers can calculate the size of a star if they know its temperature and luminosity (light output). To be so hot and yet so faint, the companion of Sirius had to be as small as the Earth, but its mass, calculated from Bessel’s astrometry, equalled that of the Sun. Here was a star with the mass of the Sun packed into a volume no larger than the Earth. It had to be about three million times more dense than water. A thimbleful of this stuff would weigh about ten tons on Earth! The companion of Sirius was made of some strange new form of matter, far beyond anything in human experience. The nature of such dense objects, now called white dwarfs, remained a complete mystery until the development of quantum mechanics—the physics of atomic particles.

In 1930, a young Indian graduate student, Subrahmanyan Chandrasekhar, on a sea voyage to England to study astronomy at Cambridge, applied the new quantum ideas to the physics of stellar structure. He realized that when a star like the Sun exhausts its nuclear fuel, it will collapse due to its own gravity until a new form of pressure comes into play. This pressure is due to the so-called Pauli exclusion principle, which prevents the electrons in matter from getting too close to one another. The fact that the electrons cannot be compressed beyond a certain point determines the very high but stable density of a white dwarf. Chandrasekhar found that electron pressure can support a white dwarf only if the star has less than 1.4 times the mass of the Sun. More massive stars would continue to collapse to some then-unknown fate. This idea was the theoretical breakthrough that pointed the way to neutron stars and black holes, and would later earn Chandrasekhar the Nobel Prize for Physics.

Although difficult to observe due to their small size, white dwarfs actually turn out to be quite common in the Galaxy. In fact, we now know that all low mass stars like the Sun collapse into white dwarfs when they run out of nuclear fuel.

The story of the companion of Sirius has a peculiar sequel. In 1950 the French anthropologist Marcel Griaule published a study of the Dogon tribe of Mali in West Africa, in which he described an elaborate Dogon ceremony centered around the star Sirius. The Dogon informed Griaule that Sirius was accompanied by a very heavy, metallic companion star that was completely invisible. Excited by this information, UFO enthusiasts took it as proof that the Dogon had been visited long ago by aliens who taught them about the white dwarf companion of Sirius. How else could they possibly have known about it? But the astronomer Carl Sagan suggested a much simpler and more human explanation. He noted that the existence of the unseen, dense companion of Sirius was widely known in Europe long before Griaule recorded the Dogon mythology. The tribe had often been visited by missionaries and travelers. It is quite possible, even probable, that one of these visitors, perhaps during an exchange of sky lore with the Dogon, told them about the companion of Sirius, particularly since the Dogon used the appearance of Sirius to mark the changing seasons. The Dogon, recognizing a good story when they heard it, incorporated the invisible companion of Sirius into their own traditions, which were later recorded by Griaule.

This is an excerpt from COSMIC HORIZONS: ASTRONOMY AT THE CUTTING EDGE, edited by Steven Soter and Neil deGrasse Tyson, a publication of the New Press. © 2000 American Museum of Natural History.