The Optical Interferometer: Completing the Work of Galileo

by Tyler Nordgren

    When Galileo first turned his telescope to the sky, only the sun, moon and occasional comet were known as anything other than simple points of light. There were five known planets in the early 1600s, but they were only points of light that moved relative to the other points of light. The night sky was a universe unresolved. Through his telescope, Galileo saw for the first time Venus transformed from a "star'' to an orb; a disk with phases just like our Moon. Jupiter too became a disk, but instead of revealing phases, the telescope revealed four new worlds: the Galilean satellites. Both of these discoveries in their own way refuted the Earth centered model of the Universe and helped usher in the revolution of modern science. But they also ushered in another revolution: the resolution revolution. Starting with Galileo, telescopes would get larger and as their sized increased their resolving ability, the ability to discern detail on far away objects, would increase as well.

    Today telescopes, both giant engineering marvels and simple back yard models, can resolve gaps in the rings of Saturn and spiral structure in the arms of distant galaxies. Browse through any book or web page on astronomy and one is presented with a kaleidescope of images of breathtaking nebulae, majestic galaxies, distant quasars and all the moons and planets our solar system has to offer. However, the one celestial object that looks today exactly like it did to Galileo is the one thing that everyone sees when they look up at night. Stars.

    If one could look through the 200 inch telescope on Mt. Palomar, one would see stars as nothing more than the same points of light you would see by simply walking outside and looking up. Why are stars the sole hold out in the resolution revolution up to now? Simply put, stars are very small, and very far away. Our sun is a star, but even though it is almost 100 times larger than the largest planet in our own solar system, it is also at least a million times smaller than the interstellar nebulae of which we have so many pictures from the Hubble Space Telescope. At its average distance of 150 million kilometers, our sun spans an angular extent (it has an angular diameter) of half a degree. Move it to the distance of even the nearest other star to our solar system, Proxima Centauri at a distance of 30 trillion kilometers, and it has an angular diameter of 2 millionth of a degree or 7 milliarseconds (1 milliarcsecond is 1 thousandth of an arcsecond which is one sixtieth of an arcminute which is one sixtieth of a degree).

    The resolution of a telescope (the size of the smallest point you can determine as being separate from another point) is proportional to the wavelength of light you're looking at divided by the diameter of your telescope. Make your telescope twice as big and you can resolve things twice as small. For the Keck telescope, 10 meters in diameter, the resolution at wavelengths used by the human eye is only 20 milliarcsecond (0.02 arcseconds). But the atmosphere through which the Keck telescope must look, blurs the ability to see detail and so on average, Keck can resolve objects only about 0.1 arcseconds in size. This is why telescopes in space, like HST, are so important. In order to resolve surface features on our sun at the distance of Proxima Centauri we'd need a telescope at least 40 meters in diameter. A telescope with a single mirror that big is currently impractical, but several smaller telescopes separated by 40 meters will yield the same resolution.

    The NPOI on Anderson Mesa is just such a telescope. With it astronomers have been conducting observations designed to measure the angular diameters of stars and over a hundred stars have had their angular diameters measured to date. Figure 1 shows the relative angular diameters of eight stars measured with the NPOI. For reference, a person standing on the moon would have an angular height of 1.0 milliarcseconds. The smallest star shown, Arneb, also known as alpha Leporis has an angular diameter of 1.77 milliarcseconds. The largest star shown, Hamal, also known as alpha Cassiopeiae, is 6.88 milliarcseconds in diameter.



Figure 1. Relative angular diameters of stars. The man on the Moon has a diameter of 1 millisecond of arc.


    But these diameters say nothing about how big the stars are themselves. Is a star that looks small really small or is it simply very far away? If one can measure the distance to a star then one can convert from an angular diameter to a true diameter. Distances to many of the brightest stars in the sky have already been determined using the Hipparcos satellite. The order in which stars overlap in Figure 1 is correct in terms of which stars are closer or farther away from us. Figure 2 shows the same stars for Figure 1, but now showing the correct relative linear size (where the size of each star in terms of how many times it is bigger than our Sun is shown). Since a person on the moon is obviously microscopic on this scale, our Sun is shown for reference. Notice that the smallest star in Figure 1, Arneb, is really the largest star of this sample.


Figure 2. Stars shown in relative proportion to their true diameters.


    So what do we learn from knowing a star's diameter? If we know how bright it is, we can determine how much energy is put out by each square centimeter of its surface. This is directly proportional to how hot it is. By measuring its size we have taken its temperature. Sometimes we learn unexpected things. For the star Polaris -- the North Star -- measuring its size also revealed how the gasses deep inside it move. Learning about things we didn't even think to ask about when we started is one of the rewards of looking at the sky in ways that have never been done before. As interferometers get bigger and better the discoveries will only increase. Soon we will not only be able to measure the diameter of stars but image light and dark spots on their surfaces as well. With that advent, we will have passed another mile post in completing the work begun by Galileo, 400 years ago.