7 June 2000
Polaris is located 431 light years away from the Solar System in the constellation of Ursa Minor (the Little Bear) often called the Little Dipper. Because of its nearly direct position over the Earth's North Pole, Polaris holds a nearly fixed position in the night sky, making it a navigation reference long used by sailors, campers, and sky watchers.
Cepheid variables, named after the first one discovered in the constellation Cepheus, are pulsating stars that change their brightness in a regular periodic way, unlike our Sun, an ordinary star whose light output over the eons has been nearly constant. In the early 1900's, Henrietta Leavitt of the Harvard College Observatory discovered that there is a relation between the length of a Cepheid's pulsational period and its total light output, or luminosity: stars with longer periods were inherently brighter than ones with shorter periods. Astronomers have also known from theory and indirect estimates of the sizes of Cepheids that, like the relation between pulsational period and luminosity, there is also a relation between period and radius, with larger Cepheids having longer periods. Cepheids are giant stars with luminosities several thousand times greater than the Sun, and can thus be used as a kind of "standard candle" for determining large distances in the Cosmos. In fact, a key project of NASA's Hubble Space Telescope is to discern Cepheids in distant galaxies and thus determine the size of the Universe.
Cepheids get brighter and dimmer because they constantly change size. A complex series of events deep in the atmosphere of these stars causes the outer layers of the stellar atmosphere to alternately expand and contract. Usually all the material in the outer atmosphere moves in the same direction at the same time. Imagine pulling on a spring with one end held fixed to a table. While the fixed end remains constant (the deepest layers) the other end moves back and forth (the surface). This is called fundamental mode pulsation.
The NPOI observations of Polaris directly confirm a discovery by a team of African and European astronomers in 1997 that Polaris is an "overtone pulsator". In other words, when Polaris pulsates, not all of its atmosphere moves in the same direction at the same time.
"By comparing the radius of Polaris to predictions for fundamental pulsation we were comparing oranges to grapefruits. They may look similar on the outside, but the difference in size told us there is something very different on the inside" says Dr. Robert Hindsley, a team member and long-time Cepheid investigator with the Naval Research Laboratory in Washington D.C.
For a few Cepheids the internal dance of gases is more complicated. At a particular depth in the atmosphere there is a boundary, called a node, inside of which all the gas moves in one direction while outside the gas moves in the opposite direction. In this case, while one hand pulls the end of the spring back and forth, the other hand pulls on the middle of the spring in the opposite direction. This type of pulsation is called "first overtone pulsation". Since the physics differs between these two kinds of pulsation, there are different period-radius relationships for fundamental and overtone pulsators. From this difference astronomers at the U.S. Naval Observatory have confirmed which type of pulsation is at work in Polaris.
The NPOI, located at Lowell Observatory's Anderson Mesa station, is a Y-shaped array of 0.5-meter (20-inch) optical telescopes capable of combining their light in order to measure the apparent diameter of a star many light years away. Dr. Nordgren and others have used the NPOI, a joint project between the U.S. Naval Observatory, the Naval Research Laboratory, and Lowell Observatory, to measure the sizes of over a hundred stars, including the four brightest Cepheid variables in the northern sky.
The NPOI observations for Polaris show that the North Star has a radius of 46 +/- 3 solar radii. With an observed period of four days, theories say that if Polaris is a fundamental mode pulsator, like most Cepheids, it should only have a radius of 38 solar radii. The period-radius relation for overtone pulsators, however, predicts larger radii for Cepheids at all periods. When compared with this other period-radius relation the observed large radius for Polaris is in perfect agreement.
Figure 1: The Navy Prototype Optical Interferometer (NPOI) is an array of 0.5-meter (20-inch) mirrors located on Anderson Mesa outside Flagstaff, Arizona. Currently the light from three mirrors (inside the rectangular buildings located at the center of the array) are combined to simulate the resolving capability of a single optical telescope 38-meters (125-feet) in diameter. When construction is completed, the NPOI will consist of ten mirrors with a total resolution of a single mirror 440-meters (1443-feet) in diameter. With this array, astronomers are able to measure the diameters of stars and eventually image features on their surfaces.
Photo Credit: Dr. Nat White (Lowell Observatory)
Figure 2: Seven stars observed by the NPOI are shown with their measured relative sizes. For comparison our own Sun is shown to the same scale. Relatively small Alshain, a third magnitude star in the constellation of Aquila the Eagle, is only three times larger than the Sun. The red giant Pi Leonis in the constellation of Leo the Lion has a radius 80 times larger than our own Sun. In the middle is Polaris, which is 46 times the size of our Sun.
Image Credit: Dr. Tyler Nordgren (U.S. Naval Observatory)
Figure 3: The relations between period and radius are shown for cepheid variable stars. The prototype cepheid variable, Delta Cephei, was measured by the NPOI to have a radius of 44 solar radii (44 times larger than our Sun). At a period of 5.3 days it agrees perfectly with the predicted size for fundamental mode pulsators (blue band). As shown in the lower right, this means all material in the outer atmosphere move outward or inward at any one time. Polaris, at a radius of 46 solar radii and period of 4.0 days is too large for a fundamental mode cepheid. However, the difference in size, shown by the dashed line, reveals the inner structure of the cepheid. Polaris agrees perfectly with the predictions for overtone pulsators (pink band). This result confirms that different depths in the atmosphere move in different directions (shown in the upper left).
Image Credit: Dr. Tyler Nordgren (U.S. Naval Observatory)