Whether reading science news or watching science fiction, one hears references to distances between objects and places in space. Distances between stars is one thing, but the great gulfs between the galaxies is vastly larger. This month we talk about what the units are for expressing stellar distances and how they were even measured in the first place.
This month is the 50th anniversary of the opening season of the original "Star Trek" series. A typical conversation might go like this when Lt. Rahda said, "It doesn't make any sense, but somehow I'd say that in a flash we've been knocked 1,000 light-years away from where we were." Then Mr. Spock gives one of his typical flat responses, "990.7 light-years to be exact, Lieutenant."
The standard unit of measure for objects in our solar system is the astronomical unit, or AU, and is used to express distances among and between the planets. The average distance between the earth and the sun is, by definition, one AU — about 93 million miles. Mercury is 0.39 AU, while distant Neptune is around 30 AU. The actual distances are measurable using techniques such as the 17th-century astronomer Johannes Keppler's laws of planetary motion.
Stellar distances are orders of magnitudes farther. After the sun, the closest star to us is a faint red dwarf named Proxima Centauri. Its distance from the sun of some 268,000 AU makes it clear that the AU is rather awkward for measuring stellar distances. A better measurement comes from the distance light travels in some unit time. Traveling at 186,000 miles per second, light travels almost six trillion miles in one year, or a distance known as the light-year. Measured this way, Proxima Centauri is some 4.2 light-years away.
A key technique for measuring stellar distance is called parallax. Stellar images of stars taken months apart as the Earth travels around the sun can be compared in order to detect small differences in the positions of the closest stars relative to the stellar background. Even for the closest stars, this difference — or parallax — is very tiny. Nearby Proxima Centauri's parallax is only 0.7716 arc-second. This small angular shift in the star's position is similar to the size of a dime two miles away.
How can we measure distances to stars farther away? There are relationships between certain stellar characteristics. For instance, a star's color is an indicator of its temperature; blue is hotter than yellow, which is hotter than red. Brightness can also be used to indicate distance. But how can you tell if a red star is a nearby red dwarf or a distant red supergiant? Astronomers have categorized stars into different spectral types. A star's color can be used to look up its intrinsic brightness on a temperature-luminosity chart. By comparing a star's intrinsic or actual brightness with the observed brightness as viewed from Earth, an investigator can calculate the star's distance from us.
But these charts must first be calibrated in order to be useful. One way to do so is by employing a certain kind of variable star known as a Cepheid. A variable star is one that changes in brightness over time, and a Cepheid is a particular type that does so in a very predictable way. If the parallax method can be used to accurately determine the distance of some Cepheids, then the brightness of the light curve from farther Cepheids can be used to infer their distance.
Then, if a star cluster has Cepheids in it, then the distance to the cluster becomes known, as do the distances of the other stars in the cluster. Those stars can then be used to calibrate the temperature-luminosity relationship based on their observed color and brightness, and their known intrinsic brightness based on their stellar type. Now we can use the chart to determine the distance to other stars.
Thus, Cepheid variable stars turn out to be a "standard candle" for measuring distances to other stars. In a future article we'll work our way out beyond the stars of our local Milky Way galaxy to learn how astronomers determine the distances between the galaxies themselves.