3. DISTANCE SCALE:

Measuring the size of the Milky Way has been one of the most challenging and important tasks in astronomy. Twenty years ago, astronomers thought that distance from the Sun to the center of the Milky Way was about twice the accepted value today. In Lesson 4, we already described two methods to measure the distances of stars: parallax; and spectroscopic parallax. By measuring the parallaxes of stars very accurately, the Hipparcos satellite enabled astronomers to measure the distances of several thousands of stars to distances of a few thousand light years. Then, by knowing the relationship between luminosity and temperature of main sequence stars, astronomers could infer the distances of clusters of stars by the spectroscopic parallax method. But before the advent of the Hubble Space Telescope, astronomers could not observe main sequence stars in globular clusters well enough to measure their distances by either of these methods.

The big breakthrough in measuring the distances of stars was accomplished in 1912 by Henrietta Leavitt, an astronomer working at the Harvard College Observatory. Ms. Leavitt observed some 1500 variable stars in two nearby galaxies, the Large and Small Magellanic Clouds, and found that their brightness was correlated with their pulsation periods. This correlation, which we now call the period-luminosity relation, gives us a powerful tool to measure the distances of these stars.

Let's review how we can infer the distance (D) of a star if we know its luminosity (L) and measure its brightness (B). These quantities are related by the inverse square law:

B = L/4p D², which implies D = (L/4p B)^1/2.

To use this method to infer a star's distance, we need to have some extra information to know its luminosity. If we know that the star is a main-sequence star and we measure its spectral type, we can infer its luminosity from the Hertzsprung-Russell diagram. That is the method of spectroscopic parallax. The problem with stars in globular clusters is that their main-sequence stars are too faint to observe with ground-based telescopes. So, before the Hubble Space Telescope was launched, we couldn't use this method to infer the distances of globular clusters.

Henrietta Leavitt found a relationship between the pulsation periods of variable stars and their luminosities. For example, RR Lyrae stars pulsate with periods between 0.3 and 1 day, and they all have approximately the same luminosity, about 50 times the Sun's luminosity. So, if we find a star that pulsates regularly with periods between 0.2 and 1 day, we know that the star's luminosity must be about 50 solar luminosities, and we can then measure its brightness and calculate its distance from the equation above. The reason that this method is so useful is that variable stars tend to be substantially more luminous than main sequence stars, so we can observe them at substantially greater distances. This was the method that Harlow Shapley used to infer the distance to the globular clusters, and hence the distance to the center of the Milky Way.

Cepheid variable stars have even longer pulsation periods. They are so luminous that they can be observed in distant galaxies, and so they provide a method for estimating the distances of those galaxies, as we shall discuss in Lesson 10.

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Last modified March 3, 2002
Copyright by Richard McCray