Chapter 14: The Milky Way

A parsec is the distance from the Sun to an astronomical object which has a parallax angle of one arcsecond (1 AU and 1 pc are not to scale (1 pc = 206265 AU)).

In the late 18th century, William Herschel's ambition was to map out the size and shape of the Milky Way. He was hampered because he had no way of measuring stellar distance. Apparent brightness alone is a very poor indicator of distance because stars have such a wide range of intrinsic properties. The most direct measure of stellar distance is parallax. In a parallax measurement, the diameter of Earth's orbit of the Sun is used as the base of a triangle to make a geometric measurement of distance. By using the data gathered by the European Space Agency's Hipparcos satellite launched in 1989, astronomers can reliably calculate distances to just over one hundred parsecs. The Hyades cluster, at about 47 pc, is pivotal in the galactic distance scale. The cluster can be measured not only by the parallax technique but also by a variety of methods, which allows a more reliable determination of distance.

Pleiades, also known as the Seven Sisters, in infrared light.

Astronomers have devised varied and sometimes ingenious methods to determine the distances to individual stars and groups. Here are details of some of the most important methods. First, we can use the collective properties of stars to determine the distances to open clusters. For example, we might use the angular size of a cluster to infer its distance. If all clusters have the same physical size, then simple geometry tells us that D ∝ 1/ Θ, where D is the distance to the cluster and Θ is the angle subtended by the cluster. Astronomers test the method with the Hyades, where parallax provides a direct measure of distance. If the Hyades subtends an angle of 7.5° at a distance of 42 parsecs, then a cluster that subtends only ½° must be (7.5/0.5) × 42 = 630 parsecs away. The problem with this method is that open clusters have a wide range in physical size, ranging from 4 parsecs for the Pleiades to 16 parsecs for h Persei. The same is true of globular clusters. So the error in using angular size to predict distance can be as large as a factor of four. This would be like saying that all humans, from newborns to adults, are about 6 feet (or 72 inches) tall.  For any given human you would be making a similar maximum error — newborns are on average 20 inches tall which is about 4 times smaller than 72 inches.

The Hyades open star cluster

Relative distances can be measured if we have spectra for the stars and can place them on an H-R diagram. We can then compare this H-R diagram of a more distant cluster to the H-R diagram for the Hyades. This technique is called main sequence fitting. Each cluster has a concentration of stars that defines its main sequence on an H-R diagram. The main sequence of each cluster has the same shape. The amount the two main sequences have to be shifted vertically to "fit" on top of each other gives the apparent brightness difference between the two clusters. The apparent brightness difference is related to the relative distance by the inverse square law. Using the inverse square law and the known distance to the Hyades, the distance of the fainter cluster can be calculated easily. For example, if main sequence stars in M 67 are 2000 times fainter than main sequence stars of the same spectral type in the Hyades, then M 67 is √ 2000 x 42 = 1900 parsecs away. Main sequence fitting gives relative distances with an accuracy of about 20 to 30%. This would be like saying that all humans between the age of 20 and 30 are the same height. Since the intrinsic range in heights you were sampling was smaller (between about 5 feet and 7 feet tall), you would have similar accuracy.