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Learning objectives

By the end of this section, you will be able to:

  • Describe the methods used to determine star diameter s
  • Identify the parts of an eclipsing binary star light curve that correspond to the diameters of the individual components

It is easy to measure the diameter of the Sun. Its angular diameter—that is, its apparent size on the sky—is about 1/2°. If we know the angle the Sun takes up in the sky and how far away it is, we can calculate its true (linear) diameter, which is 1.39 million kilometers, or about 109 times the diameter of Earth.

Unfortunately, the Sun is the only star whose angular diameter is easily measured. All the other stars are so far away that they look like pinpoints of light through even the largest ground-based telescopes. (They often seem to be bigger, but that is merely distortion introduced by turbulence in Earth’s atmosphere.) Luckily, there are several techniques that astronomers can use to estimate the sizes of stars.

Stars blocked by the moon

One technique, which gives very precise diameters but can be used for only a few stars, is to observe the dimming of light that occurs when the Moon passes in front of a star. What astronomers measure (with great precision) is the time required for the star’s brightness to drop to zero as the edge of the Moon moves across the star’s disk. Since we know how rapidly the Moon moves in its orbit around Earth, it is possible to calculate the angular diameter of the star. If the distance to the star is also known, we can calculate its diameter in kilometers. This method works only for fairly bright stars that happen to lie along the zodiac, where the Moon (or, much more rarely, a planet) can pass in front of them as seen from Earth.

Eclipsing binary stars

Accurate sizes for a large number of stars come from measurements of eclipsing binary    star systems, and so we must make a brief detour from our main story to examine this type of star system. Some binary stars are lined up in such a way that, when viewed from Earth, each star passes in front of the other during every revolution ( [link] ). When one star blocks the light of the other, preventing it from reaching Earth, the luminosity of the system decreases, and astronomers say that an eclipse has occurred.

Light curve of an eclipsing binary.

Light Curve of an Eclipsing Binary. In this plot the vertical axis is labeled “Brightness” in arbitrary units, and the horizontal axis is labeled “Time” in arbitrary units. The plotted line is labeled “Light curve”. The plot begins as a horizontal line at upper left and is labeled “1”. The line then drops very sharply downward as it moves to the right, then quickly becomes horizontal again. This horizontal section is labeled “2”. The curve then rises sharply again back to the same brightness level as segment 1. This horizontal section is labeled “3”. After a time, the horizontal line drops, but not as deeply as segment 2, and becomes horizontal again. This horizontal segment is labeled “4”. The curve then rises again to the level of segment 1. Inset is a diagram of the binary star system. The larger star is drawn as a red sphere. A blue elliptical arrow surrounds the larger star with an arrowhead pointing to the right, indicating the motion of the companion star. The companion star is drawn on the elliptical arrow in four places corresponding to the sections 1-4 on the light curve. At position 1 the smaller star is separated from the larger star and the light curve is at its brightest. At position 2 the smaller star is behind the larger star and the light curve dips to its lowest brightness. At position 3 the smaller star emerges from behind the larger star and the full brightness is restored. Finally, at position 4, the smaller star is in front of the larger star, and the light curve dips to its next lowest level.
The light curve of an eclipsing binary star system shows how the combined light from both stars changes due to eclipses over the time span of an orbit. This light curve shows the behavior of a hypothetical eclipsing binary star with total eclipses (one star passes directly in front of and behind the other). The numbers indicate parts of the light curve corresponding to various positions of the smaller star in its orbit. In this diagram, we have assumed that the smaller star is also the hotter one so that it emits more flux (energy per second per square meter) than the larger one. When the smaller, hotter star goes behind the larger one, its light is completely blocked, and so there is a strong dip in the light curve. When the smaller star goes in front of the bigger one, a small amount of light from the bigger star is blocked, so there is a smaller dip in the light curve.

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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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