Stellar Diameters
There are few direct methods for determining the diameter of stars. One of the most important uses
eclipses of binary star systems. By carefully examining the light curve, it is possible to determine
how long it takes one star to pass in front of the other and this can be used to infer the sizes of the
stars.
The following animation illustrates the relationship of eclipse timing and stellar diameters.
Analysis of an Eclipse
Let us now examine such an eclipse in more detail and see how we can use timing of
the eclipse to extract information about the sizes of the stars.
The following comments refer to the figure
adjacent right,
where the smaller star is totally eclipsed by the larger one and the orbits are
assumed circular. Although most eclipsing binaries are more complicated than this, this simple
example will illustrate basic principles in a transparent way.
The smaller star is assumed to be moving from left to right.
At point 1 the eclipse starts and the light begins to decrease.
At point 2 the
eclipse becomes total and the light output is constant until point 3. At point 3, the
smaller star begins to emerge and the light output grows until
finally at point 4 the eclipse is complete.
Diameter of the Smaller Star
From point 1 to point 2 the smaller star moves a distance on its orbit equal to
its diameter D. But if the magnitude of the
velocity v for the smaller star can be determined from Doppler
methods and we carefully measure the time t
from point 1 to point 2, the diameter
follows from multiplying the velocity by this time: D = v t.
Diameter of the Larger Star
By similar reasoning, in the time from when the eclipse begins until it ends, the
smaller star covers a distance equal to the diameter of the larger star. Thus, by
carefully measuring this interval and multiplying by the velocity, we can determine
the diameter of the larger star.