Re: How do you tell how big a star is?

Stellar sizes have been measured directly for a few hundred stars. Only the sizes of very big stars near our solar system can be measured with present techniques. The reason is that movement of air in the atmosphere blurs the image of star as seen in a telescope, and makes it look like a blob of light that does not correspond to the true size of the star even in the largest telescopes. Telescopes in satellites can avoid the atmosphere blurring problem, but are not sufficiently large to show a true image of a star.

Several techniques have been developed to measure stellar radii directly. One technique can be applied to binary stars, i.e., stars that orbit each other. If the orbit of the stars is oriented in such a way that one star passes in front of the other when we see it from Earth, there will be an eclipse---we will see a dimming of the light. The duration of the eclipse will depend on the sizes of the two stars. If the velocity at which one star revolves around the other is known, the sizes of the two stars can be measured. You can find a simulation of how this method works for measuring stellar radii in Properties of Stars. One star in which this measurement has been done is Algol, one of the brightest stars in the constellation of Perseus.

For most stars their size can be estimated by looking how bright and how hot they are. Brighter stars are bigger, but a star can also be brighter because it is hotter even it is small. There is a formula that relates the luminosity, L, radius, R, and surface temperature, T for a star. That formula is L=R²(T/5777)⁴ Here L, and R are measured in solar luminosities and radii respectively, i.e., L=1 for star with the same luminosity as that of the Sun and R=2 for a star with twice the solar radius. As you see, we can determine R for a star is we know its L and T by solving for R: R=square root of L/(T/5777)⁴. The radius of the Sun is 6.96 × 10¹⁰ cm.

Now the question is how to determine L and T. The luminosity L of a star is the total power of light emitted by the star per second. It can be measured from Earth if we know how far the star is. The distance is important because the brightness of a star decreases with distance. The luminosity of the Sun is 3.83 × 10³³ ergs/second. The temperature T can be determined by measuring the spectrum of the star. The spectrum of the star is simply the distribution of its light in different wavelengths or colors. Hotter stars emit more light in the blue than in the red. It is difficult to measure L and T with high precision for most stars. Therefore the values of R determined with this method are very uncertain.

Vladimir Escalante Ramírez