Calculation of Color Indices

The star Spica has apparent magnitudes B = 0.77, and V = 1.0 in the blue and photovisual regions, respectively. The corresponding color index is

B - V = 0.77 - 1.0 = - 0.23

Generally, the negative values of the color index indicates that Spica is a hot star, with most of its radiation coming at shorter wavelengths. On the other hand, for Antares B = 2.73 and V=0.9, and the B - V color index is

B - V = 2.73 - 0.9 = 1.83

The positive value of B - V indicates that Antares is a cool star, with most of its radiation coming at longer wavelengths.

Color Indices

The section on radiation laws indicated that there is a relationship between the temperature of a blackbody and the location of the peak in the radiation distribution as a function of wavelength (Wien's law). This allows definition of some continuous quantities called color indices that can be determined directly from observations and that are indirect indicators of temperature for the star.
Definition of a Color Index
A color index is defined by taking the difference in magnitudes (which are related logarithmically to intensity) at two different wavelengths. Using the U, B, and V color filters, there are several possibilities for such differences. For example, the B-V color index is defined by taking the difference between the magnitudes in the blue and visual regions of the spectrum and the U-B color index is the analogous difference between the UV and blue regions of the spectrum. For our discussion we will normally mean the B-V color index when we refer to a color index.

Color Index and Surface Temperature
The adjacent false color infrared image shows an emission nebula in the constellation Orion called the Flame Nebula (NGC 2024). The bright star in the lower right is Alnitak (Zeta Orionis or 50 Orionis; the popular name derives from the Arabic Al Nitak: "the belt or girdle"), which is the easternmost star in the belt of Orion. It is a hot blue supergiant (see the Harvard spectral sequence and HR diagram later in this chapter), about 15 times larger than the Sun and a little over 800 light years away, with a negative B-V color index (-0.21).

The negative color index indicates that this star outputs much of its light in the UV region of the spectrum. The color and structure of the nearby Flame Nebula is largely because of the ionization of hydrogen by the intense UV flux from Alnitak. Light is emitted when electrons knocked from hydrogen by the UV radiation recombine with the hydrogen ions.