Explain the relationship between B-V and stellar temperature.

Question

How is B-V related to temperature? Explain the relationship between B-V and stellar temperature.

Answer 1

B-V (or "color index") is a difference in brightness expressed in magnitudes. The B stands for the brightness of an object when the observer is using a "blue" filter -- which is a filter that lets blue light pass somewhat better than most other wavelengths. The V stands for "visual," which is astronomer talk for yellow.

Every hot object has a characteristic "blackbody" distribution in radiant power versus wavelength (it's the Planck distribution, q.v.). The higher the temperature, the further toward the blue end of the spectrum the distribution's peak is shifted. By measuring the magnitude difference in apparent brightness through two different filters whose transmissive qualities are known, it becomes possible to interpolate (or extrapolate) where the distribution maximum is located, and, from that, estimate the "color temperature" of the star or other object.

Actually, you ought to use a third filter, which is usually an ultraviolet filter, to find another color index called U-B. That resolves an ambiguity that can arise. With only two filters, you would usually have two blackbody curves that would fit the points: one with the beak between B and V, and one with the peak beyond whichever of those were the higher. The third filter makes it clear which of those two distributions is correct.

If you discover a new Cepheid variable star, you can use the famous "period-luminosity relationship" with the observed period of the light curve to find the luminosity of the star at maximum light. Then you'd find the color index of the star at maximum light to determine the color temperature at that moment. Then you'd use the Stefan-Boltzmann equation to calculate the star's radius at maximum light. Clever, huh?

B-V to color temperature.

If B-V > -0.0413, then

T = 10^{ [14.551 - (B-V)] / 3.684 }

If B-V < -0.0413, then

T = 10^{ 4.945 - sqrt[ 1.087353 + 2.906977 (B-V) ] }

Color temperature to B-V.

If T < 9141 K

B-V = -3.684 log T + 14.551

If T > 9141 K

B-V = 0.344 (log T)^2 - 3.402 log T + 8.037

Logarithms are base 10.

(Just what does a guy have to do around here to avoid getting the thumbs down on his answer?)