In astronomy, color is a quantity comparing the brightness of a given object measured at two different wavelengths of light. It is most commonly used to determine the temperature of an individual star, the age of a composite stellar population, or the amount of extinction caused by interstellar dust.

### Definition

Astronomers use the somewhat archaic logarithmic units of magnitudes to measure brightness. The color of an object is the arithmetic difference of the brightness of an object measured in two different band-pass filters. If A is the magnitude of an object measured in one filter, and B is the magnitude measured in another filter, then the color is

(A - B) = A - B

The notation (A - B) (including the parentheses) is the standard notation for color or the color index. It is standard to measure the color with the shorter wavelength magnitude measurement first, as in

(mblue - mred)

If you come across a book or magazine article on astronomy, and it mentions quantities like (B - V), (V - R), or (u - y), these are colors, measured in the two filter band-passes contained within the parentheses.

Because lower magnitudes correspond to brighter objects, low and negative color indices correspond to "blue" spectra. Suppose, for example, you measure a star in the B (blue) and V (visual, green-yellow) filters, and find mB=7.8 and mV=8.0. Then, the (B - V) color index would be -0.2, corresponding to a very blue object. If mB=11.4 and mV=8.0 then the color index would be +3.4, a very red star.

It's important to note that "bluer" and "redder" are only convenient shorthand for saying "brighter at shorter wavelengths" and "brighter at longer wavelengths" -- astronomers can and do measure "colors" in everything from X-rays to the infrared.

Finally, since the color index is measured in logarithmic magnitudes, this corresponds to a ratio of brightnesses in linear units.

### Temperature, luminosity and chemical abundances

The color is often used to determine the temperature of individual stars. Most stars have stellar spectra similar to that of a blackbody. The blackbody spectrum is only a function of the wavelength of light and of the temperature of the emitting object. The spectrum doesn't change shape as the temperature changes, but the peak wavelength of the spectrum -- defined by Wien's Displacement Law -- does change; as the object gets hotter, more light gets emitted at shorter (bluer) wavelengths.

The blackbody function has well-defined logarithmic slopes, depending upon whether you are blueward or redward of the peak. Redward of the peak, the function follows the Rayleigh-Jeans Law where the brightness, Bλ is inversely proportional to the wavelength to the fourth power:

Bλ,R-J = 2 c k T / λ4

Blueward of the peak, the blackbody curve nearly follows Wien's Law, which is a modified exponential relation,

Bλ,Wien = (2 h c / λ5) exp (-h c/&lambdakT)

If you want to determine the temperature of an object, then in theory you

1. measure the brightness in four or five different band-pass filters
2. determine where the slope of the spectrum changes from the Rayleigh-Jeans to the Wien regime,
3. estimate where the peak of the function should be located, and then
4. obtain the temperature from Wien's Displacement Law.

In practice, it is a little trickier since stars aren't perfect blackbodies. What is normally done is to measure the color in several filters, and then compare the measured colors to tabulated values of colors for stars with precisely-measured spectral types. You can then determine the star's spectral type based on only a few observations. It is usually easier to determine a spectral type this way because it takes less time to measure the brightness in four or five wide-band filters than it does to obtain a spectrum.

Certain photometric colors are also used as indicators of other intrinsic properties of stars. Perhaps the most important is the chemical composition of a star, specifically the amount of metals in the stellar atmosphere. Metals cause what is called line blanketing in stellar atmospheres -- metal atoms absorb blue light, and re-emit this light in red light. Thus, metals "blanket" the blue side of the spectrum. So what happens is that at a given effective temperature, a metal-rich star might appear redder than a metal-poor star with similar effective temperature.

You can also obtain the luminosity of a star with colors, though in a slightly more convoluted way. In the near-ultraviolet, there is a spectral feature called the Balmer decrement, caused by the strong absorption of ultraviolet light by hydrogen. The strength of this decrement is partly a function of the surface gravity of the star, which is a function of the mass of the star and its radius. A star with a lower surface gravity is likely to be an evolved, giant star, while one with higher surface gravity is likely closer to the main sequence. Since giant stars are more luminous, there is a difference between the spectra of giant stars and those of main sequence stars, even if they have the same temperature and chemical composition. You can use some photometric color indices to measure the strength of the Balmer decrement, and thus obtain the luminosity.

### Ages of star clusters and galaxies

The color can also be used to measure the age of a star or a group of stars in star clusters and galaxies. When individual stars in a star cluster can be resolved, the color can be used to build a Hertzsprung-Russell diagram in the form of a color-magnitude diagram. The color-magnitude diagram is almost identical to the Hertzsprung-Russell diagram, but with color replacing the temperature, and magnitude replacing the absolute luminosity. The age of the cluster can be determined by fitting isochrones to the diagram.

If you can't resolve individual stars and assemble a color-magnitude diagram, then you can measure the color of a population by determining the surface brightness of the diffuse light in two different filters. This is commonly done when observing galaxies too far away to resolve individual stars. If you find that galaxy has a low color index (for example, (mblue - mred) = 0.1), then most of the light in that galaxy is coming from bluer stars, suggesting that the galaxy is still forming stars today. If the color index is higher, then most of the light is probably coming from older, redder stars (like old red giant stars). Often, different parts of a galaxy may have different colors. For example, the bulge of a spiral galaxy will have a redder color than the spiral arms because bulges are usually very old (and red), while spiral arms may contain lots of newborn, hot, blue stars.

### Interstellar reddening and extinction

Our Milky Way galaxy, like most spiral galaxies, is filled with dust. This dust has the effect of reddening any light that passes through it -- blue light is preferentially scattered away by dust particles in space, while red light passes through relatively unimpeded. This can and does foul up our attempts to measure the intrinsic color of stars when there is dust in the interstellar medium between us and them. However, there's one way around this. Suppose we take a finely-detailed spectrum of a bright star in the region we're interested in, rather than relying on the colors. The shape of its blackbody curve will still be distorted, but we can use other things like the strength of the hydrogen absorption lines or other absorption and emission lines in the spectrum to determine the spectral type. We can then measure the difference between the colors we should see and the colors we actually measure to determine the amount of reddening toward the area we're observing. This difference is known as the color excess, given by

E(A - B) = (A - B)observed - (A - B)intrinsic

If you then make the (often unwise) assumption that the reddening is the same for all stars in that same general direction, then you can use the measured color excess to determine the intrinsic colors of other stars in the same area. However, this is not always a good idea, given that dust in our Milky Way is very patchy and uneven. It is better to take several spectra in the same region to see whether all stars have similar reddening in their spectra.

Sources:
Increasingly dim memory.