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
- measure the brightness in four or five different
band-pass filters
- determine where the slope of the spectrum changes from the
Rayleigh-Jeans to the Wien regime,
- estimate where the peak of the function should be located, and then
- 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.
Also, Radiative Processes in Astrophysics.