A color-magnitude diagram is a scattergraph of astronomical objects showing the relationship between each object’s absolute magnitude and its estimated surface temperature or between optical or perceptual proxies for these quantities.
Humankind has always wanted to understand the bodies in the night sky, and one step to understanding them is to categorize them.
The first tool available to assign these categories was the human visual system – the unaided eye. Hipparchus (c. 190 BCE–c. 120 BCE) developed a scale for stars based on visual brightness, which eventually became quantified as stellar magnitude. The convention that dimmer stars have higher magnitude is a historical precedent that dates from Hipparchus (1). However, whereas Hipparchus attached magnitude 1 to the brightest star within each constellation, Ptolemy (c. 140 AD) refined the system so that the brightest stars had magnitude 1 and the barely visible stars had magnitude 6 .
From the time of Galilei (1564–1642) and Kepler (1571–1630), the unaided eye became augmented by telescopes, whose main function in astronomy is to gather light from a much larger area than is available at the pupil of the eye. Telescopes were at first very limited in their light-gathering ability but later developed enough aperture so that the stars became accessible to color vision. At that point, a new categorization was possible, in which color and brightness could be conjoined.
Of course, stars have spectra that are close to black-body radiators, and such radiators have only two physical variables: intensity and temperature . In perceptual terms, the color ranges from reddish through bluish through yellow and white, on a curve in the chromaticity diagram called the black-body locus. It is therefore possible to render the visible character of a star by two numbers: the brightness (magnitude) and a single variable of color (or temperature).
Diagram for Stars
At the beginning of the twentieth century, aided by the mature technology of telescopes, Danish astronomer  and American astronomer  developed the first color-magnitude diagram, called the Hertzsprung–Russell diagram (H-R diagram) [3, 4, 5]. Originally the diagram was based on visual estimation of magnitude and color, and it was a research tool to help characterize stellar evolution before the mechanism of nuclear fusion was understood. After about the 1930s, the H-R diagram became based on objective measurements but was used less as a research tool and more as a way to illustrate the theoretically predicted evolution of stars through trajectories in the diagram.
The objective measurements that replaced direct human perception were as follows: A star’s absolute magnitude is the attenuation (in factors 10−0.4) of the star Vega’s power (as received at 10 pc viewing distance [32.6 light years]) to equal that of the star (also corrected to 10 pc).
A star’s surface temperature is estimated in one of three ways: by the observed color (an old way), by a comparison of two sensor outputs such as blue and violet (a newer way), or by a model prediction of the temperature of a black-body radiator with the same radiation power per unit star-surface area (the most modern way). The third way requires independent inference of the star’s radius but assumes the star has an emissivity of 1. To acknowledge the lack of compensation for the true emissivity, the temperature on an H-R diagram is called “effective temperature.”
It is important to note the coordinate conventions of the H-R diagram: Temperature on a log scale (5) increases from right to left and magnitude (i.e., dimness) increases from bottom to top. Hence dim red stars (red giants) appear near the upper right of the diagram, and bluish bright stars (such as white dwarfs) appear in the lower left. A long cluster of stars called the Main Sequence extends from the upper left to lower right. Higher-mass stars occur at the upper left of this sequence, and the Sun appears approximately in the middle. The Main Sequence is composed of stars that are currently dominated by hydrogen that is fusing into helium. According to currently accepted theory of stellar evolution, such stars will eventually migrate either to the red-giant or white-dwarf domain of the H-R diagram.
H-R diagrams are often depicted in color, either pseudo-color with a thermal code to show the temperature or coded according to star categories such as cluster membership. No matter how the measurements were obtained, the data representation for the end user returns to visual perception as the way to see the color and brightness relationships of stars.
Diagram for Galaxies
One further stage in telescope evolution occurred in 1990 when the Hubble Space Telescope was launched into orbit. The Hubble Space Telescope was able to render high-contrast images outside the Earth’s atmosphere without encountering the absorption, scattering, and haze that beset Earth-bound telescopes. In digital images conveyed to earth from the Space Telescope, it was possible to see the colors, not only of stars, but of whole galaxies that are so distant as to be too dim to measure on the Earth. The color-magnitude diagram developed by Hertzsprung and Russell then evolved to accommodate galaxies. Thus was born the galaxy color-magnitude diagram . The construction of such a diagram is similar to that of the Hertzsprung–Russell diagram, but the interpretation in terms of physical properties is not as precise.
To compute a galaxy’s absolute magnitude, it is treated as a point-like object, whereupon its radiation is corrected (by the inverse-square law) to a distance of 10 pc, and the absolute magnitude is computed as the number of 10−0.4 attenuations of similarly compensated power from a reference to achieve a match.
The temperature is also the same “effective temperature” as is used in the H-R diagram. However, galaxies are visible from much farther away than individual stars, so a galaxy’s recessional red shift exerts an appreciable influence on its effective temperature. Because light from farther galaxies (and greater red shift) requires more time for light to travel to the Earth, the galaxy color-magnitude diagram, if it were not red-shift-corrected, would depict an earlier universe at the red end of the temperature scale. However, in practice, the temperature is red-shift-corrected to be in the “rest frame” of the galaxy. In this case, the galaxies divide into two clusters: bright and reddish as opposed to dim and bluish. The existence of such clusters places strong constraints on theories of galactic formation.
Color-magnitude diagrams are not always defined in terms of fundamental physical properties such as those described above. In one embodiment, the galaxy color-magnitude diagram coordinates are defined by the log outputs of two sensors, typically called g and r, the sensors having different spectral sensitivities: the abscissa records r (which stands in lieu of the absolute magnitude) and the ordinate records g – r (which relates to the temperature). At the top of the diagram, one finds the red sequence of galaxies (elliptical galaxies), and at the bottom, one finds the blue cloud (spiral galaxies).
- 1.Astronomical Society of South Australia: Stellar photometry. http://www.assa.org.au/articles/stellarphotometry. Accessed 30 May 2013
- 2.Wyszecki, G., Stiles, W.S.: Color Science, 2nd edn. Wiley, New York (1982)Google Scholar
- 3.Gribbin, J.: Companion to the Cosmos. Little, Brown, New York (1996)Google Scholar
- 4.Pasachoff, J.M.: A Brief View of Astronomy. Saunders College Publishing, New York (1986)Google Scholar
- 5.Wikipedia, Hertzsprung-Russell Diagram: http://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram. Accessed 30 May 2013
- 6.Shapley, A.E.: Physical Properties of Galaxies from z = 2 – 4. http://arxiv.org/abs/1107.5060v2. Accessed 26 Feb 2013