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A color temperature (TC) of an electromagnetic radiation (EMR) source is a measure of the temperature based upon a color index, a form of the ratio of the brightness of the source within two different bands. In effect, it is the temperature of the black-body spectrum for which that color index best matches that of the source.
Note that outside astronomy, the term color temperature means something a bit different. There is some relation regarding the meaning, but the criteria used undoubtedly differs. For example, descriptions of light produced by artificial lighting (e.g., light bulbs) may cite a color temperature that is the approximate temperature of a black body that is perceived (by human eyes) as the same color as the light source.