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In [[astronomy]], the '''colourcolor index''' is a simple [[Numerical analysis|numerical]] [[Expression (mathematics)|expression]] that determines the [[color|colour]] of an object, which in the case of a [[star]] gives its [[temperature]]. The lower the colourcolor index, the more [[blue]] (or hotter) the object is. Conversely, the larger the color index, the more [[red]] (or cooler) the object is. This is a consequence of the [[Logarithmic scale|logarithmic magnitude scale]], in which brighter objects have smaller (more negative) magnitudes than dimmer ones. For comparison, the whitish [[Sun]] has a B−V index of {{nowrap|0.656 ± 0.005}},<ref name=sun/> whereas the bluish [[Rigel]] has a B−V of −0.03 (its B magnitude is 0.09 and its V magnitude is 0.12, B−V = −0.03).<ref name=rigel/> Traditionally, the colourcolor index uses [[Vega]] as a [[Zero Point (photometry)|zero point]]. The [[blue supergiant]] [[Theta Muscae]] has one of the lowest B−V indices at −0.41,<ref>{{Cite book |url=https://www.taylorfrancis.com/books/mono/10.1201/9781003220435/encyclopedia-astronomy-astrophysics-murdin |title=Encyclopedia of Astronomy & Astrophysics |date=2001-01-01 |publisher=CRC Press |isbn=978-1-003-22043-5 |editor-last=Murdin |editor-first=P. |___location=Boca Raton |doi=10.1888/0333750888/2862}}</ref> while the [[red giant]] and [[carbon star]] [[R Leporis]] has one of the largest, at +5.74.<ref>{{Cite web |title=VizieR |url=http://webviz.u-strasbg.fr/viz-bin/VizieR-5?-out.add=.&-source=V/50/catalog&recno=1607 |access-date=2024-04-02 |website=webviz.u-strasbg.fr}}</ref>
To measure the index, one observes the [[Magnitude (astronomy)|magnitude]] of an object successively through two different [[Astronomical filter|filter]]s, such as U and B, or B and V, where U is sensitive to [[ultraviolet]] rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also: [[UBV system]]). The set of passbands or filters is called a [[photometric system]]. The difference in magnitudes found with these filters is called the U−B or B−V color index respectively.
:<math>T = 4600\,\mathrm{K} \left( \frac{1}{0.92\;(B\text{-}\!V) + 1.7} + \frac{1}{0.92\;(B\text{-}\!V) + 0.62} \right). </math>
Color indices of distant objects are usually affected by [[extinction (astronomy)|interstellar extinction]], that is, they are [[interstellar reddening|redder]] than those of closer stars. The amount of reddening is characterized by [[Interstellar reddening|colourcolor excess]], defined as the difference between the '''observed colourcolor index''' and the '''normal colourcolor index''' (or '''intrinsic colourcolor index'''), the hypothetical true colourcolor index of the star, unaffected by extinction.
For example, in the UBV photometric system we can write it for the B−V color:
:<math>E_{\text{B-}\!\text{V}} = {B\text{-}\!V}_\text{observed} - {B\text{-}\!V}_\text{intrinsic}.</math>
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