# Color index

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Color of an astronomical object

For the colorant reference database, see [Colour Index International](/source/Colour_Index_International). For the term in geology, see [Color index (geology)](/source/Color_index_(geology)). For the digital image compression method, see [Indexed color](/source/Indexed_color).

Sample calibration colors[1][failed verification] Class B−V U−B V−R R−I Teff (K) O5V −0.33 −1.19 −0.15 −0.32 42,000 B0V −0.30 −1.08 −0.13 −0.29 30,000 A0V −0.02 −0.02 0.02 −0.02 9,790 F0V 0.30 0.03 0.30 0.17 7,300 G0V 0.58 0.06 0.50 0.31 5,940 K0V 0.81 0.45 0.64 0.42 5,150 M0V 1.40 1.22 1.28 0.91 3,840

In [astronomy](/source/Astronomy), the **color index** is a simple [numerical](/source/Numerical_analysis) [expression](/source/Expression_(mathematics)) that determines the [color](/source/Color) of an object, which in the case of a [star](/source/Star) gives its [temperature](/source/Temperature). The lower the color index, the more [blue](/source/Blue) (or hotter) the object is. Conversely, the larger the color index, the more [red](/source/Red) (or cooler) the object is. This is a consequence of the inverse [logarithmic magnitude scale](/source/Logarithmic_scale), in which brighter objects have smaller (more negative) magnitudes than dimmer ones. For comparison, the whitish [Sun](/source/Sun) has a B−V index of 0.656 ± 0.005,[2] whereas the bluish [Rigel](/source/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).[3] Traditionally, the color index uses [Vega](/source/Vega) as a [zero point](/source/Zero_Point_(photometry)). The [blue supergiant](/source/Blue_supergiant) [Theta Muscae](/source/Theta_Muscae) has one of the lowest B−V indices at −0.41,[4] while the [red giant](/source/Red_giant) and [carbon star](/source/Carbon_star) [R Leporis](/source/R_Leporis) has one of the largest, at +5.74.[5]

To measure the index, one observes the [magnitude](/source/Magnitude_(astronomy)) of an object successively through two different [filters](/source/Astronomical_filter), such as U and B, or B and V, where U is sensitive to [ultraviolet](/source/Ultraviolet) rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also: [UBV system](/source/UBV_system)). The set of passbands or filters is called a [photometric system](/source/Photometric_system). The difference in magnitudes found with these filters is called the U−B or B−V color index respectively.

In principle, the temperature of a star can be calculated directly from the B−V index, and there are several formulae to make this connection.[6] A good approximation can be obtained by considering stars as [black bodies](/source/Black_body), using Ballesteros' formula[7] (also implemented in the PyAstronomy package for Python):[8]

- T = 4600 K ( 1 0.92 ( B - V ) + 1.7 + 1 0.92 ( B - V ) + 0.62 ) . {\displaystyle T=4600\,\mathrm {K} \left({\frac {1}{0.92\;(B{\text{-}}\!V)+1.7}}+{\frac {1}{0.92\;(B{\text{-}}\!V)+0.62}}\right).}

Color indices of distant objects are usually affected by [interstellar extinction](/source/Extinction_(astronomy)), that is, they are [redder](/source/Interstellar_reddening) than those of closer stars. The amount of reddening is characterized by [color excess](/source/Interstellar_reddening), defined as the difference between the **observed color index** and the **normal color index** (or **intrinsic color index**), the hypothetical true color index of the star, unaffected by extinction. For example, in the UBV photometric system we can write it for the B−V color:

- E B- V = B - V observed − B - V intrinsic . {\displaystyle E_{{\text{B-}}\!{\text{V}}}={B{\text{-}}\!V}_{\text{observed}}-{B{\text{-}}\!V}_{\text{intrinsic}}.}

The [passbands](/source/Passband) most optical [astronomers](/source/Astronomer) use are the [UBVRI](/source/UBVRI) filters, where the U, B, and V filters are as mentioned above, the R filter passes red light, and the I filter passes [infrared](/source/Infrared) light. This [system of filters](/source/Photometric_system) is sometimes called the Johnson–Kron–Cousins filter system, named after the originators of the system (see references).[9] These filters were specified as particular combinations of glass filters and [photomultiplier tubes](/source/Photomultiplier). [M. S. Bessell](https://en.wikipedia.org/w/index.php?title=Michael_S._Bessell&action=edit&redlink=1) specified a set of filter transmissions for a flat response detector, thus quantifying the calculation of the color indices.[10] For precision, appropriate pairs of filters are chosen depending on the object's color temperature: B−V are for mid-range objects, U−V for hotter objects, and R−I for cool ones.

Color indices can also be determined for other celestial bodies, such as planets and moons:

Color indices of Solar System bodies[11][12] Celestial body B-V color index U-B color index Mercury 0.97 0.40 Venus 0.81 0.50 Earth 0.20 0.0 Moon 0.92 0.46 Mars 1.43 0.63 Jupiter 0.87 0.48 Saturn 1.09 0.58 Uranus 0.56 0.28 Neptune 0.41 0.21

## Quantitative color index terms

Quantitative color index terms[12] Color (Vega reference) Color index (B-V) Spectral class (main sequence) Spectral class (giant stars) Spectral class (supergiant stars) Examples Red ≥1.40 M K4-M9 K3-M9 Betelgeuse, Antares Orange 0.80-1.40 K G4-K3 G1-K2 Arcturus, Pollux Yellow 0.60-0.80 G G0-G3 F8-G0 Sun, Rigil Kent Green 0.30-0.60 F F F4-7 Procyon White 0.00-0.30 A A A0-F3 Sirius, Vega Blue -0.33-0.00 OB OB OB Spica, Rigel

The common color labels (e.g. red supergiant) are subjective and taken using the star Vega as the reference. However, these labels, which have a quantifiable basis, do not reflect how the human eye would perceive the colors of these stars. For instance, Vega has a bluish white color, while the Sun, from outer space, would look like a neutral white somewhat warmer than the [illuminant D65](/source/Illuminant_D65) (which may be considered a slightly cool white). "Green" stars would be perceived as white by the human eye.[12]

## See also

- [Asteroid color indices](/source/Asteroid_color_indices)

- [Color–color diagram](/source/Color%E2%80%93color_diagram)

- [Distant object color indices](/source/Distant_object_color_indices)

- [Spectral index](/source/Spectral_index)

- [UBV photometric system](/source/UBV_photometric_system)

- [Zero point](/source/Zero_point_(photometry))

## Notes

## References

1. **[^](#cite_ref-zombeck_1-0)** Zombeck, Martin V. (1990). "Calibration of MK spectral types". [*Handbook of Space Astronomy and Astrophysics*](https://archive.org/details/handbookspaceast00zomb_311) (2nd ed.). [Cambridge University Press](/source/Cambridge_University_Press). p. [105](https://archive.org/details/handbookspaceast00zomb_311/page/n104). [ISBN](/source/ISBN_(identifier)) [0-521-34787-4](https://en.wikipedia.org/wiki/Special:BookSources/0-521-34787-4).

1. **[^](#cite_ref-sun_2-0)** David F. Gray (1992), *[The Inferred Color Index of the Sun](http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992PASP..104.1035G&db_key=AST&data_type=HTML&format=&high=44b52c369023103)*, Publications of the Astronomical Society of the Pacific, vol. 104, no. 681, pp. 1035–1038 (November 1992).

1. **[^](#cite_ref-rigel_3-0)** ["* bet Ori"](http://simbad.u-strasbg.fr/simbad/sim-basic?Ident=%2A+bet+Ori). *[SIMBAD](/source/SIMBAD)*. [Centre de données astronomiques de Strasbourg](/source/Centre_de_donn%C3%A9es_astronomiques_de_Strasbourg).

1. **[^](#cite_ref-4)** Murdin, P., ed. (2001). ["Tycho Star Catalogs: The 2.5 Million Brightest Stars"](https://archive.org/details/paul-murdin-encyclopedia-of-astronomy-and-astrophysics-vol.-1-a-gel.-institute-o/page/n4971/mode/2up). [*Encyclopedia of Astronomy & Astrophysics*](https://archive.org/details/paul-murdin-encyclopedia-of-astronomy-and-astrophysics-vol.-1-a-gel.-institute-o/mode/2up). Boca Raton: CRC Press. [doi](/source/Doi_(identifier)):[10.1888/0333750888/2862](https://doi.org/10.1888%2F0333750888%2F2862). [ISBN](/source/ISBN_(identifier)) [978-1-003-22043-5](https://en.wikipedia.org/wiki/Special:BookSources/978-1-003-22043-5).

1. **[^](#cite_ref-5)** ["VizieR"](http://webviz.u-strasbg.fr/viz-bin/VizieR-5?-out.add=.&-source=V/50/catalog&recno=1607). *webviz.u-strasbg.fr*. Retrieved 2024-04-02.

1. **[^](#cite_ref-Sekiguchi_6-0)** Maki Sekiguchi and Masataka Fukugita (2000). ["A Study of the *B−V* Color-Temperature Relation"](https://doi.org/10.1086%2F301490). *Astrophysical Journal*. **120** (2): 1072. [arXiv](/source/ArXiv_(identifier)):[astro-ph/9904299](https://arxiv.org/abs/astro-ph/9904299). [doi](/source/Doi_(identifier)):[10.1086/301490](https://doi.org/10.1086%2F301490).

1. **[^](#cite_ref-Ballesteros_7-0)** Ballesteros, F. J. (2012). "New insights into black bodies". *EPL*. **97** (3). 34008. [arXiv](/source/ArXiv_(identifier)):[1201.1809](https://arxiv.org/abs/1201.1809).

1. **[^](#cite_ref-PyAstronomy_8-0)** BallesterosBV_T API [http://www.hs.uni-hamburg.de/DE/Ins/Per/Czesla/PyA/PyA/index.html](http://www.hs.uni-hamburg.de/DE/Ins/Per/Czesla/PyA/PyA/index.html).

1. **[^](#cite_ref-9)** Landolt, Arlo U. (1992-07-01). ["UBVRI Photometric Standard Stars in the Magnitude Range 11.5 < V < 16.0 Around the Celestial Equator"](https://ui.adsabs.harvard.edu/abs/1992AJ....104..340L). *The Astronomical Journal*. **104**: 340. [Bibcode](/source/Bibcode_(identifier)):[1992AJ....104..340L](https://ui.adsabs.harvard.edu/abs/1992AJ....104..340L). [doi](/source/Doi_(identifier)):[10.1086/116242](https://doi.org/10.1086%2F116242). [ISSN](/source/ISSN_(identifier)) [0004-6256](https://search.worldcat.org/issn/0004-6256).

1. **[^](#cite_ref-filters_10-0)** Michael S. Bessell (1990), *[UBVRI passbands](http://adsabs.harvard.edu/abs/1990PASP..102.1181B)*, Publications of the Astronomical Society of the Pacific, vol. 102, Oct. 1990, p. 1181–1199.

1. **[^](#cite_ref-11)** Pace, G. (February 15, 1971), [*UBV: Subroutine to Compute Photometric Magnitudes of the Planets and Their Satellites*](https://ntrs.nasa.gov/api/citations/19710009758/downloads/19710009758.pdf) (PDF) (Technical report), [Jet Propulsion Laboratory](/source/Jet_Propulsion_Laboratory)

1. ^ [***a***](#cite_ref-:0_12-0) [***b***](#cite_ref-:0_12-1) [***c***](#cite_ref-:0_12-2) Neuhäuser, R; Torres, G; Mugrauer, M; Neuhäuser, D L; Chapman, J; Luge, D; Cosci, M (2022-07-29). ["Colour evolution of Betelgeuse and Antares over two millennia, derived from historical records, as a new constraint on mass and age"](https://doi.org/10.1093%2Fmnras%2Fstac1969). *Monthly Notices of the Royal Astronomical Society*. **516** (1): 693–719. [arXiv](/source/ArXiv_(identifier)):[2207.04702](https://arxiv.org/abs/2207.04702). [Bibcode](/source/Bibcode_(identifier)):[2022MNRAS.516..693N](https://ui.adsabs.harvard.edu/abs/2022MNRAS.516..693N). [doi](/source/Doi_(identifier)):[10.1093/mnras/stac1969](https://doi.org/10.1093%2Fmnras%2Fstac1969). [ISSN](/source/ISSN_(identifier)) [0035-8711](https://search.worldcat.org/issn/0035-8711).

## Further reading

- [Query](http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1953ApJ...117..313J&db_key=AST&high=3c321cbf8303780) for [Johnson, H. L.](/source/Harold_Johnson_(astronomer)) and [Morgan](/source/William_Wilson_Morgan), ApJ 117, 313 (1953)

- [Query](http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1974MNRAS.166..711C&db_key=AST&high=3c321cbf8304063) for [Cousins, A. W. J.](/source/Alan_William_James_Cousins), MNRAS 166, 711 (1974)

- [Query](http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1974MNSSA..33..149C&db_key=AST&high=3c321cbf8304063) for [Cousins, A. W. J.](/source/Alan_William_James_Cousins), MNASSA 33, 149 (1974)

- [Query](http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990PASP..102.1181B&db_key=AST&high=3c321cbf8304649) for [Bessell, M. S.](https://en.wikipedia.org/w/index.php?title=Michael_S._Bessell&action=edit&redlink=1), PASP 102, 1181 (1990)

[Portals](https://en.wikipedia.org/wiki/Wikipedia:Contents/Portals):
- [Physics](https://en.wikipedia.org/wiki/Portal:Physics)
- [Mathematics](https://en.wikipedia.org/wiki/Portal:Mathematics)
- [Astronomy](https://en.wikipedia.org/wiki/Portal:Astronomy)
- [Stars](https://en.wikipedia.org/wiki/Portal:Stars)
- [Outer space](https://en.wikipedia.org/wiki/Portal:Outer_space)
- [Solar System](https://en.wikipedia.org/wiki/Portal:Solar_System)
- [Science](https://en.wikipedia.org/wiki/Portal:Science)

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Adapted from the Wikipedia article [Color index](https://en.wikipedia.org/wiki/Color_index) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Color_index?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.