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{{Short description|
{{About||the colorant reference database|Colour Index International|the term in geology|Color index (geology)}}
{| class="wikitable sortable" style="float: right; text-align: center; border: 1px; margin-left: 0.5em;"
|+ Sample calibration colors<ref name=zombeck/> {{Failed verification|date=December 2023}}
! [[Stellar classification|Class]] || B−V || U−B || V−R || R−I
! [[Effective temperature|''T''<sub>eff</sub>]] ([[Kelvin|K]])
|- BGCOLOR="
| O5V || −0.33 || −1.19 || −0.15 || −0.32 || 42,000
|- BGCOLOR="
| B0V || −0.30 || −1.08 || −0.13 || −0.29 || 30,000
|- BGCOLOR="
| A0V || −0.02 || −0.02 || 0.02 || −0.02 || 9,790
|- BGCOLOR="
| F0V || 0.30 || 0.03 || 0.30 || 0.17 || 7,300
|- BGCOLOR="
| G0V || 0.58 || 0.06 || 0.50 || 0.31 || 5,940
|- BGCOLOR="
| K0V || 0.81 || 0.45 || 0.64 || 0.42 || 5,150
|- BGCOLOR="
| M0V || 1.40 || 1.22 || 1.28 || 0.91 || 3,840
|}
In [[astronomy]], the '''color index''' is a simple [[Numerical analysis|numerical]] [[Expression (mathematics)|expression]] that determines the [[color]] of an object, which in the case of a [[star]] gives its [[temperature]]. The lower the color 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 inverse [[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 color 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 |title=Encyclopedia of Astronomy & Astrophysics |chapter=Tycho Star Catalogs: The 2.5 Million Brightest Stars |date=2001 |publisher=CRC Press |isbn=978-1-003-22043-5 |editor-last=Murdin |editor-first=P. |___location=Boca Raton |doi=10.1888/0333750888/2862 |chapter-url=https://archive.org/details/paul-murdin-encyclopedia-of-astronomy-and-astrophysics-vol.-1-a-gel.-institute-o/page/n4971/mode/2up<!--?q=%22Tycho+Star+Catalogs%22--> |url=https://archive.org/details/paul-murdin-encyclopedia-of-astronomy-and-astrophysics-vol.-1-a-gel.-institute-o/mode/2up}}</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.
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.<ref name=Sekiguchi>
:<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>
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:<math>E_{\text{B-}\!\text{V}} = {B\text{-}\!V}_\text{observed} - {B\text{-}\!V}_\text{intrinsic}.</math>
The [[passband]]s most optical [[astronomer]]s use are the [[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]] light. This [[photometric system|system of filters]] is sometimes called the Johnson–Kron–Cousins filter system, named after the originators of the system (see references).<ref>{{Cite journal |last=Landolt |first=Arlo U. |date=1992-07-01 |title=UBVRI Photometric Standard Stars in the Magnitude Range 11.5 < V < 16.0 Around the Celestial Equator |url=https://ui.adsabs.harvard.edu/abs/1992AJ....104..340L |journal=The Astronomical Journal |volume=104 |pages=340 |doi=10.1086/116242 |bibcode=1992AJ....104..340L |issn=0004-6256}}</ref> These filters were specified as particular combinations of glass filters and [[photomultiplier|photomultiplier tubes]]. [[Michael S. Bessell|M. S. Bessell]] specified a set of filter transmissions for a flat response detector, thus quantifying the calculation of the color indices.<ref name=filters/> 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:
{| class="wikitable sortable"
|+Color indices of Solar System bodies<ref>{{Citation|last = Pace |first = G. |title = UBV: Subroutine to Compute Photometric Magnitudes of the Planets and Their Satellites |type = Technical report |publisher = [[Jet Propulsion Laboratory]] |pages = |date = February 15, 1971 |url = https://ntrs.nasa.gov/api/citations/19710009758/downloads/19710009758.pdf}}</ref><ref name=":0" />
!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 ==
{| class="wikitable sortable"<!-- Do not change; these are not literal and just quantify ranges of certain B-V values. Stick to what the source says.-->
|+Quantitative color index terms<ref name=":0">{{Cite journal |last1=Neuhäuser |first1=R |last2=Torres |first2=G |last3=Mugrauer |first3=M |last4=Neuhäuser |first4=D L |last5=Chapman |first5=J |last6=Luge |first6=D |last7=Cosci |first7=M |date=2022-07-29 |title=Colour evolution of Betelgeuse and Antares over two millennia, derived from historical records, as a new constraint on mass and age |journal=Monthly Notices of the Royal Astronomical Society |volume=516 |issue=1 |pages=693–719 |doi=10.1093/mnras/stac1969 |doi-access=free |issn=0035-8711|arxiv=2207.04702 |bibcode=2022MNRAS.516..693N }}</ref>
!Color<br />(Vega reference)
!Color index<br />(B-V)
!Spectral class<br />([[main sequence]])
!Spectral class<br />([[giant star]]s)
!Spectral class<br />([[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 (star)|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]] (which may be considered a slightly cool white). "Green" stars would be perceived as white by the human eye.
==See also==
{{div col|colwidth=20em}}
* [[Asteroid color indices]]
* [[Color–color diagram]]
* [[Distant object color indices]]
* [[Spectral index]]
* [[UBV photometric system]]
* [[Zero point (photometry)|Zero point]]
{{div col end}}
== Notes ==
{{notelist}}
== References ==
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* [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990PASP..102.1181B&db_key=AST&high=3c321cbf8304649 Query] for [[Michael S. Bessell|Bessell, M. S.]], PASP 102, 1181 (1990)
{{Portal bar|Physics|Mathematics|Astronomy|Stars|Outer space|Solar System|Science}}
[[Category:Photometric systems]]
[[Category:Index numbers]]
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