Color index: Difference between revisions

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{{Short description|The colorColor of an astronomical object}}

{{About||the colorant reference database|Colour Index International|the term in geology|Color index (geology)}}

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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 |url=https://www.taylorfrancis.com/books/mono/10.1201/9781003220435/encyclopedia-astronomy-astrophysics-murdin |title=Encyclopedia of Astronomy & Astrophysics |chapter=Tycho Star Catalogs: The 2.5 Million Brightest Stars |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 |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>Sekiguchi{{cite M.journal and|author1=Maki Sekiguchi |author2=Masataka Fukugita (|name-list-style=and |date=2000). "|title=A STUDYStudy OFof THEthe B-V''B−V'' COLORColor-TEMPERATURETemperature RELATION".Relation AJ (|journal=Astrophysical Journal) |volume=120 (2000)|number=2 |page=1072. http://iopscience|doi=10.iop.org1086/1538301490 |doi-3881access=free|arxiv=astro-ph/120/2/1072.9904299 }}</ref> A good approximation can be obtained by considering stars as [[black body|black bodies]], using Ballesteros' formula<ref name=Ballesteros>{{cite journal |last=Ballesteros, |first=F. J. (|date=2012). "|title=New insights into black bodies". |journal=EPL |volume=97 (2012)|number=3 |at=34008. {{ArXiv|arxiv=1201.1809}}.</ref> (also implemented in the PyAstronomy package for Python):<ref name=PyAstronomy>BallesterosBV_T API http://www.hs.uni-hamburg.de/DE/Ins/Per/Czesla/PyA/PyA/index.html.</ref>

:<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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{| 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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

|-

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==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 ==