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)}}

{| 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''_eff]] ([[Kelvin|K]])

|- BGCOLOR="#7070ff{{Color temperature|42000|hexval}}"

| O5V || −0.33 || −1.19 || −0.15 || −0.32 || 42,000

|- BGCOLOR="#50a0ff{{Color temperature|30000|hexval}}"

| B0V || −0.30 || −1.08 || −0.13 || −0.29 || 30,000

|- BGCOLOR="#c0cfff{{Color temperature|9790|hexval}}"

| A0V || −0.02 || −0.02 || 0.02 || −0.02 || 9,790

|- BGCOLOR="#cfffff{{Color temperature|7300|hexval}}"

| F0V || 0.30 || 0.03 || 0.30 || 0.17 || 7,300

|- BGCOLOR="#efffdf{{Color temperature|5940|hexval}}"

| G0V || 0.58 || 0.06 || 0.50 || 0.31 || 5,940

|- BGCOLOR="#ffff7f{{Color temperature|5150|hexval}}"

| K0V || 0.81 || 0.45 || 0.64 || 0.42 || 5,150

|- BGCOLOR="#ff7f7f{{Color temperature|3840|hexval}}"

| 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 [[yellow]]ishwhitish [[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>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) + 1.6(-)7} + \frac{1}{10.592\;(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|color excess]], 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.

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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.

the [[Johnson–Cousins filter system]], named after the originators of the system (see references). 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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

|-

|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 Pointpoint (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]]