Content deleted Content added
The denominator of the first expression was incorrectly shown as 0.92(B-V)+1.6(-). This was corrected to 0.92(B-V)+1.7 <ref>https://arxiv.org/pdf/1201.1809.pdf</ref> |
No edit summary |
||
| (42 intermediate revisions by 24 users not shown) | |||
Line 1:
{{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
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}{
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.
Line 34:
:<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
{{div col end}}
== Notes ==
{{notelist}}
== References ==
Line 63 ⟶ 167:
* [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]]
| |||