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Color index

January 01, 1970

For the colorant reference database, see Colour Index International. For the term in geology, see Color index (geology).
Sample calibration colors[1]
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, the color index is a simple numerical 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 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 0.656 ± 0.005,[2] 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).[3] Traditionally, the color index uses Vega as a zero point. The blue supergiant Theta Muscae has one of the lowest B−V indices at −0.41,[4] while the red giant and carbon star R Leporis has one of the largest, at +5.74.[5]

To measure the index, one observes the magnitude of an object successively through two different filters, 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.[6] A good approximation can be obtained by considering stars as black bodies, using Ballesteros' formula[7] (also implemented in the PyAstronomy package for Python):[8]

Color indices of distant objects are usually affected by interstellar extinction, that is, they are redder than those of closer stars. The amount of reddening is characterized by 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. For example, in the UBV photometric system we can write it for the B−V color:

The passbands most optical astronomers 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 system of filters is sometimes called 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 tubes. M. S. Bessell specified a set of filter transmissions for a flat response detector, thus quantifying the calculation of the color indices.[9] 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[10][11]
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 edit

Quantitative color index terms[11]
Color (Vega reference) Color (human eye) Color index (B-V) Spectral class (main sequence) Spectral class (giant stars) Spectral class (supergiant stars) Examples     
Red Orange ≥1.40 M K4-M9 K3-M9 Betelgeuse, Antares
Orange Cream 0.80-1.40 K G4-K3 G1-K2 Arcturus, Pollux
Yellow Warm white 0.60-0.80 G G0-G3 F8-G0 Sun, Rigil Kent
"Green"[a] Cool white 0.30-0.60 F F F4-7 Procyon
White Bluish white 0.00-0.30 A A A0-F3 Sirius, Vega
Blue Blue -0.33-0.00 OB OB OB Spica, Rigel

The common color labels (eg. red supergiant) are taken using the star Vega as the reference. However, these labels don't reflect how the human eye would perceive the colors of these stars. Vega has a bluish white color. From outer space, the Sun would look like a neutral white somewhat warmer than the illuminant D65 (which may be considered a slightly cool white).

See also edit

Notes edit

  1. ^ Such stars would not be seen as green, but either as whitish or yellow.

References edit

  1. ^ Zombeck, Martin V. (1990). "Calibration of MK spectral types". Handbook of Space Astronomy and Astrophysics (2nd ed.). Cambridge University Press. p. 105. ISBN 0-521-34787-4.
  2. ^ David F. Gray (1992), The Inferred Color Index of the Sun, Publications of the Astronomical Society of the Pacific, vol. 104, no. 681, pp. 1035–1038 (November 1992).
  3. ^ "* bet Ori". SIMBAD. Centre de données astronomiques de Strasbourg.
  4. ^ Murdin, P., ed. (2001-01-01). Encyclopedia of Astronomy & Astrophysics. Boca Raton: CRC Press. doi:10.1888/0333750888/2862. ISBN 978-1-003-22043-5.
  5. ^ "VizieR". webviz.u-strasbg.fr. Retrieved 2024-04-02.
  6. ^ Sekiguchi M. and Fukugita (2000). "A STUDY OF THE B-V COLOR-TEMPERATURE RELATION". AJ (Astrophysical Journal) 120 (2000) 1072. http://iopscience.iop.org/1538-3881/120/2/1072.
  7. ^ Ballesteros, F. J. (2012). "New insights into black bodies". EPL 97 (2012) 34008. arXiv:1201.1809.
  8. ^ BallesterosBV_T API http://www.hs.uni-hamburg.de/DE/Ins/Per/Czesla/PyA/PyA/index.html.
  9. ^ Michael S. Bessell (1990), UBVRI passbands, Publications of the Astronomical Society of the Pacific, vol. 102, Oct. 1990, p. 1181–1199.
  10. ^ Pace, G. (February 15, 1971), UBV: Subroutine to Compute Photometric Magnitudes of the Planets and Their Satellites (PDF) (Technical report), Jet Propulsion Laboratory
  11. ^ a b 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". Monthly Notices of the Royal Astronomical Society. 516 (1): 693–719. arXiv:2207.04702. doi:10.1093/mnras/stac1969. ISSN 0035-8711.

Further reading edit

January 01, 1970
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For the colorant reference database see Colour Index International For the term in geology see Color index geology Sample calibration colors 1 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 the color index is a simple numerical 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 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 0 656 0 005 2 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 3 Traditionally the color index uses Vega as a zero point The blue supergiant Theta Muscae has one of the lowest B V indices at 0 41 4 while the red giant and carbon star R Leporis has one of the largest at 5 74 5 To measure the index one observes the magnitude of an object successively through two different filters 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 6 A good approximation can be obtained by considering stars as black bodies 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 that is they are redder than those of closer stars The amount of reddening is characterized by 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 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 most optical astronomers 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 system of filters is sometimes called 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 tubes M S Bessell specified a set of filter transmissions for a flat response detector thus quantifying the calculation of the color indices 9 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 10 11 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 21Quantitative color index terms editQuantitative color index terms 11 Color Vega reference Color human eye Color index B V Spectral class main sequence Spectral class giant stars Spectral class supergiant stars Examples Red Orange 1 40 M K4 M9 K3 M9 Betelgeuse Antares Orange Cream 0 80 1 40 K G4 K3 G1 K2 Arcturus Pollux Yellow Warm white 0 60 0 80 G G0 G3 F8 G0 Sun Rigil Kent Green a Cool white 0 30 0 60 F F F4 7 Procyon White Bluish white 0 00 0 30 A A A0 F3 Sirius Vega Blue Blue 0 33 0 00 OB OB OB Spica Rigel The common color labels eg red supergiant are taken using the star Vega as the reference However these labels don t reflect how the human eye would perceive the colors of these stars Vega has a bluish white color From outer space the Sun would look like a neutral white somewhat warmer than the illuminant D65 which may be considered a slightly cool white See also editAsteroid color indices Color color diagram Distant object color indices UBV photometric system Zero pointNotes edit Such stars would not be seen as green but either as whitish or yellow References edit Zombeck Martin V 1990 Calibration of MK spectral types Handbook of Space Astronomy and Astrophysics 2nd ed Cambridge University Press p 105 ISBN 0 521 34787 4 David F Gray 1992 The Inferred Color Index of the Sun Publications of the Astronomical Society of the Pacific vol 104 no 681 pp 1035 1038 November 1992 bet Ori SIMBAD Centre de donnees astronomiques de Strasbourg Murdin P ed 2001 01 01 Encyclopedia of Astronomy amp Astrophysics Boca Raton CRC Press doi 10 1888 0333750888 2862 ISBN 978 1 003 22043 5 VizieR webviz u strasbg fr Retrieved 2024 04 02 Sekiguchi M and Fukugita 2000 A STUDY OF THE B V COLOR TEMPERATURE RELATION AJ Astrophysical Journal 120 2000 1072 http iopscience iop org 1538 3881 120 2 1072 Ballesteros F J 2012 New insights into black bodies EPL 97 2012 34008 arXiv 1201 1809 BallesterosBV T API http www hs uni hamburg de DE Ins Per Czesla PyA PyA index html Michael S Bessell 1990 UBVRI passbands Publications of the Astronomical Society of the Pacific vol 102 Oct 1990 p 1181 1199 Pace G February 15 1971 UBV Subroutine to Compute Photometric Magnitudes of the Planets and Their Satellites PDF Technical report Jet Propulsion Laboratory a b Neuhauser R Torres G Mugrauer M Neuhauser 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 Monthly Notices of the Royal Astronomical Society 516 1 693 719 arXiv 2207 04702 doi 10 1093 mnras stac1969 ISSN 0035 8711 Further reading editQuery for Johnson H L and Morgan ApJ 117 313 1953 Query for Cousins A W J MNRAS 166 711 1974 Query for Cousins A W J MNASSA 33 149 1974 Query for Bessell M S PASP 102 1181 1990 Portals nbsp Physics nbsp Mathematics nbsp Astronomy nbsp Stars nbsp Outer space nbsp Solar System nbsp Science Retrieved from https en wikipedia org w index php title Color index amp oldid 1223140801, wikipedia, wiki, book, books, library,

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