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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 smaller 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 yellowish 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.

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.[4] A good approximation can be obtained by considering stars as black bodies, using Ballesteros' formula[5] (also implemented in the PyAstronomy package for Python):[6]

\( {\displaystyle T=4600\,\mathrm {K} \left({\frac {1}{0.92(B-V)+1.7}}+{\frac {1}{0.92(B-V)+0.62}}\right).} \)

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:

\( {\displaystyle E_{B-V}=(B-V)_{\text{observed}}-(B-V)_{\text{intrinsic}}.} \)

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.[7] 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.
See also

Asteroid color indices
Color–color diagram
Distant object color indices
UBV photometric system
Zero point

References

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 données astronomiques de Strasbourg.
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.

Further reading

Johnson, H. L. and Morgan, ApJ 117, 313 (1953)
Cousins, A. W. J., MNRAS 166, 711 (1974)
Cousins, A. W. J., MNASSA 33, 149 (1974)
Bessell, M. S., PASP 102, 1181 (1990)

Stars
Formation

Accretion Molecular cloud Bok globule Young stellar object
Protostar Pre-main-sequence Herbig Ae/Be T Tauri FU Orionis Herbig–Haro object Hayashi track Henyey track

Evolution

Main sequence Red-giant branch Horizontal branch
Red clump Asymptotic giant branch
super-AGB Blue loop Protoplanetary nebula Planetary nebula PG1159 Dredge-up OH/IR Instability strip Luminous blue variable Blue straggler Stellar population Supernova Superluminous supernova / Hypernova

Spectral classification

Early Late Main sequence
O B A F G K M Brown dwarf WR OB Subdwarf
O B Subgiant Giant
Blue Red Yellow Bright giant Supergiant
Blue Red Yellow Hypergiant
Yellow Carbon
S CN CH White dwarf Chemically peculiar
Am Ap/Bp HgMn Helium-weak Barium Extreme helium Lambda Boötis Lead Technetium Be
Shell B[e]

Remnants

White dwarf
Helium planet Black dwarf Neutron
Radio-quiet Pulsar
Binary X-ray Magnetar Stellar black hole X-ray binary
Burster

Hypothetical

Blue dwarf Green Black dwarf Exotic
Boson Electroweak Strange Preon Planck Dark Dark-energy Quark Q Black Gravastar Frozen Quasi-star Thorne–Żytkow object Iron Blitzar

Stellar nucleosynthesis

Deuterium burning Lithium burning Proton–proton chain CNO cycle Helium flash Triple-alpha process Alpha process Carbon burning Neon burning Oxygen burning Silicon burning S-process R-process Fusor Nova
Symbiotic Remnant Luminous red nova

Structure

Core Convection zone
Microturbulence Oscillations Radiation zone Atmosphere
Photosphere Starspot Chromosphere Stellar corona Stellar wind
Bubble Bipolar outflow Accretion disk Asteroseismology
Helioseismology Eddington luminosity Kelvin–Helmholtz mechanism

Properties

Designation Dynamics Effective temperature Luminosity Kinematics Magnetic field Absolute magnitude Mass Metallicity Rotation Starlight Variable Photometric system Color index Hertzsprung–Russell diagram Color–color diagram

Star systems

Binary
Contact Common envelope Eclipsing Symbiotic Multiple Cluster
Open Globular Super Planetary system

Earth-centric
observations

Sun
Solar System Sunlight Pole star Circumpolar Constellation Asterism Magnitude
Apparent Extinction Photographic Radial velocity Proper motion Parallax Photometric-standard

Lists

Proper names
Arabic Chinese Extremes Most massive Highest temperature Lowest temperature Largest volume Smallest volume Brightest
Historical Most luminous Nearest
Nearest bright With exoplanets Brown dwarfs White dwarfs Milky Way novae Supernovae
Candidates Remnants Planetary nebulae Timeline of stellar astronomy

Related articles

Substellar object
Brown dwarf Sub-brown dwarf Planet Galactic year Galaxy Guest Gravity Intergalactic Planet-hosting stars Tidal disruption event

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