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Colour Indices

Absolute magnitude is measured relative to the reference star Alpha Lyrae (Vega). However, different stars do not have the same energy distribution across the spectrum as Vega.  Some have more flux (radiate more strongly) in the visual part of the spectrum and therefore have a smaller visual magnitude, V. Or they might have more flux in the blue region, B, or the ultraviolet, U. Thus, the differences between V, B and U tell us something about the energy distribution of the star. Stars which have relatively more energy at visual rather than blue wavelengths than Vega have a positive B–V value, and appear more red (recall that stellar magnitudes decrease with increasing brightness). Conversely, stars with a negative B–V appear more blue.
By convention the U, B and V wavelength bands are defined as:
  • U = 3650 ± 680 Å
  • B = 4400 ± 980 Å
  • V = 5500 ± 890 Å

The B–V and U–B values are sometimes known as Johnson Indices (after H.L. Johnson who, with W.W. Morgan, introduced the UBV system in the early 1950s) and are correlated with the object’s effective temperature. Very roughly:
B-V = 7000 K/Teff - 0.56 (1)
The results of more accurate calculations are shown in Table 1.
  Effective Temperatures Bol. Correction
B - V Type V Type III Type I Type V Type I
-0.32 37,000 37,000      
-0.31 33,000 33,000 35,000    
-0.30 30,500 30,500 34,770    
-0.29 28,700 28,700 34,400    
-0.28 27,200 27,200 33,800    
-0.27 25,700 25,700 32,500    
-0.26 24,500 24,500 26,000    
-0.25 24,500   26,000 +2.30 +2.20
-0.24 22,000 22,000 23,500    
-0.23 21,000   23,500 +2.15 +2.05
-0.22 19,800 19,800 21,200    
-0.20 17,700 17,700 19,100 +1.80 +1.72
-0.15 14,000   14,500 +1.20 +1.12
-0.10 11,800   12,700 +0.61 +0.53
-0.05 10,500   11,000 +0.33 +0.14
0.00 9,480 9,480 9,800 +0.15 -0.01
+0.10 8,530   8,500 +0.04 -0.09
+0.50 6,310 6,270 6,020 +0.03 -0.07
+1.00 4,840 4,780 4,770 +0.40 +0.30
Table 1: B-V versus Teff and bolometric corrections for Hot Stars (after Böhm-Vitense 1989a, tables 6.1 and 8.1).
Stars having the lowest (most negative) B-V values are the bluest and hottest, such as the early O star, Zeta Puppis (B-V = -0.27) and those having the largest values are the reddest and coolest, such as the Garnet Star, Mu Cephei (B-V = 2.26).  B-V values for some well-known stars are given in Table 2.
Star Type B-V U-B
U Ant N (C5,3) 2.88 7.1
Y CVn N 2.54 6.62
m Cep M 2.26 2.45
a Ori (Betelgeuse) M 1.89 2.07
a Tau (Aldebaran) K 1.54 1.92
a1 Cen G 0.71 0.33
a CMi (Procyon) F 0.42 0.03
40 Eri B DA 0.04 -0.68
a CMa (Sirius) A 0.00 -0.04
a Eri (Achernar) B -0.16 -0.66
z Pup O -0.27 -1.09
Table 2: B-V values for some well-known stars (after Ochsenbein & Halbwachs 1987 and various other sources). For some further examples, see the ARI Data Base for Nearby Stars.
Of course the Johnson colour indices do not span the entire spectrum; the scheme has been extended in both directions - longwards to include red and infrared wavelengths, and shortwards to include violet and ultraviolet. Another popular index is the set of Strömgren magnitudes: u (ultraviolet), v (violet), b (blue) and y (yellow, which is very close to the Johnson V).

References

Böhm-Vitense, Erika (1989a): Introduction to Stellar Astrophysics. Volume 1 - Basic Stellar Observations and Data. Cambridge.

Kaler, James B. (1997): Stars and Their Spectra. Cambridge. (Corrected paperback ed.) 300 pp.

Ochsenbein F.; Halbwachs J.L. 1987: Le Catalogue des Etoiles les Plus Brillantes (Catalogue of the Brightest Stars). Bull. Inform. CDS 32, 83.  NASA Astronomical Data Centre, catalogue 5053A.
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