Color index

Sample calibration colors<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a><table> <tbody><tr><th><a href="/facts/Stellar_classification/dYrIuK9H">Class</a></th><th>B−V</th><th>U−B</th><th>V−R</th><th>R−I</th><th><a href="/facts/Effective_temperature/RY30DaSY"><i>T</i>eff</a> (<a href="/facts/Kelvin/E3trzC4C">K</a>)</th></tr><tr><td>O5V</td><td>−0.33</td><td>−1.19</td><td>−0.15</td><td>−0.32</td><td>42,000</td></tr><tr><td>B0V</td><td>−0.30</td><td>−1.08</td><td>−0.13</td><td>−0.29</td><td>30,000</td></tr><tr><td>A0V</td><td>−0.02</td><td>−0.02</td><td>0.02</td><td>−0.02</td><td>9,790</td></tr><tr><td>F0V</td><td>0.30</td><td>0.03</td><td>0.30</td><td>0.17</td><td>7,300</td></tr><tr><td>G0V</td><td>0.58</td><td>0.06</td><td>0.50</td><td>0.31</td><td>5,940</td></tr><tr><td>K0V</td><td>0.81</td><td>0.45</td><td>0.64</td><td>0.42</td><td>5,150</td></tr><tr><td>M0V</td><td>1.40</td><td>1.22</td><td>1.28</td><td>0.91</td><td>3,840</td></tr></tbody></table>
<p>In <a href="/facts/Astronomy/0ArJVM1p">astronomy</a>, the color index is a simple <a href="/facts/Numerical_analysis/QT9cYa9z">numerical</a> <a href="/facts/Expression_(mathematics)/MPrMlYbE">expression</a> that determines the <a href="/facts/Color/XDvW7ESP">color</a> of an object, which in the case of a <a href="/facts/Star/PFbd6ICx">star</a> gives its <a href="/facts/Temperature/QyGe4gmj">temperature</a>. The lower the color index, the more <a href="/facts/Blue/DHWb8MUa">blue</a> (or hotter) the object is. Conversely, the larger the color index, the more <a href="/facts/Red/gLnFAVx4">red</a> (or cooler) the object is. This is a consequence of the <a href="/facts/Logarithmic_scale/CvIGK5TQ">logarithmic magnitude scale</a>, in which brighter objects have smaller (more negative) magnitudes than dimmer ones. For comparison, the whitish <a href="/facts/Sun/CadPCVHh">Sun</a> has a B−V index of 0.656 ± 0.005, whereas the bluish <a href="/facts/Rigel/WeeIXAAv">Rigel</a> has a B−V of −0.03 (its B magnitude is 0.09 and its V magnitude is 0.12, B−V = −0.03). Traditionally, the color index uses <a href="/facts/Vega/G3wJwhhl">Vega</a> as a <a href="/facts/Zero_Point_(photometry)/u0Eto333">zero point</a>. The <a href="/facts/Blue_supergiant/8Bnl7Xpz">blue supergiant</a> <a href="/facts/Theta_Muscae/fg8bsIgF">Theta Muscae</a> has one of the lowest B−V indices at −0.41, while the <a href="/facts/Red_giant/lla6Bsvy">red giant</a> and <a href="/facts/Carbon_star/zK6vSgYn">carbon star</a> <a href="/facts/R_Leporis/NxsQa0KK">R Leporis</a> has one of the largest, at +5.74.
</p><p>To measure the index, one observes the <a href="/facts/Magnitude_(astronomy)/f4FbscJu">magnitude</a> of an object successively through two different <a href="/facts/Astronomical_filter/eWWMxCvt">filters</a>, such as U and B, or B and V, where U is sensitive to <a href="/facts/Ultraviolet/kncBUqn5">ultraviolet</a> rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also: <a href="/facts/UBV_system/eoJL34eN">UBV system</a>). The set of passbands or filters is called a <a href="/facts/Photometric_system/7tUmLBGR">photometric system</a>. The difference in magnitudes found with these filters is called the U−B or B−V color index respectively.
</p><p>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. A good approximation can be obtained by considering stars as <a href="/facts/Black_body/f0fHghDy">black bodies</a>, using Ballesteros' formula (also implemented in the PyAstronomy package for Python):
</p>

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).}

<p>Color indices of distant objects are usually affected by <a href="/facts/Extinction_(astronomy)/rLNLDfe1">interstellar extinction</a>, that is, they are <a href="/facts/Interstellar_reddening/rLNLDfe1">redder</a> than those of closer stars. The amount of reddening is characterized by <a href="/facts/Interstellar_reddening/rLNLDfe1">color excess</a>, 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:
</p>

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}}.}

<p>The <a href="/facts/Passband/VebMrazm">passbands</a> most optical <a href="/facts/Astronomer/ronF8j4a">astronomers</a> use are the <a href="/facts/UBVRI/eoJL34eN">UBVRI</a> filters, where the U, B, and V filters are as mentioned above, the R filter passes red light, and the I filter passes <a href="/facts/Infrared/44XdJNcc">infrared</a> light. This <a href="/facts/Photometric_system/7tUmLBGR">system of filters</a> is sometimes called the Johnson–Kron–Cousins filter system, named after the originators of the system (see references). These filters were specified as particular combinations of glass filters and <a href="/facts/Photomultiplier/lVDdAH5d">photomultiplier tubes</a>. M. S. Bessell specified a set of filter transmissions for a flat response detector, thus quantifying the calculation of the color indices. 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.
</p><p>Color indices can also be determined for other celestial bodies, such as planets and moons:
</p>
Color indices of Solar System bodies<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a><table><tbody><tr><th>Celestial body</th><th>B-V color index</th><th>U-B color index</th></tr><tr><td>Mercury</td><td>0.97</td><td>0.40</td></tr><tr><td>Venus</td><td>0.81</td><td>0.50</td></tr><tr><td>Earth</td><td>0.20</td><td>0.0</td></tr><tr><td>Moon</td><td>0.92</td><td>0.46</td></tr><tr><td>Mars</td><td>1.43</td><td>0.63</td></tr><tr><td>Jupiter</td><td>0.87</td><td>0.48</td></tr><tr><td>Saturn</td><td>1.09</td><td>0.58</td></tr><tr><td>Uranus</td><td>0.56</td><td>0.28</td></tr><tr><td>Neptune</td><td>0.41</td><td>0.21</td></tr></tbody></table>

Color index open-in-new

Color index