1<sect1 id="ai-colorandtemp"> 2 3<sect1info> 4 5<author> 6<firstname>Jasem</firstname> 7<surname>Mutlaq</surname> 8<affiliation><address> 9</address></affiliation> 10</author> 11</sect1info> 12 13<title>Star Colors and Temperatures</title> 14<indexterm><primary>Star Colors and Temperatures</primary> 15<seealso>Blackbody Radiation</seealso> 16<seealso>Magnitude Scale</seealso> 17</indexterm> 18 19<para> 20Stars appear to be exclusively white at first glance. 21But if we look carefully, we can notice a range of colors: blue, 22white, red, and even gold. In the winter constellation of Orion, a 23beautiful contrast is seen between the red Betelgeuse at Orion's 24"armpit" and the blue Bellatrix at the shoulder. What causes stars to 25exhibit different colors remained a mystery until two centuries ago, 26when Physicists gained enough understanding of the nature of light and 27the properties of matter at immensely high temperatures. 28</para> 29 30<para> 31Specifically, it was the physics of 32<link linkend="ai-blackbody">blackbody radiation</link> that enabled 33us to understand the variation of stellar colors. Shortly after 34blackbody radiation was understood, it was noticed that the spectra of 35stars look extremely similar to blackbody radiation curves of 36various temperatures, ranging from a few thousand Kelvin to ~50,000 37Kelvin. The obvious conclusion is that stars are similar to 38blackbodies, and that the color variation of stars is a direct 39consequence of their surface temperatures. 40</para> 41 42<para> 43Cool stars (i.e., Spectral Type K and M) radiate most 44of their energy in the red and infrared region of the 45electromagnetic spectrum and thus appear red, while hot stars (i.e., 46Spectral Type O and B) emit mostly at blue and ultra-violet 47wavelengths, making them appear blue or white. 48</para> 49 50<para> 51To estimate the surface temperature of a star, we can use the known 52relationship between the temperature of a blackbody, and the 53wavelength of light where its spectrum peaks. That is, as you 54increase the temperature of a blackbody, the peak of its spectrum 55moves to shorter (bluer) wavelengths of light. 56This is illustrated in Figure 1 where the intensity of three 57hypothetical stars is plotted against wavelength. The "rainbow" 58indicates the range of wavelengths that are visible to the human eye. 59</para> 60 61<para> 62<mediaobject> 63<imageobject> 64 <imagedata fileref="star_colors.png" format="PNG"/> 65</imageobject> 66<caption><para><phrase>Figure 1</phrase></para></caption> 67</mediaobject> 68</para> 69 70<para> 71This simple method is conceptually correct, but it cannot be used to 72obtain stellar temperatures accurately, because stars are 73<emphasis>not</emphasis> perfect blackbodies. The presence of various 74elements in the star's atmosphere will cause certain wavelengths of 75light to be absorbed. Because these absorption lines are not uniformly 76distributed over the spectrum, they can skew the position of 77the spectral peak. 78Moreover, obtaining a usable spectrum of a star 79is a time-intensive process and is prohibitively inefficient for large 80samples of stars. 81</para> 82 83<para> 84An alternative method utilizes photometry to measure the intensity of 85light 86passing through different filters. Each filter allows 87<emphasis>only</emphasis> a specific part of the spectrum 88of light to pass through while rejecting all others. A widely used 89photometric system is called the <firstterm>Johnson UBV 90system</firstterm>. It employs three bandpass filters: U 91("Ultra-violet"), B ("Blue"), and V ("Visible"); each occupying different regions of the 92electromagnetic spectrum. 93</para> 94 95<para> 96The process of UBV photometry involves using light sensitive devices 97(such as film or CCD cameras) and aiming a telescope at a star to 98measure the intensity of light that passes through each of the 99filters individually. This procedure gives three apparent 100brightnesses or <link linkend="ai-flux">fluxes</link> (amount of 101energy per cm<superscript>2</superscript> per second) designated by Fu, Fb, and Fv. The ratio of 102fluxes Fu/Fb and Fb/Fv is a quantitative measure of the star's 103"color", and these ratios can be used to establish a temperature scale 104for stars. Generally speaking, the larger the Fu/Fb and Fb/Fv ratios 105of a star, the hotter its surface temperature. 106</para> 107 108<para> 109For example, the star Bellatrix in Orion has Fb/Fv = 1.22, indicating 110that it is brighter through the B filter than through the V filter. 111furthermore, its Fu/Fb ratio is 2.22, so it is brightest through the U 112filter. This indicates that the star must be very hot indeed, since 113the position of its spectral peak must be somewhere in the range of 114the U filter, or at an even shorter wavelength. The surface 115temperature of Bellatrix (as determined from comparing its spectrum to 116detailed models that account for its absorption lines) is about 25,000 117Kelvin. 118</para> 119 120<para> 121We can repeat this analysis for the star Betelgeuse. Its Fb/Fv and 122Fu/Fb ratios are 0.15 and 0.18, respectively, so it is brightest 123in V and dimmest in U. So, the spectral peak of Betelgeuse must be 124somewhere in the range of the V filter, or at an even longer 125wavelength. The surface temperature of Betelgeuse is only 2,400 126Kelvin. 127</para> 128 129<para> 130Astronomers prefer to express star colors in terms of a difference in 131<link linkend="ai-magnitude">magnitudes</link>, rather than a ratio of 132<link linkend="ai-flux">fluxes</link>. Therefore, going back to blue 133Bellatrix we have a color index equal to 134</para> 135 136<para> 137 B - V = -2.5 log (Fb/Fv) = -2.5 log (1.22) = -0.22, 138</para> 139 140<para> 141Similarly, the color index for red Betelgeuse is 142</para> 143 144<para> 145 B - V = -2.5 log (Fb/Fv) = -2.5 log (0.18) = 1.85 146</para> 147 148<para> 149The color indices, like the <link linkend="ai-magnitude">magnitude 150scale</link>, run backward. <emphasis>Hot and blue</emphasis> 151stars have <emphasis>smaller and negative</emphasis> values of B-V 152than the cooler and redder stars. 153</para> 154 155<para> 156An Astronomer can then use the color indices for a star, after 157correcting for reddening and interstellar extinction, to obtain an accurate temperature of that star. 158The relationship between B-V and temperature is illustrated in Figure 1592. 160</para> 161 162<para> 163<mediaobject> 164<imageobject> 165 <imagedata fileref="color_indices.png" /> 166</imageobject> 167<caption><para><phrase>Figure 2</phrase></para></caption> 168</mediaobject> 169</para> 170 171<para> 172The Sun with surface temperature of 5,800 K has a B-V index of 0.62. 173</para> 174</sect1> 175