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0001 <sect1 id="ai-colorandtemp"> 0002 0003 <sect1info> 0004 0005 <author> 0006 <firstname>Jasem</firstname> 0007 <surname>Mutlaq</surname> 0008 <affiliation><address> 0009 </address></affiliation> 0010 </author> 0011 </sect1info> 0012 0013 <title>Star Colors and Temperatures</title> 0014 <indexterm><primary>Star Colors and Temperatures</primary> 0015 <seealso>Blackbody Radiation</seealso> 0016 <seealso>Magnitude Scale</seealso> 0017 </indexterm> 0018 0019 <para> 0020 Stars appear to be exclusively white at first glance. 0021 But if we look carefully, we can notice a range of colors: blue, 0022 white, red, and even gold. In the winter constellation of Orion, a 0023 beautiful contrast is seen between the red Betelgeuse at Orion's 0024 "armpit" and the blue Bellatrix at the shoulder. What causes stars to 0025 exhibit different colors remained a mystery until two centuries ago, 0026 when Physicists gained enough understanding of the nature of light and 0027 the properties of matter at immensely high temperatures. 0028 </para> 0029 0030 <para> 0031 Specifically, it was the physics of 0032 <link linkend="ai-blackbody">blackbody radiation</link> that enabled 0033 us to understand the variation of stellar colors. Shortly after 0034 blackbody radiation was understood, it was noticed that the spectra of 0035 stars look extremely similar to blackbody radiation curves of 0036 various temperatures, ranging from a few thousand Kelvin to ~50,000 0037 Kelvin. The obvious conclusion is that stars are similar to 0038 blackbodies, and that the color variation of stars is a direct 0039 consequence of their surface temperatures. 0040 </para> 0041 0042 <para> 0043 Cool stars (i.e., Spectral Type K and M) radiate most 0044 of their energy in the red and infrared region of the 0045 electromagnetic spectrum and thus appear red, while hot stars (i.e., 0046 Spectral Type O and B) emit mostly at blue and ultra-violet 0047 wavelengths, making them appear blue or white. 0048 </para> 0049 0050 <para> 0051 To estimate the surface temperature of a star, we can use the known 0052 relationship between the temperature of a blackbody, and the 0053 wavelength of light where its spectrum peaks. That is, as you 0054 increase the temperature of a blackbody, the peak of its spectrum 0055 moves to shorter (bluer) wavelengths of light. 0056 This is illustrated in Figure 1 where the intensity of three 0057 hypothetical stars is plotted against wavelength. The "rainbow" 0058 indicates the range of wavelengths that are visible to the human eye. 0059 </para> 0060 0061 <para> 0062 <mediaobject> 0063 <imageobject> 0064 <imagedata fileref="star_colors.png" format="PNG"/> 0065 </imageobject> 0066 <caption><para><phrase>Figure 1</phrase></para></caption> 0067 </mediaobject> 0068 </para> 0069 0070 <para> 0071 This simple method is conceptually correct, but it cannot be used to 0072 obtain stellar temperatures accurately, because stars are 0073 <emphasis>not</emphasis> perfect blackbodies. The presence of various 0074 elements in the star's atmosphere will cause certain wavelengths of 0075 light to be absorbed. Because these absorption lines are not uniformly 0076 distributed over the spectrum, they can skew the position of 0077 the spectral peak. 0078 Moreover, obtaining a usable spectrum of a star 0079 is a time-intensive process and is prohibitively inefficient for large 0080 samples of stars. 0081 </para> 0082 0083 <para> 0084 An alternative method utilizes photometry to measure the intensity of 0085 light 0086 passing through different filters. Each filter allows 0087 <emphasis>only</emphasis> a specific part of the spectrum 0088 of light to pass through while rejecting all others. A widely used 0089 photometric system is called the <firstterm>Johnson UBV 0090 system</firstterm>. It employs three bandpass filters: U 0091 ("Ultra-violet"), B ("Blue"), and V ("Visible"); each occupying different regions of the 0092 electromagnetic spectrum. 0093 </para> 0094 0095 <para> 0096 The process of UBV photometry involves using light sensitive devices 0097 (such as film or CCD cameras) and aiming a telescope at a star to 0098 measure the intensity of light that passes through each of the 0099 filters individually. This procedure gives three apparent 0100 brightnesses or <link linkend="ai-flux">fluxes</link> (amount of 0101 energy per cm<superscript>2</superscript> per second) designated by Fu, Fb, and Fv. The ratio of 0102 fluxes Fu/Fb and Fb/Fv is a quantitative measure of the star's 0103 "color", and these ratios can be used to establish a temperature scale 0104 for stars. Generally speaking, the larger the Fu/Fb and Fb/Fv ratios 0105 of a star, the hotter its surface temperature. 0106 </para> 0107 0108 <para> 0109 For example, the star Bellatrix in Orion has Fb/Fv = 1.22, indicating 0110 that it is brighter through the B filter than through the V filter. 0111 furthermore, its Fu/Fb ratio is 2.22, so it is brightest through the U 0112 filter. This indicates that the star must be very hot indeed, since 0113 the position of its spectral peak must be somewhere in the range of 0114 the U filter, or at an even shorter wavelength. The surface 0115 temperature of Bellatrix (as determined from comparing its spectrum to 0116 detailed models that account for its absorption lines) is about 25,000 0117 Kelvin. 0118 </para> 0119 0120 <para> 0121 We can repeat this analysis for the star Betelgeuse. Its Fb/Fv and 0122 Fu/Fb ratios are 0.15 and 0.18, respectively, so it is brightest 0123 in V and dimmest in U. So, the spectral peak of Betelgeuse must be 0124 somewhere in the range of the V filter, or at an even longer 0125 wavelength. The surface temperature of Betelgeuse is only 2,400 0126 Kelvin. 0127 </para> 0128 0129 <para> 0130 Astronomers prefer to express star colors in terms of a difference in 0131 <link linkend="ai-magnitude">magnitudes</link>, rather than a ratio of 0132 <link linkend="ai-flux">fluxes</link>. Therefore, going back to blue 0133 Bellatrix we have a color index equal to 0134 </para> 0135 0136 <para> 0137 B - V = -2.5 log (Fb/Fv) = -2.5 log (1.22) = -0.22, 0138 </para> 0139 0140 <para> 0141 Similarly, the color index for red Betelgeuse is 0142 </para> 0143 0144 <para> 0145 B - V = -2.5 log (Fb/Fv) = -2.5 log (0.18) = 1.85 0146 </para> 0147 0148 <para> 0149 The color indices, like the <link linkend="ai-magnitude">magnitude 0150 scale</link>, run backward. <emphasis>Hot and blue</emphasis> 0151 stars have <emphasis>smaller and negative</emphasis> values of B-V 0152 than the cooler and redder stars. 0153 </para> 0154 0155 <para> 0156 An Astronomer can then use the color indices for a star, after 0157 correcting for reddening and interstellar extinction, to obtain an accurate temperature of that star. 0158 The relationship between B-V and temperature is illustrated in Figure 0159 2. 0160 </para> 0161 0162 <para> 0163 <mediaobject> 0164 <imageobject> 0165 <imagedata fileref="color_indices.png" /> 0166 </imageobject> 0167 <caption><para><phrase>Figure 2</phrase></para></caption> 0168 </mediaobject> 0169 </para> 0170 0171 <para> 0172 The Sun with surface temperature of 5,800 K has a B-V index of 0.62. 0173 </para> 0174 </sect1>