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 <sect1 id="ai-colorandtemp">
 
 <sect1info>
 
 <author>
 <firstname>Jasem</firstname>
 <surname>Mutlaq</surname>
 <affiliation><address>
 </address></affiliation>
 </author>
 </sect1info>
 
 <title>Star Colors and Temperatures</title>
 <indexterm><primary>Star Colors and Temperatures</primary>
 <seealso>Blackbody Radiation</seealso>
 <seealso>Magnitude Scale</seealso>
 </indexterm>
 
 <para>
 Stars appear to be exclusively white at first glance.
 But if we look carefully, we can notice a range of colors: blue,
 white, red, and even gold. In the winter constellation of Orion, a
 beautiful contrast is seen between the red Betelgeuse at Orion's
 "armpit" and the blue Bellatrix at the shoulder. What causes stars to
 exhibit different colors remained a mystery until two centuries ago,
 when Physicists gained enough understanding of the nature of light and
 the properties of matter at immensely high temperatures.
 </para>
 
 <para>
 Specifically, it was the physics of
 <link linkend="ai-blackbody">blackbody radiation</link> that enabled
 us to understand the variation of stellar colors.  Shortly after
 blackbody radiation was understood, it was noticed that the spectra of
 stars look extremely similar to blackbody radiation curves of
 various temperatures, ranging from a few thousand Kelvin to ~50,000
 Kelvin.  The obvious conclusion is that stars are similar to
 blackbodies, and that the color variation of stars is a direct
 consequence of their surface temperatures.
 </para>
 
 <para>
 Cool stars (i.e., Spectral Type K and M) radiate most
 of their energy in the red and infrared region of the
 electromagnetic spectrum and thus appear red, while hot stars (i.e.,
 Spectral Type O and B) emit mostly at blue and ultra-violet
 wavelengths, making them appear blue or white.
 </para>
 
 <para>
 To estimate the surface temperature of a star, we can use the known
 relationship between the temperature of a blackbody, and the
 wavelength of light where its spectrum peaks.  That is, as you
 increase the temperature of a blackbody, the peak of its spectrum
 moves to shorter (bluer) wavelengths of light.
 This is illustrated in Figure 1 where the intensity of three
 hypothetical stars is plotted against wavelength.  The "rainbow"
 indicates the range of wavelengths that are visible to the human eye.
 </para>
 
 <para>
 <mediaobject>
 <imageobject>
   <imagedata fileref="star_colors.png" format="PNG"/>
 </imageobject>
 <caption><para><phrase>Figure 1</phrase></para></caption>
 </mediaobject>
 </para>
 
 <para>
 This simple method is conceptually correct, but it cannot be used to
 obtain stellar temperatures accurately, because stars are
 <emphasis>not</emphasis> perfect blackbodies.  The presence of various
 elements in the star's atmosphere will cause certain wavelengths of
 light to be absorbed.  Because these absorption lines are not uniformly
 distributed over the spectrum, they can skew the position of
 the spectral peak.
 Moreover, obtaining a usable spectrum of a star
 is a time-intensive process and is prohibitively inefficient for large
 samples of stars.
 </para>
 
 <para>
 An alternative method utilizes photometry to measure the intensity of
 light
 passing through different filters. Each filter allows
 <emphasis>only</emphasis> a specific part of the spectrum
 of light to pass through while rejecting all others. A widely used
 photometric system is called the <firstterm>Johnson UBV
 system</firstterm>.  It employs three bandpass filters: U
 ("Ultra-violet"), B ("Blue"), and V ("Visible"); each occupying different regions of the
 electromagnetic spectrum.
 </para>
 
 <para>
 The process of UBV photometry involves using light sensitive devices
 (such as film or CCD cameras) and aiming a telescope at a star to
 measure the intensity of light that passes through each of the
 filters individually. This procedure gives three apparent
 brightnesses or <link linkend="ai-flux">fluxes</link> (amount of
 energy per cm<superscript>2</superscript> per second) designated by Fu, Fb, and Fv. The ratio of
 fluxes Fu/Fb and Fb/Fv is a quantitative measure of the star's
 "color", and these ratios can be used to establish a temperature scale
 for stars.  Generally speaking, the larger the Fu/Fb and Fb/Fv ratios
 of a star, the hotter its surface temperature.
 </para>
 
 <para>
 For example, the star Bellatrix in Orion has Fb/Fv = 1.22, indicating
 that it is brighter through the B filter than through the V filter.
 furthermore, its Fu/Fb ratio is 2.22, so it is brightest through the U
 filter.  This indicates that the star must be very hot indeed, since
 the position of its spectral peak must be somewhere in the range of
 the U filter, or at an even shorter wavelength.  The surface
 temperature of Bellatrix (as determined from comparing its spectrum to
 detailed models that account for its absorption lines) is about 25,000
 Kelvin.
 </para>
 
 <para>
 We can repeat this analysis for the star Betelgeuse.  Its Fb/Fv and
 Fu/Fb ratios are 0.15 and 0.18, respectively, so it is brightest
 in V and dimmest in U.  So, the spectral peak of Betelgeuse must be
 somewhere in the range of the V filter, or at an even longer
 wavelength.  The surface temperature of Betelgeuse is only 2,400
 Kelvin.
 </para>
 
 <para>
 Astronomers prefer to express star colors in terms of a difference in
 <link linkend="ai-magnitude">magnitudes</link>, rather than a ratio of
 <link linkend="ai-flux">fluxes</link>.  Therefore, going back to blue
 Bellatrix we have a color index equal to
 </para>
 
 <para>
    B - V = -2.5 log (Fb/Fv) = -2.5 log (1.22) = -0.22,
 </para>
 
 <para>
 Similarly, the color index for red Betelgeuse is
 </para>
 
 <para>
  B - V = -2.5 log (Fb/Fv) = -2.5 log (0.18) =  1.85
 </para>
 
 <para>
 The color indices, like the <link linkend="ai-magnitude">magnitude
 scale</link>, run backward. <emphasis>Hot and blue</emphasis>
 stars have <emphasis>smaller and negative</emphasis> values of B-V
 than the cooler and redder stars.
 </para>
 
 <para>
 An Astronomer can then use the color indices for a star, after
 correcting for reddening and interstellar extinction, to obtain an accurate temperature of that star.
 The relationship between B-V and temperature is illustrated in Figure
 2.
 </para>
 
 <para>
 <mediaobject>
 <imageobject>
   <imagedata fileref="color_indices.png" />
 </imageobject>
 <caption><para><phrase>Figure 2</phrase></para></caption>
 </mediaobject>
 </para>
 
 <para>
 The Sun with surface temperature of 5,800 K has a B-V index of 0.62.
 </para>
 </sect1>