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