diff options
Diffstat (limited to 'doc/kstars/colorandtemp.docbook')
-rw-r--r-- | doc/kstars/colorandtemp.docbook | 174 |
1 files changed, 174 insertions, 0 deletions
diff --git a/doc/kstars/colorandtemp.docbook b/doc/kstars/colorandtemp.docbook new file mode 100644 index 00000000..d0a762e6 --- /dev/null +++ b/doc/kstars/colorandtemp.docbook @@ -0,0 +1,174 @@ +<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^2 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> |