17-4 A star’s color depends on its surface temperature

The image that opens this chapter shows that stars come in different colors. You can see these colors even with the naked eye. For example, you can easily see the reddish color of Betelgeuse (the star in the “armpit” of the constellation Orion) and the blue tint of Bellatrix at Orion’s other “shoulder” (see Figure 2-2). Colors are most evident for the brightest stars, because human color vision works poorly at low light levels.

CAUTION!

It is true that the light from a star will appear redshifted if the star is moving away from you and blueshifted if it is moving toward you. But for even the fastest stars, these color shifts are so tiny that it takes sensitive instruments to measure them. The red color of Betelgeuse and the blue color of Bellatrix are not due to their motions; they are the actual colors of the stars.

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Color and Temperature

We saw in Section 5-3 that a star’s color is directly related to its surface temperature. The intensity of light from a relatively cool star peaks at long wavelengths, making the star look red (Figure 17-7a). A hot star’s intensity curve peaks at shorter wavelengths, so the star looks blue (Figure 17-7c). For a star with an intermediate temperature, such as the Sun, the intensity peak is near the middle of the visible spectrum. The human visual system interprets an object with this spectrum of wavelengths as yellowish in color (Figure 17-7b). This leads to an important general rule about star colors and surface temperatures:

Red stars are relatively cold, with low surface temperatures; blue stars are relatively hot, with high surface temperatures.

Figure 17-7: Temperature and Color These graphs show the intensity of light emitted by three hypothetical stars plotted against wavelength (compare with Figure 5-11). The rainbow band indicates the range of visible wavelengths. The star’s apparent color depends on whether the intensity curve has larger values at the short-wavelength (blue) or long-wavelength (red) end of the visible spectrum. However, the human brain combines all of the colors in a spectrum, so where the intensity peaks is just one factor shaping the color perceived by the eye. The image insets show stars of about these surface temperatures. UV stands for ultraviolet, which extends from 10 to 400 nm. See Figure 5-12 for more on wavelengths of the spectrum.
(inset a: Andrea Dupree [Harvard-Smithsonian CfA], Ronald Gilliland [STScI, NASA, and ESA]; inset b: NSO/AURA/NSF; inset c: NASA, H. E. Bond, and E. Nelan [STScI]; M. Barstow and M. Burleigh [U. of Leicester, U.K.]; and J. B. Holberg [U. of Arizona])

Astronomers use a set of filters in their telescopes to measure the surface temperatures of stars

Figure 17-7 shows that astronomers can accurately determine the surface temperature of a star by carefully measuring its color. To measure color, the star’s light is collected by a telescope and passed through various color filters. For example, a red filter passes red light while blocking other wavelengths. The filtered light is then collected by a light-sensitive device such as a CCD (see Section 6-4). The process is then repeated with each of the filters in the set. The star’s image will have a different brightness through each colored filter, and by comparing these brightnesses, astronomers can find the wavelength at which the star’s intensity curve has its peak—and hence the star’s temperature.

UBV Photometry

Let’s look at this procedure in more detail. The most commonly used filters are called U, B, and V, and the technique that uses them is called UBV photometry. Each filter is transparent to a different band of wavelengths: the ultraviolet (U), the blue (B), and the yellow-green (V, for visual) region in and around the visible spectrum (Figure 17-8). The transparency of the V filter mimics the sensitivity of the human eye.

Figure 17-8: U, B, and V Filters This graph shows the wavelengths to which the standard filters are transparent. The U filter is transparent to near-ultraviolet light. The B filter is transparent to violet, blue, and green light, while the V filter is transparent to green and yellow light. By measuring the apparent brightness of a star with each of these filters and comparing the results, an astronomer can determine the star’s surface temperature.

To determine a star’s temperature using UBV photometry, the astronomer first measures the star’s brightness through each of the filters individually. This gives three apparent brightnesses for the star, designated bU, bB, and bV. The astronomer then compares the intensity of starlight in neighboring wavelength bands by taking the ratios of these brightnesses: bV/bB and bB/bU. Table 17-1 gives values for these color ratios for several stars with different surface temperatures.

Table 17-1: Colors of Selected Stars
Star Surface temperature (K) bV/bB bB/bU Apparent color
Bellatrix (γ Orionis) 21,500 0.81 0.45 Blue
Regulus (α Leonis) 12,000 0.90 0.72 Blue-white
Sirius (α Canis Majoris) 9400 1.00 0.96 Blue-white
Megrez (δ Ursae Majoris) 8630 1.07 1.07 White
Altair (α Aquilae) 7800 1.23 1.08 Yellow-white
Sun 5800 1.87 1.17 Yellow-white
Aldebaran (α Tauri) 4000 4.12 5.76 Orange
Betelgeuse (α Orionis) 3500 5.55 6.66 Red
Source: J.-C Mermilliod, B. Hauck, and M. Mermilliod, University of Lausanne

If a star is very hot, its radiation is skewed toward short, ultraviolet wavelengths as in Figure 17-7c. This makes the star dim through the V filter, brighter through the B filter, and brightest through the U filter. Hence, for a hot star bV is less than bB, which in turn is less than bU, and the ratios bV/bB and bB/bU are both less than 1. One such star is Bellatrix (see Table 17-1), which has a surface temperature of 21,500 K.

In contrast, if a star is cool, its radiation peaks at long wavelengths as in Figure 17-7a. Such a star appears brightest through the V filter, dimmer through the B filter, and dimmest through the U filter (see Figure 17-8). In other words, for a cool star bV is greater than bB, which in turn is greater than bU. Hence, the ratios bV/bB and bB/bU will both be greater than 1. The star Betelgeuse (surface temperature 3500 K) is an example.

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You can see these differences between hot and cool stars in parts a and c of Figure 6-27, which show the constellation Orion at ultraviolet wavelengths (a bit shorter than those transmitted by the U filter) and at visible wavelengths that approximate the transmission of a V filter. The hot star Bellatrix is brighter in the ultraviolet image (Figure 6-27a) than at visible wavelengths (Figure 6-27c). (Figure 6-27d shows the names of the stars.) The situation is reversed for the cool star Betelgeuse: It is bright at visible wavelengths, but at ultraviolet wavelengths it is too dim to show up in the image.

Figure 17-9 graphs the relationship between a star’s bV/bB color ratio and its temperature. If you know the value of the bV/bB color ratio for a given star, you can use this graph to find the star’s surface temperature. As an example, for the Sun bV/bB equals 1.87, which corresponds to a surface temperature of 5800 K.

Figure 17-9: Temperature, Color, and Color Ratio The bV/bB color ratio is the ratio of a star’s apparent brightnesses through a V filter and through a B filter. This ratio is small for hot, blue stars but large for cool, red stars. After measuring a star’s brightness with the B and V filters, an astronomer can estimate the star’s surface temperature from a graph like this one.

CAUTION!

As we will see in Chapter 18, tiny dust particles that pervade interstellar space cause distant stars to appear redder than they really are. (In the same way, particles in Earth’s atmosphere make the setting Sun look redder; see Box 5-4.) Astronomers must take this reddening into account whenever they attempt to determine a star’s surface temperature from its color ratios. A star’s spectrum provides a more precise measure of a star’s surface temperature, as we will see next. But it is quicker and easier to observe a star’s colors with a set of U, B, and V filters than it is to take the star’s spectrum with a spectrograph.

CONCEPT CHECK 17-6

Which is hotter: a star with an orange color or one with a more blue color?