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Chapter 17: Problem 53

Astronomers usually express a star's color using apparent magnitudes. The star's apparent magnitude as viewed through a B filter is called \(m_{\mathrm{B}}\), and its apparent magnitude as viewed through a V filter is \(m_{\mathrm{V}}\). The difference \(m_{\mathrm{B}}-m_{\mathrm{V}}\) is called the \(B-V\) color index ("B minus \(V\) "). Is the \(B-V\) color index positive or negative for very hot stars? What about very cool stars? Explain your answers.

Short Answer

Expert verified
The B-V color index for very hot stars is generally negative as they appear brighter in blue light and hence have a lower \(m_{\mathrm{B}}\). Conversely, the B-V color index for very cool stars is generally positive because they appear less bright in blue light, resulting in a higher \(m_{\mathrm{B}}\).

Step by step solution

01

Understand B-V color index and its relationship with temperature

The B-V color index is calculated as the difference between the star's apparent magnitude as viewed through a B filter (\(m_{\mathrm{B}}\)) and its apparent magnitude as viewed through a V filter (\(m_{\mathrm{V}}\)). The B filter corresponds to blue light and the V filter corresponds to green-yellow light. The index gives an idea about the star's color and consequently its temperature: a negative B-V color index indicates that the star is blue, corresponding to higher temperature, while a positive value suggests that the star is red, corresponding to a lower temperature.
02

Determine the B-V color index for very hot stars and explain

For very hot stars, they emit more light in the blue part of the spectrum. This means that the star will appear brighter in a blue filter, resulting in a lower \(m_{\mathrm{B}}\). As the B-V color index is calculated as \(m_{\mathrm{B}}-m_{\mathrm{V}}\), a lower \(m_{\mathrm{B}}\) results in a smaller B-V color index. As such, the B-V color index for very hot stars is generally negative.
03

Determine the B-V color index for very cool stars and explain

On the other hand, very cool stars emit more light in the red part of the spectrum. This would result in a higher \(m_{\mathrm{B}}\) because stars appear less bright in a blue filter. Hence, calculating the B-V color index as \(m_{\mathrm{B}}-m_{\mathrm{V}}\), a higher \(m_{\mathrm{B}}\) results in a larger B-V color index. This means the B-V color index of very cool stars is generally positive.

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Most popular questions from this chapter

Briefly describe how you would determine the luminosity of a nearby star. Of what value is knowing the luminosity of various stars?

Give two reasons why a visual binary star is unlikely to also be a spectroscopic binary star.

Kapteyn's star (named after the Dutch astronomer who found it) has a parallax of \(0.255\) arcsec, a proper motion of \(8.67\) arcsec per year, and a radial velocity of \(+246 \mathrm{~km} / \mathrm{s}\). (a) What is the star's tangential velocity? (b) What is the star's actual speed relative to the Sun? (c) Is Kapteyn's star moving toward the Sun or away from the Sun? Explain.

It is desirable to be able to measure the radial velocity of stars (using the Doppler effect) to an accuracy of \(1 \mathrm{~km} / \mathrm{s}\) or better. One complication is that radial velocities refer to the motion of the star relative to the Sun, while the observations are made using a telescope on the Earth. Is it important to take into account the motion of the Earth around the Sun? Is it important to take into account the Earth's rotational motion? To answer this question, you will have to calculate the Earth's orbital speed and the speed of a point on the Earth's equator (the part of the Earth's surface that moves at the greatest speed because of the planet's rotation). If one or both of these effects are of importance, how do you suppose astronomers compensate for them?

Use the Starry Night Enthusiast'M program to examine the nearby stars. Click on Favourites \(>\) Stars > Local Neighborhood and Stop time. Select View \(>\) Feet to hide the spacesuit image. Center this view upon the Sun by opening the Find pane and doubleclicking on Sun. You are now \(16.41\) light years from the Sun, looking at the labeled nearby stars. Increase current elevation to about 70,000 light-years using the button on the toolbar below the Viewing Location box (an upward-pointing triangle) to see these nearby stars within the Milky Way Galaxy. You can rotate the galaxy by placing the mouse cursor over the image and holding down the Shift key while holding down the mouse button and moving the mouse. (On a twobutton mouse, hold down the left mouse button). Decrease current elevation to a distance of about 100 light-years from the Sun to return to the solar neighborhood. Again, you can rotate this swarm of stars by holding down the Shift key while holding down the mouse button and moving the mouse. Open the Info pane. If you click the mouse while the cursor is over a star, you will see the star's apparent magnitude as seen from Earth in the Other Data layer and its distance from the Sun in the Position in Space layer of the Info pane. (a) Select at least 5 stars within 50 light-years of the Sun and note their names, apparent magnitudes, luminosities, and distances from the Sun in a list. Which of these stars would be visible from Earth with the naked eye from a dark location? Which are visible with the naked eye from a brightly lit city? (Hint: The naked eye can see stars as faint as apparent magnitude \(m=+6\) from a dark location, but only as faint as \(m=+4\) from an inner city.) (b) Increase current elevation once more to about 1000 light- years from Earth and locate at least 5 stars that are further than 500 light- years from the Sun, making a list of these stars, their names, apparent magnitudes, luminosities and distances from the Sun. Which of these stars are visible from Earth with the naked eye from a dark location? Are the naked-eye stars more likely to be giants or supergiants, or are they more likely to be main-sequence stars? Explain your answer.
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