22.5 The evolution of more massive stars  (Page 3/28)

Is the Sun on the zero-age main sequence? Explain your answer.

How are planetary nebulae comparable to a fluorescent light bulb in your classroom?

Which of the planets in our solar system have orbits that are smaller than the photospheric radius of Betelgeuse listed in in [link] ?

Would you expect to find an earthlike planet (with a solid surface) around a very low-mass star that formed right at the beginning of a globular cluster’s life? Explain.

In the H–R diagrams for some young clusters, stars of both very low and very high luminosity are off to the right of the main sequence, whereas those of intermediate luminosity are on the main sequence. Can you offer an explanation for that? Sketch an H–R diagram for such a cluster.

If the Sun were a member of the cluster NGC 2264, would it be on the main sequence yet? Why or why not?

If all the stars in a cluster have nearly the same age, why are clusters useful in studying evolutionary effects (different stages in the lives of stars)?

Suppose a star cluster were at such a large distance that it appeared as an unresolved spot of light through the telescope. What would you expect the overall color of the spot to be if it were the image of the cluster immediately after it was formed? How would the color differ after 10 ¹⁰ years? Why?

Suppose an astronomer known for joking around told you she had found a type-O main-sequence star in our Milky Way Galaxy that contained no elements heavier than helium. Would you believe her? Why?

Stars that have masses approximately 0.8 times the mass of the Sun take about 18 billion years to turn into red giants. How does this compare to the current age of the universe? Would you expect to find a globular cluster with a main-sequence turnoff for stars of 0.8 solar mass or less? Why or why not?

Automobiles are often used as an analogy to help people better understand how more massive stars have much shorter main-sequence lifetimes compared to less massive stars. Can you explain such an analogy using automobiles?

The text says a star does not change its mass very much during the course of its main-sequence lifetime. While it is on the main sequence, a star converts about 10% of the hydrogen initially present into helium (remember it’s only the core of the star that is hot enough for fusion). Look in earlier chapters to find out what percentage of the hydrogen mass involved in fusion is lost because it is converted to energy. By how much does the mass of the whole star change as a result of fusion? Were we correct to say that the mass of a star does not change significantly while it is on the main sequence?

The text explains that massive stars have shorter lifetimes than low-mass stars. Even though massive stars have more fuel to burn, they use it up faster than low-mass stars. You can check and see whether this statement is true. The lifetime of a star is directly proportional to the amount of mass (fuel) it contains and inversely proportional to the rate at which it uses up that fuel (i.e., to its luminosity). Since the lifetime of the Sun is about 10 ¹⁰ y, we have the following relationship:
$T={10}^{10}\frac{M}{L}\text{y}$
where T is the lifetime of a main-sequence star, M is its mass measured in terms of the mass of the Sun, and L is its luminosity measured in terms of the Sun’s luminosity.

1. Explain in words why this equation works.
2. Use the data in [link] to calculate the ages of the main-sequence stars listed.
3. Do low-mass stars have longer main-sequence lifetimes?
4. Do you get the same answers as those in [link] ?

You can use the equation in [link] to estimate the approximate ages of the clusters in [link] , [link] , and [link] . Use the information in the figures to determine the luminosity of the most massive star still on the main sequence. Now use the data in [link] to estimate the mass of this star. Then calculate the age of the cluster. This method is similar to the procedure used by astronomers to obtain the ages of clusters, except that they use actual data and model calculations rather than simply making estimates from a drawing. How do your ages compare with the ages in the text?

You can estimate the age of the planetary nebula in image (c) in [link] . The diameter of the nebula is 600 times the diameter of our own solar system, or about 0.8 light-year. The gas is expanding away from the star at a rate of about 25 mi/s. Considering that distance = velocity $\times$ time, calculate how long ago the gas left the star if its speed has been constant the whole time. Make sure you use consistent units for time, speed, and distance.

If star A has a core temperature T , and star B has a core temperature 3 T , how does the rate of fusion of star A compare to the rate of fusion of star B?