1. Due to the mass-luminosity relationship, main sequence stars with higher masses have higher luminosities. This means they use up their core hydrogen at a faster rate than main sequence stars with lower masses. So, even though high-mass stars have more core hydrogen to start with than low-mass stars, they nevertheless live shorter lives on the main sequence.

3. Five billion years from now, the Sun will exhaust the hydrogen in its core, having fused it all into helium. The nuclear reactions in the core will shut down, causing the core's pressure to become too weak to support its own weight. The core will contract, and heat up. Soon, the extra heat from the collapsing core will cause a shell of hydrogen around the core to get hot enough to fuse. The energy released by this shell will make the Sun's envelope expand, even as its core continues to contract. The envelope will expand by a factor of 10-100, so the Sun's luminosity will become very large even though its surface temperature will become much lower. When the Sun is in this phase, it will be a red giant.

7. A star spends most of its life (roughly 90%) in the main sequence phase. Thus, when we look at thousands of stars in the sky, most of them (roughly 90%) will be in that phase of their lives at that moment.

8. When a star's luminosity, surface temperature, and radius change, the dot that represents that star on an H-R diagram will move to a different position on that diagram. (This "motion," of course, has absolutely nothing to do with how the star moves through space.)

10. On a cluster's H-R diagram, the turnoff point indicates which stars are just now leaving the main sequence, due to having just exhausted all of their core hydrogen. Since less massive stars take longer to run out of fuel than more massive stars, the turnoff point will move down the main sequence as the cluster ages: first its most massive stars will turn off the main sequence, then successively less and less massive stars will turn off.

12. a) Look at Table 21-1. Vega is an A0 star, so according to the table, its main sequence lifetime is roughly 500 million years. So, how old is Vega right now? No idea -- but we do know that it must be younger than 500 million years old. Astronomers think that the Sun is currently 4.6 billion years old, so clearly Vega is younger than the Sun. You can make a similar argument for the other stars mentioned. (Note that you CANNOT determine exactly how old any of these stars are from this argument -- you can only put an upper limit on how old they can be.)

b) Since Alpha Centauri A is a G2 star, it (like the Sun) has a main sequence lifetime of 10 billion years. So we know that Alpha Centauri A must presently be younger than that. Unfortunately, however, we cannot say what its age actually is, so there's no way to know (from this line of reasoning) whether it's younger, older, or the same age as the Sun.

16. a) According to Figure 21-9, the horizontal branch stars have surface temperatures of around 7,500-15,000 K. These hot stars will look somewhat bluish, thus explaining why they look blue in Figure 21-8.

b) Red giants look reddish because of their cool surface temperatures. But when helium fusion begins in the red giant's core, its envelope starts to contract, which heats it up. As the shrinking star makes the transition between the red giant phase and the horizontal branch phase, its surface temperature will increase, changing its overall color from reddish to bluish.

34. You might think that you would look at the star's spectrum to determine its chemical composition: if it's burning hydrogen, you see hydrogen lines in the spectrum; if it's burning helium, you see helium lines. However, this is NOT correct. A star's spectrum only tells you about the star's outermost layers (where the absorption lines are made). Whether a star's core is burning hydrogen or helium, its outermost layers will be completely unaffected. Both kinds of stars will have spectra that show that roughly 75% of their outer layers are hydrogen, and most of the rest is helium.

To tell if a star is fusing hydrogen or helium in its core, you must measure the star's luminosity and surface temperature (using the tools that we learned in Chapter 19), and plot it on the H-R diagram. If the star's dot falls on the main sequence, then it is burning hydrogen in its core, as all main sequence stars do. If the star's dot falls on the horizontal branch, then it must be fusing helium in its core.

Last edited 04 Apr 04 M. A. Weinstein.