Answers

ConceptChecks

ConceptCheck 19-1: To leave the main sequence, a red dwarf has to finish converting all of its hydrogen to helium. This takes hundreds of billions of years for a red dwarf—longer than the age of the universe.

ConceptCheck 19-2: When main-sequence hydrogen burning stops, core pressure decreases, and the core contracts. As the core contracts, gravitational energy is converted into heat, and the core’s temperature increases well beyond the temperature it had during its main-sequence burning.

ConceptCheck 19-3: The higher temperatures in a red giant’s core lead to an increased rate of shell hydrogen fusion. The additional energy released by this fusion produces a greater pressure outside the core than before, which greatly expands the star.

ConceptCheck 19-4: In a red giant, the core is at a significantly higher temperature and density that allows helium atoms to combine and fuse together, releasing energy.

ConceptCheck 19-5: Compared to when it was on the main sequence, a red giant is hotter in the core and cooler on the surface.

ConceptCheck 19-6: If fusion in a main-sequence star increases its energy output, the higher temperatures increase the internal pressure. This in turn expands the core’s gas, lowers its temperature, and reduces the rate of nuclear reactions. The “safety valve” aspect is that increased nuclear reactions end up reducing further reactions so that the rate of reactions remains stable. When a red giant’s core is supported by degenerate-electron pressure, an increase in temperature from an increase in nuclear reactions does not increase the pressure to expand the core, and does not reduce further reaction rates.

ConceptCheck 19-7: At high enough temperatures the core is no longer supported by degenerate-electron pressure and the core begins to expand. By expanding, the core cools somewhat, nuclear reaction rates slow down, and luminosity of the star decreases. This is shown on the right of Figure 19-8.

ConceptCheck 19-8: Yes. After 30 million years you can see in Figure 19-10e a few red giants just as low-mass stars are finally approaching the main sequence.

ConceptCheck 19-9: In Figure 19-10c, showing the cluster after 100,000 years, the most massive stars are just joining the main sequence.

ConceptCheck 19-10: The turnoff point in Figure 19-13 corresponds to 0.8-M_⊙ stars that stay on the main sequence for about 12 billion years. If the turnoff point were instead at around 10,000 K, these stars would be more massive and spend less time on the main sequence, and the cluster would be younger.

ConceptCheck 19-11: Recall that lower-mass stars are less luminous. Therefore, the lower the luminosity of the turnoff point, the lower the mass of the main-sequence star at the turnoff point. Lower-mass stars remain on the main sequence longer, indicating an older cluster when these stars finally leave the main sequence.

ConceptCheck 19-12: Population I stars are enriched with heavier atomic elements (they are metal rich). The heavier elements can only be made by an earlier generation of stars through supernova explosions. The earlier generation lacks the heavier elements (they are metal poor) and are called Population II stars.

ConceptCheck 19-13: You can see that the Cepheid in Figure 19-18a peaks in luminosity on day 1. This is about when the temperature peaks as well in Figure 19-18c. However, when the star reaches its maximum size in Figure 19-18d, the luminosity is already declining. Therefore, surface temperature contributes more to the peak luminosity.

ConceptCheck 19-14: Figure 19-20 indicates that a variable star with a 30-day period has an intrinsic luminosity (L) about 10,000 times brighter than our Sun. Direct observations of the star also tell you its apparent brightness (b). Section 17-2 describes how these two quantities are directly related to the distance (d) of the star, so the distance is easily determined.

ConceptCheck 19-15: If a star expands enough that some of its mass enters the Roche lobe of its binary companion, the matter becomes gravitationally bound to the binary companion. Over time, this can transfer a significant amount of mass to the companion.