Physics 110: Homework #5 Solutions

5.1

During the entire course of evolution on the main sequence the Sun will increase in size by 40% and in luminosity by 100%. Over the next 5 billion years the Sun is expected to increase in luminosity by some 60%. This will cause the average temperature of the Earth's surface to increase to 125 F, making it harder for life as we know it now to survive. These changes will occur gradually, so natural selection will give life an opportunity to adjust and evolve.

5.2

The minimum mass of a star is believed to be 0.08 . Protostars that are less massive than this do not become hot enough in their cores to begin fusing hydrogen. This is because during their collapse their central densities become high enough that electrons become degenerate before temperatures sufficient for fusion are reached. Once the electrons are degenerate, then further increases in pressure do not increase the temperature. The most massive stars are believed to be less than 130 . Mass loss from either winds or stellar pulsations would reduce the mass of a larger star to less than the limit of approximately 130 .

5.3

Clusters are associations of stars all with the same age and composition. However, cluster stars do have different masses and therefore different main sequence lifetimes. Since the cluster mentioned in the question contains O-type stars, it must be younger than the main sequence lifetime of an O star, which is less than yrs. Astronomically speaking, this would be considered a young cluster. Yes, this cluster could contain M stars but not main sequence M stars, because it takes M stars longer than yrs to reach the main sequence.

5.4

Cepheid variables are massive, horizontal branch stars that exhibit luminosity variations. These variations are due to pulsations in the outer layers of the stars in which gravity and pressure are analogous to gravity and tension for an oscillating weight hanging from a spring. Cepheid stars are important because there is a correlation between their pulsation period and luminosity which allows astronomers to determine the intrinsic luminosity of the star (which gives the true distance to the star) from relatively simple measurements of the pulsation period. Cepheid stars have been critical in mapping out distances in astronomy.

5.5

Fusion of elements more massive than the iron-group (Fe, Co, and Ni) requires the input of energy, instead of resulting in the release of energy. Hence elements heavier than the iron-group cannot be fuel for stars and so are not created in the same way that the lighter elements are. There are two processes that can produce the elements heavier than iron, both of which rely on the capture of neutrons by the heavy nucleus The s-process (slow process) builds-up nuclei as massive as bismuth during the red-giant phase of evolution. Very heavy or neutron-rich nuclei are built-up during supernova explosions through the r-process (rapid process) when the density of neutrons in the core is large enough.

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