"What is thermal pressure? What are the two energy sources that can help a star maintain its internal thermal pressure?"
Thermal pressure is "the ordinary pressure of a gas arising from motions of particles that can be attributed to the object's temperature" (CP Glossary).
Thermal pressure increases when temperature or thermal energy increases. Stars can maintain internal thermal pressure with help from nuclear fusion and gravitational contraction. Internal thermal pressure can only be maintained if the energy a star radiates into space is replaced.
"What is a molecular cloud? Briefly describe the process by which a protostar and a protostellar disk form from gas in a molecular cloud."
A molecular cloud is a cloud from which stars form. They're called molecular clouds because their hydrogen atoms form hydrogen molecules due to low temperatures.
As a molecular cloud fragment collapses it becomes more dense. Radiation has a difficult time escaping and the central regions grow opaque. Thermal energy produced by gravitational contraction becomes trapped in the center which causes temperature and pressure to rise. At the start of collapse this thermal energy was radiated away, but now that the cloud is more dense there is enough pressure to resist gravity. When this happens the cloud fragment becomes a protostar. It isn't a star yet because the center isn't hot enough for fusion. The fragment spins faster as it collapses, causing it to flatten to become a protostellar disk.
"What happens to the core when it exhausts its hydrogen supply? Why does hydrogen shell burning begin around the inert core?"
When the core exhausts its hydrogen supply nuclear fusion stops, temperature decreases, and the core begins to shrink from gravity as the outer layers expand. When the core shrinks the temperature increases, so the hydrogen fusion begins again, this time in the shell of hydrogen around the helium core.
"As the helium in the core builds up, the core temperature does not necessarily diminish. The very center of the core begins to shrink and heat up as gravity pulls it inward with no helium fusion to counteract it. All this occurs even while hydrogen fusion is continuing in the rest of the core. So as the outer layers are expanding and cooling off, the core is shrinking and heating up. And, as you pointed out, the heat from the contracting core keeps some hydrogen fusion going in the shell of hydrogen around the helium core" -- Professor X
"Why does helium fusion require much higher temperatures than hydrogen fusion? Briefly describe the overall reaction by which helium fuses into carbon."
Helium fusion requires much higher temperatures than hydrogen fusion because the nuclei carry a much greater positive charge. This means higher speeds are necessary in order to overcome the nuclei repelling each other.
The process of converting helium into carbon is sometimes called the "triple-alpha reaction" because it takes three helium nuclei (sometimes called "alpha" particles) to make a carbon nucleus. After hydrogen fusion begins in the shell, new mass is added to the helium core. More gravitational contraction takes place and the core shrinks and becomes hotter and denser. This increases the shell's hydrogen fusion, which means more helium mass is added, which means the core continues to shrink and increase in temperature. Eventually the core becomes hot enough for helium to begin fusing into carbon.
"Explain why a star's overall radius shrinks from its peak size as a red giant after helium fusion begins. Why do helium-burning stars in a star cluster all fall on a horizontal branch on an H-R diagram?"
When helium fusion begins the core doesn't inflate because degeneracy pressure doesn't increase with temperature. The helium fusion rate increases rapidly with the rise of temperature in what is called a "helium flash." After the flash dumps thermal energy in the core, the core expands because now the pressure is thermal and not degenerate.
Core expansion in the red giant phase causes the core's shell to expand, so it becomes cooler and hydrogen fusion decreases. This means less energy, so the star's luminosity decreases, the outer layers contract, and the surface temperature increases. As a result of all this the star shrinks from its red giant size.
Stars in a helium burning phase tend to have the same luminosity because low mass stars fuse carbon at about the same rate. However, the outer layers have different masses and thus surface temperature varies. Therefore they are in the same place vertically on the H-R diagram but differing places horizontally.
"The main difference between helium fusion generating internal pressure and helium contraction generating the pressure is in the nature of the energy released. Contraction generates heat energy which is a collisional energy between molecules of the super-hot core and atoms of the hydrogen surrounding it, so the collisions directly push the hydrogen atoms away from the core causing the rest of the star to expand.
"When helium fusion begins, however, the primary energy release is in the form of gamma rays which pass right through many hydrogen atoms before eventually being absorbed. And when the photons are absorbed, they are often re-radiated as lower energy photons many times before finally turning into heat in absorption in the convection layer.
"So, the bottom line is that heating causes the star to expand, while fusion allows it to re-contract somewhat because the gamma rays do not exert the same kind of pressure as heat. However, this is not exactly degeneracy pressure. Degeneracy pressure is when electrons are so close to other electrons (or neutrons close to other neutrons) that their force of repulsion counteracts any further compression." -Professor X
"What is a planetary nebula? What happens to the core of a star after a planetary nebula occurs."
A planetary nebula is a phase near the end of the life of a low-mass star, the hot core left after the star ejects its outer layers. The gas around the core is ionized by the intense ultraviolet radiation and thus glows brightly. After a planetary nebula occurs, the ejected gas disperses and the exposed core cools to become a white dwarf.
"Briefly describe how the Sun will change, and how Earth will be affected by these changes, over the next several billion years."
The Sun will continue to burn hydrogen until, in about 4 billion years, its hydrogen supply is used up. As it runs out of hydrogen its core will gradually shrink and become hotter and the star will become more luminous. When the hydrogen is gone the core will shrink more rapidly and the outer layers will expand.
First the Sun will become a subgiant and will be three times as large and twice as luminous as it is now. The Earth's oceans will disappear and Earth will probably experience a runaway greenhouse effect and become hotter than Venus. Next the Sun will become a red giant. This will take about several hundred million years. Before the helium flash it will be 100x larger and 1000x more luminous. The oceans will be gone and the Earth's temperature will be over 1000K.
Eventually the shrinking core will lead to hydrogen shell burning, followed by helium fusion. After about 100 million years the core helium will be depleted and the Sun will grow thousands of times more luminous and solar prominences might touch the Earth. The outer layers will be ejected, the Sun will become a white dwarf, and the Earth will either be destroyed or no more than a cold and dark rock.
"Describe some of the nuclear reactions that can occur in high-mass stars after they exhaust their core helium. Why does this continued nuclear burning occur in high-mass stars but not in low-mass stars?"
After high-mass stars exhaust their core helium, other kinds of fusion follow: carbon, oxygen, neon, magnesium, and silicon. Eventually this leads to an iron core. This burning doesn't occur in low-mass stars because they don't reach the necessary temperature for carbon fusion to begin.
"What special feature of iron nuclei determines how massive stars end their lives? What happens during a supernova?"
After the core becomes iron, energy can't be created through fusion because heavier elements have increased mass. Iron's low mass means energy also can't be created through fission. Therefore once a star has an iron core it can only resist gravity with degeneracy pressure. When the gravity gets so great that electrons and protons combine to create neutrons, the core collapses to a very small size (a few kilometers across). The energy created in this collapse drives off the outer layers of the core, which is what is called a supernova.
"Summarize some of the observational evidence supporting our ideas about how the elements formed and showing that supernovae really occur."
Evidence for the formation of elements and existence of supernovae includes a rising presence of heavier elements in new stars compared to old stars, more even-numbered nuclei than odd-numbered, and the confirmed rarity of elements which would only found briefly before and after a supernova.
"Observational evidence now also includes observations of the creation of certain heavy elements during the aftermath of Supernova 1987A." -- Professor X
"What is the Algol paradox? What is its resolution? Use your answer to summarize how the lives of stars in close binaries can differ from the lives of single stars."
The Algol paradox refers to a situation seen with close binary stars, named for the one(s) called Algol. Even though they were born at the same time, the more massive star is still on the main sequence and the less massive one is a subgiant when it should be the other way around. The explanation for this is that because of their closeness they are exerting significant tidal forces and are tidally locked. When the one star expands enough, gravity causes a mass exchange to occur as the other star gains the expanding star's outer layers. The second star's lifetime accelerates through this unusual gain of mass, and when it has gained enough mass it may contribute mass back to the first star. Therefore close binaries don't follow the usual pattern of single stars, since they can gain and lose mass in addition to what's expected in a star's usual life cycle.
"The smaller star actually WAS the larger of the two originally, and that is why it is already near the end of its life. However, as it moved into the giant phase, it dumped most of its mass onto the other star, so that the main sequence star now has grown into the larger of the two." -- Professor X
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