ASTR 321
Test 1

1. Sketch a Hertzsprung-Russell (H-R) diagram. Label the axes and indicate the locations of the Super-giants, normal giants, Main Sequence stars, and white dwarfs. Sketch the evolutionary track followed by the Sun and a 5 Solar mass star. Indicate the stages of evolution, the energy sources for each phase, the dominant energy transport mechanism, and whether the core is degenerate or nondegenerate.

2. State the Russell-Vogt Theorem. Describe some counter-examples to the Russell-Vogt Theorem.

3. The orbit of the Earth is increasing slowly in size by 15 cm per year. If the increase in orbital size arises from a change in the mass of the Sun, find the rate at which the Solar mass must be changing. Compare this rate to the rate of mass loss produced by nuclear fusion. Compare this rate to the rate of mass loss carried off by the Solar Wind.

4. Thermal Pulses occur at which phase of the Sun's evolution? Why does the nuclear generation output of the Sun "pulse"? How does the pulsing combined with the properties of the envelope of the Sun combine to produce a planetary nebula?

5. Using dimensional arguments, find the density above which the electrons in a pure hydrogen plasma at temperature T become degnerate. The Helium Flash occurs when the mass density is 100,000 gm per cubic centimeter and the temperature is aroudn 200,000,000 K. At what temperature is degeeneracy lifted in the core of the Sun during the flash? Compare the energy generation rate at the end of the flash to the beginning of the flash.

6. Solve the stellar structure equations to find the pressure structure for a star whose density distribution falls off as the inverse of the radius, that is, as 1/r. If the pressure in the star is given by the perfect gas law, find the temperature structure of the star. Find the radius within which 50 % of the star's luminosity is generated for the proton-proton chain.

7. In a Type Ia SN, carbon ignites when the density is around 1,000,000,000 gm per cubic centimeter. For a 1.2 Solar mass white dwarf, this corresponds to what radius? Show that the burning of carbon will disrupt the white dwarf. Suppose the white dwarf is composed of equal parts Mg and Ne. These elements ignite at a density of 3,000,000,000 gm per cubic centimeter. Will a Ne-Mg produce a Type Ia SN? Both reactions yield about 0.001 Mc² where M is the amount of mass processed.

8. Use dimensional arguments to show how the radius of a white dwarf scales with its mass. Consider both nonrelativistic and relativistic white dwarfs. Argue why there is an upper mass limit for white dwarf stars. What is the name of this limit? Using dimensional arguments find and evaluate this limit.

9. Describe in words, the different stages of white dwarf cooling. Using dimensional arguments find an expression for the white dwarf cooling time. Roughly how long does it take a white dwarf to cool to 0.0001 of its initial luminosity, according to your expression.

10. At the current time, the Sun generates energy through the proton-proton chain. The proton-proton chain is around 0.7 % efficient. What does this mean? If nuclear reactions in the core of the Sun were to shut-down today, estimate the time it would take for us to observe the event.

19. Define the term nuclesosynthesis. Compare and contract the r-process and the s-process. The s-process is known to occur in AGB stars. What is the evidence which supports this?

20. Stars are categorized as low or high mass stars based on what criterion? Whydoes the Sun's nuclear processing in its core stop after helium burning?