Exam 2

Due: Friday, March 3, 1995

Answer 4 out of the 5 following questions.

Question 1

• The Sun is currently in the Main Sequence phase of its evolution (see notes of January xx, 1995). In ~ 5 billion years, it will run out of hydrogen in its core.
  • In response, the core will start to contract. Estimate how quickly it will contract. Explain how you arrive at your answer.
  • Helium ignites at around 100,000,000 Kelvins. Estimate how large the core will be and the density of the core material at this point in time? Will the core be degenerate?
  • After the helium in the core is exhausted, the core will again contract. Carbon burning starts at around 800,000,000 Kelvins. Estimate how large the core of the Sun would be and what the density of the core material would be at this time?
  • The Sun will not burn carbon. Use your answer to the previous part to justify this statement.

Question 2

The Russell-Vogt Theorem is not an actual theorem but it is still a useful idea for understanding stellar structure and evolution. Suppose that I relaxed some of the conditions of the Russell-Vogt Theorem (as stated in class); would the theorem still remain valid? Cite counter-examples to the theorem if you argue that the theorem is not valid and provide explanations when the answer is not obvious. Loosen the constraint of:

• similar chemical composition
• energy generation by nuclear fusion
• thermal equilibrium

Question 3

Describe the evolution of a 25 solar mass star whose initial chemical composition was pure helium (and not 90 % hydrogen and 10 % helium and trace amounts of everything else). Ignore the star formation process. Trace the path that the star would follow on the Hertzsprung-Russell diagram. Be sure to indicate where and how the properties of the star would differ from those of a 25 solar mass star with normal chemical composition.

Question 4

Before a 25 solar mass star undergoes a Supernova outburst, it has a radius of around 680,000,000 kilometers. During the Supernova explosion, a neutron star of 1.4 solar masses and radius of 10 kilometers is formed and the outer 23.6 solar masses is ejected and escapes to infinity with a speed of around 10,000 kilometers per second. The Supernova radiates visible radiation at a rate of around 10,000,000,000 L(Sun) at its peak brightness.

How much total energy is contained in the:

• Photons (use this typical light curve for your estimate).
  • How does thi energy compare to say the energy radiated by a star like the Sun over its lifetime?
• Kinetic energy of the exploding star?
• How much energy is not yet accounted for?

This energy goes into neutrinos. The neutrinos are produced for around 10 - 30 seconds. What is the luminosity in neutrinos? How does this compare the peak visible luminosity?

Question 5

Based on things which were discussed in this course and covered in the text concering stellar structure and evolution, answer the following question. Suppose that you leave the Milky Way galaxy and return in 20 billion years, what will the Milky Way galaxy look like (and what will the Solar System be like)? Consider star formation rates, the kinds of stars you are likely to find (sketch what the HR diagram is likely to look like), the overall appearance of the Galaxy, ... . Be sure to provide explanations for your answer.