ASTR 321
Final

1. Solve the stellar structure equations to find the pressure structure for a star with uniform density distribution. If the pressure in the star is given by the perfect gas law, find the temperature structure of the star. Find the radius at which the nuclear energy generation rate (assuming the proton-proton chain) falls by 50 % compared to its value at the center of the star. Repeat the calculation for a star dominated by radiation pressure.

2. In a Type Ia SN, carbon ignites when the density is around 1,000,000,000 gm per cubic centimeter. For a 1.4 Solar mass white dwarf, this density corresponds to what radius? Show that carbon burning will disrupt the white dwarf. Carbon burning reactions yield ~0.001 Mc² where M is the amount of mass processed.

3. Sketch a typical Type Ia SN light curve. Be sure to label your plot. Describe the energy source for each phase of the evolution of the light curve. Be quantitative. Note

Ni⁵⁶+e^- ---> Co⁵⁶ + neutrino + 2.72x10^-6erg, and
Co⁵⁶+e^- ---> Fe⁵⁶ + neutrino + 5.76x10^-6erg

4. SN 1987a is, arguably, the single most important observational result in stellar evolution over the last 50 years. Argue why this is so and cite results which support your answer.

5. Calculate the energy released during the SN 1987a outburst. How long did the different parts of the outburst last? What were the significant parts of SN 1987a's energy budget? Support your answer with rough, but appropriate, observational results.

6. Estimate the energy liberated in the following stellar events:

• normal nuclear burning lifetime of the Sun
• normal nuclear burning lifetime of a 25 solar mass star
• Type Ia SN event
• Type II SN event

7. Estimate the lifetime of the horizontal branch of stellar evoution of a star like the Sun.

• Compute the energy released in the triple-alpha (helium burning) reactions. The mass of He and C are 4.00026 a.m.u. and 12.00000 a.m.u., respectively, where 1 a.m.u. (atomic mass unit) is 1.6606x10^-24 gm.
• Assume that the helium core contains 10 $ of the mass of the star. Comment on this estimate for a star like the Sun. How much energy is released during the triple-alpha process for the helium core?
• On the horizontal branch, a sun-like star has luminosity around 100 times larger than its main sequence luminosity. Find the horizontal branch lifetime for a sun-like star.