1) Two stars, Rigel and Procyon, have the same composition and the same surface temperature. Neither star has a significant rotation velocity. When spectra are taken of the two stars, Astronomers notice that the absorption lines in Procyon's spectrum are much narrower than those in Rigel's spectrum. You may assume for this problem that there is no interstellar material (gas or dust) that is found along our line of sight to either star.

a) (3 pts) Rigel is probably (larger, smaller, the same size) compared to Procyon.

b) (8 pts) Explain your answer to part (a). Just saying something like, "Rigel is ____________ compared to Procyon because it has narrower lines." will result in no credit. You need to explain why line width has anything to do (or nothing to do) with the size of a star.

2) Energy in stars is typically transported from the core to the surface by radiation, convection or a combination of the two.

a) (3 pts) In the region of the Sun's envelope close to the core, energy is transported mainly via (radiation, convection).

b) (8 pts) Explain your answer to part (a).

3) Suppose we were to design a catalog of all binary star systems close enough to the Earth that we can measure the angular separation of the central star and the companion star. Would this be a representative sample of binary star systems? Justify your answer.

4) A star like Sirius (surface temperature of 12,000 K) has very strong Helium absorption lines. A nearby star in the sky, Betelgeuse (surface temperature of 3,500 K) has no Helium absorption lines. Helium's atomic structure is such that it can only be excited if temperatures are higher than about 9,000 K.

a) (3 pts) The abundance of Helium in Sirius is (greater than, the same as, less than, can't be determined) the abundance of Helium in Betelgeuse.

b) (8 pts) Explain your answer to part (a). Just saying "Abundance in Sirius is ______________ compared to the abundance in Betelgeuse because Sirius is hotter" will result in no credit. You must explain why or why not temperature has something to do with Helium abundance in this case.

5) In a face-on binary system, Astronomers try to measure the mass of the central star using the equation of orbital velocity:

System A and System B are both measured to have identical orbital distances from the central star to the companion star. System A's companion, however, is found to have an orbital period twice as long as System B.

a) (4 pts) Explain why the orbital velocity for this system is not directly observable.

b) (7 pts) Which system's central star is more massive? Justify your answer either mathematically or in a couple of sentences.

6) Suppose you're an alien astronomer looking at our own solar system with an edge-on perspective. From your vantage point, your spectral observations show that as the Earth orbits the Sun, the absorption lines seen from Earth's atmosphere will shift from red to blue depending on the Earth's motion. Suppose you decide to point your telescope at Venus, a planet closer to the Sun than Earth. Will the spectral lines caused by Venus shift more or less than Earth's spectral lines? Use the equation of orbital velocity (elsewhere in this exam) to help explain your answer.

7) The Sun's corona is often studied during solar eclipses when light from the photosphere is completely blocked by the Moon.

a) (3 pts) When viewing a spectrum of the corona during a total eclipse, what kind of spectrum would you see (emission lines, absorption lines, continuous)?

b) (8 pts) Explain what causes the corona to have an extremely high temperature.

8) Aldebaran has a surface temperature of approximately 4,000 K (compared to our own Sun's surface temperature of 6,000 K).

a) (3 pts) The intensity of light emitted by Aldebaran peaks at (a higher frequency, a lower frequency, the same frequency) compared to the Sun's intensity.

b) (8 pts) Explain your answer to part (a). Just saying something like, "Aldebaran peaks at ___________ frequency compared to the Sun because it is hotter." will result in no credit. You need to explain why temperature has anything to do (or nothing to do) with the location of peak frequency.

9) The atom below contains an electron in the energy level E=8. The electron can move as shown in A, B, C, D or E depending on the circumstances.

a) (3 pts) Which case represents the electron emitting the longest wavelength of light?

b) (8 pts) Explain your answer to part (a).

10) The equation for absolute luminosity and the inverse square law are given below:

Star A has the same apparent luminosity and the same size as star B, but star A has a lower surface temperature (6,000 K) than star B (12,000 K). Assuming there is no need for a correction factor due to reddening and/or extinction...

a) (3 pts) Which of these two stars is closer to Earth (A, B, same distance)?

b) (8 pts) Explain your answer to part (a).