1) Suppose we are observing a face-on binary system from the Earth. Careful study has allowed us to measure the angular size of the system, the period of the companion starıs orbit and (via parallax) the distance of this system from the Earth. Describe how you would combine all of this information to discover the mass of the central star in the system.

2) Suppose we construct a sample of the 10,000 stars that are closest to our own Sun (the only condition for being included in the sample is that it is one of the 10,000 closest stars). We find that this sample contains very few stars with high absolute luminosity.

a) (7 pts) Is this sample probably representative of the stars in the galaxy as a whole? Explain.

b) (7 pts) Why are there so few high absolute luminosity stars in this sample?

3) A common feature among gaseous nebula in our galaxy is the presence of ³forbidden² emission lines, usually from ions of Oxygen and Nitrogen. First, explain how forbidden emission lines are different from normal emission lines. Second, use this information to help explain why forbidden lines are typically not seen in lab spectra on Earth.

4) The Orion Nebula is an example of a star-forming region. In it, there are several newly formed stars with a variety of masses that have formed from a still-collapsing nearby molecular cloud.

a) (7 pts) Explain why the light emanating from this region is largely blue, even though most of the stars in the region are yellow or red.

b) (7 pts) Explain how and why the color of this region of stars will change over the next several billion years, assuming no new stars form from this point forward.

5) Binary system A has a central star exactly like our Sun. The companion star to system A has an orbital distance of 100 million miles and an orbital period of about one year. Binary system B has a companion star also with an orbital distance of about 50 million miles, but its orbital period is the same as the companion to star A (about one year).

a) (7 pts) Which of these two systems has a central star that is more massive? Justify your answer.

b) (7 pts) Assuming both of these central stars are at the end of their main sequence lifetimes, which one probably has a higher metallicity? Explain both how you know which star probably formed first and why that fact is relevant to metallicity.

6) Studies of brown dwarf stars in the past have indicated that brown dwarfs are quite rare in the galaxy, but more recent studies that have avoided past problems with bias show that brown dwarfs are actually quite common.

a) (7 pts) The major feature distinguishing brown dwarfs from ordinary red stars is in the Lithium lines. Which type of star will tend to show Lithium lines in its spectrum and why?

b) (7 pts) Explain why past searches for brown dwarfs (which focused mainly on looking for them as binary companions to sun-like stars) turned up so few brown dwarfs compared to current searches. Specifically, how and why were the past searches biased against finding lots of brown dwarfs?

7) During a starıs main sequence lifetime, the density and temperature of the original core grows, which causes the absolute luminosity and outward-pushing pressure of the core to grow. Since the outward-pushing pressure is (temporarily, at certain times after the absolute luminosity has built up) larger than the self-gravity of the star, the star expands.

a) (6 pts) As the star gets larger, explain what happens to the density and temperature of the star. State how each changes and why each changes.

b) (8 pts) Explain what happens to the outward-pushing pressure and the self-gravity of the star during this expansion. Also answer: Why does the star stop expanding?

8) During their post-main-sequence evolution, stars with masses similar to the mass of the Sun will lose their outer layers in a planetary nebula.

a) (8 pts) Explain what a planetary nebula is and what causes it, and describe why very high mass stars do not undergo a planetary nebula phase.

b) (6 pts) Near the end of the massive starıs life, its core will attempt to fuse iron and collapse in the process, forming a neutron star during a supernova explosion. Explain why some of these neutron stars appear to us on Earth as pulsars while some do not (as part of your answer, briefly explain/show how pulsars work).