1) Below is a view of a binary star system seen almost edge-on from an observer on the Earth. You may assume that the central star is motionless with respect to the Earth. The direction of motion of the companion star is indicated. In position A, the companion star is *not* eclipsing the central star, but it is moving transverse to the line of sight of the observer. When the companion star moves around to point B in its orbit, itıs observed Doppler shift is at its maximum value.

a) (7 pts) When the companion star is in position A, are the spectral line fingerprints from the two stars in this system merged or split? Explain your answer in 1 sentence.

b) (7 pts) When the companion star is in position B, we can calculate its radial velocity based on its Doppler shift. Is this radial velocity equal to, greater than or less than its orbital velocity? Explain your answer.

2) 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 100 million miles, but its orbital period is longer (about two years).

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

b) (7 pts) Based on your research about brown dwarfs in binary systems, which of these two companion stars is more likely to be a brown dwarf? Explain your answer.

3) Suppose weıre looking at a region of the sky that we know has a uniform density of stars. However, when we observe and count the stars in the region, we see more stars in direction A than direction B.

Suppose we observe an individual star in region A and a star in region B. Both stars are known to have the same size (radius) since they are both main sequence stars, and both stars appear to have the same red color. Also, both stars have the same apparent luminosity. Which star is probably further away from the Earth? Explain your answer.

4) A 10-solar-mass molecular cloud collapses to form a star. While it is forming and during its main sequence lifetime, it undergoes changes in its interior.

a) (6 pts) As the cloud collapses to form a star in the first place (but before Hydrogen fusion begins), explain what happens to the density and temperature of the cloud. State how each changes and why each changes.

b) (8 pts) During the main sequence lifetime of the star (before Helium fusion begins), explain what happens to the density and temperature of the material that originally makes up the core of the star. State how each changes and why each changes.

5) 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?

6) At the end of the Sunıs main sequence lifetime, the Helium in the core will begin fusing into Carbon, and the star will swell to a size 100 times greater than it is today, becoming a red giant.

a) (6 pts) Explain why the Sun will have a red color, despite the fact that its core will be producing much more energy (absolute luminosity) than it did during its main sequence lifetime.

b) (8 pts) Explain why Helium fusion in the core of the Sun requires a much higher temperature and much higher density than Hydrogen fusion (explain each separately).

7) 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) A lot of ultraviolet light is also coming from the stars in this region. As it shines on the nearby molecular cloud, it helps in the formation of complex organic molecules often seen in these clouds. Explain how UV light helps these molecules form.

8) Suppose I plot the H-R diagram for a cluster of stars as shown below. The Sunıs location on the diagram is shown only for reference. The Sun is not actually a part of this cluster.

a) (7 pts) Compared to the Sunıs main sequence lifetime of 10 billion years, would you say this cluster is younger than 10 billion years, older than 10 billion years or about 10 billion years old? Explain your answer.

b) (7 pts) Assume there is a star X out there that is 10 billion years old. Based on your answer to part (a), would you expect the metallicity of this cluster to be greater than, less than or about the same as that of star X? As part of your answer, explain why metallicity is related to the age of a cluster.