1) Star Alpha and Beta have the apparent luminosity and the same color, and we know there is no interstellar material along the line of sight to either star. However, the spectral absorption lines in the atmosphere of star Alpha are much broader than that of star Beta. Which of these two stars will show a larger parallax angle when measured from Earth? Explain your reasoning fully.

2) Suppose that, in order to try to create a representative sample of stars, we choose to determine the properties of the 10,000 stars that show the largest parallax angles as seen from the Earth.

a) (7 pts) Will our set of stars be representative of the Milky Way as a whole? Why or why not?

b) (7 pts) If our sample is truly representative, would you expect most of the stars to fall along the main sequence part of the H-R diagram or instead to be scattered all over the diagram? Explain.

3) Explain what the "brown dwarf desert" is and why most surveys that have looked for brown dwarfs as companions to other stars have been biased against finding brown dwarfs.

4) On the H-R diagram below the positions of two stars, A and B, are plotted relative to the location of the Sun. For each of the two stars, state whether it is larger, smaller or the same size as the Sun and justify your answer mathematically or in words. You donıt need to write down an exact value for the size, just indicate how you came to your answer.

5) Binary system A and B are both binary systems measured to have identical companion star Doppler shifts and identical orbital distances between central star and companion star. However, system A is discovered to be an eclipsing binary while system B is not eclipsing. Which systemıs central star has a higher absolute luminosity based on this information, A or B? Justify your answer fully.

6) Suppose two stars, A and B, have the same size, same red color and the same apparent luminosity as seen from Earth . Star A, however, is measured to have a much thicker concentration of interstellar dust and gas along the line of sight to it from interstellar absorption/emission lines. If we donıt correct for the effects of the ISM, our estimate of the distances to both stars is that they are equal.

a) (6 pts) Assuming we determine the distance to these two stars by using the color to estimate temperature and thus absolute luminosity, which of these two stars is truly further away? Justify your answer.

b) (8 pts) Some of the interstellar emission lines along our line of sight are "forbidden lines". In 1-2 sentences, state how a "forbidden line" differs from an ordinary spectral emission line, then explain why such lines only occur in regions of very low density.

7) During the main sequence lifetime of the Sun, over the past 4.5 billion years, it has gradually gotten brighter by a total of about 30% of its original absolute luminosity.

a) (7 pts) Describe one change in the core that has led to this increase in size and thus absolute luminosity for the entire star.

b) (7 pts) The increased brightness of the Sun is related to the "Faint Sun Paradox". Briefly explain what this paradox is and how the Earth has "resolved" the paradox.

8) A certain globular cluster is observed closely so that the properties of its stars can be plotted on an H-R diagram. The resulting data looks like the graph below, with the Sunıs location on the diagram shown for reference only (the Sun is not a part of this globular cluster). Are the stars in this cluster likely younger, older or the same age as the Sun? Justify your answer.