Physics 2083 - Introductory Astronomy - Spring 1998
Final Exam - Version D

Answer any 12 of the following 14 questions. Each is worth 8 points.

1) During the Helium-burning phase of a star's life, an "inner" core of inert Carbon slowly grows over time while the outer layers of the star expand.

a) (4 pts) Explain why the outer layers of the star expand.

b) (4 pts) Explain why the inner core, in which no fusion occurs, doesn't collapse under the force of its own gravity.

2) Suppose we want to measure the orbital velocity and orbital distance of an eclipsing binary system in order to determine the mass of the central star in the system. But we have a problem: our spectrograph is broken, so we can’t use Doppler shifts to determine the orbital velocity of the companion star! Assuming we know the orbital distance from the central star to the companion star via other means and that we can measure the period of the orbit from the light curve, explain how we can find the orbital velocity of the companion star.

3) Star Gamma has the same size (R) and temperature (T) as our Sun. Star Delta is twice the size of our Sun and half the temperature. Be sure to show your work on this problem if you wish to possibly receive partial credit for an incorrect answer.

a) (4 pts) Which star has a higher absolute luminosity (Gamma, Delta, same luminosity)?

b) (4 pts) Assuming both stars have the same apparent brightness and that there is no intervening material, which star is further away? (Gamma, Delta, same distance)

4) As a star ends its main-sequence lifetime, it expands to hundreds of times its original size and the surface temperature drops considerably.

a) (4 pts) Explain what happens to the rotation speed of the star during this expansion and why.

b) (4 pts) Explain why the surface temperature of the star appears cooler.

5) A crucial factor in directly detecting extrasolar planets is resolving the angular separation between the planets and the stars they’re orbiting and then actually trying to see the planet in the glare of the bright star.

a) (4 pts) Why might observing at relatively long infrared wavelengths actually make resolving the separation between the star and the planet more difficult?

b) (4 pts) How does observing in the infrared make this observation easier? You may wish to use a graph or a diagram to help answer this question.

6) Suppose we’re looking at a region of the sky that we know has a uniform distribution of stars. The apparent distribution of stars is not uniform for some reason, as shown in the diagram below. Region A appears to have a higher density of stars than region B.

a) (2 pts) Stars in region B will typically be (redder, bluer, no different) compared to stars in region A.

b) (6 pts) Explain your answer to part (a).

7) Extremely hot stars are known to be quite young and so they must have a fairly high metallicity. However, if you take a spectrum of such a star, you’ll see very few (if any!) spectral absorption lines. Explain why.

8) When we plot the radial velocities of galaxies against their redshifts, we come up with a graph like the one shown below.

a) (2 pts) Which of the three labeled galaxies is most likely to be an elliptical galaxy?

b) (6 pts) Explain your answer to part (a).

9) The fact that the Sun looks cooler and darker near its edges is a phenomenon known as limb darkening. Explain what this proves about the temperature structure of the Sun from the photosphere inward. Don’t just state what the Sun is like...state how we know this!

10) Below are parts of two stellar spectra (both containing the same pattern of Carbon absorption lines), one for Altair and one for Procyon. Both stars have the same size, rotation speed and orientation, and the star Altair is at rest relative to the Earth (it is not moving toward us or away from us).

a) (2 pts) Which star is hotter (Altair, Procyon, same temperature)?

b) (6 pts) Explain your answer to part (a).

11) Describe how you would go about calibrating the “standard ruler” method by finding the average linear size of a nearby collection of the galaxies. Also, describe why this method is not considered to be very reliable for determining distances.

12) Below is the spectrum of Arcturus, compared to that of our Sun, which peaks in the middle of the visible region (yellow) of the spectrum as seen below.

a) (2 pts) What color does Arcturus appear to have (assume no intervening material)?

b) (2 pts) Using a filter that only allowed us to see red light, which of the two stars would appear brighter (assume no intervening material)? (Arcturus, the Sun, same)

c) (4 pts) Explain your answer to part (b).

13) When we look out at the distribution of stars in the Milky Way, we find that most red stars are found at high galactic latitudes. Explain in detail why red stars (more so than blue stars) are seen at high galactic latitudes.

14) When we look at the absorption line spectrum of the star Aldebaran, one of the visible lines there is singly-ionized Oxygen (O II). The absorption line spectrum of the star Mizar contains absorption lines from triply-ionized Oxygen (O IV).

a) (2 pts) Which of the two stars probably has the higher metallicity (you must choose one or the other and argue your case below)?

b) (6 pts) Explain your answer to part (a).