Answer any 9 of the following 10 questions. Each is worth 11 points.
1) A common emission line seen in interstellar nebulae corresponds to a particular electron transition in singly-ionized Oxygen (also called O II). Because this transition is extremely unlikely to occur at any given time, this kind of emission line is often referred to by astronomers as a "forbidden line".
2) In some binary star systems, the two stars are so close together than one of them will actually transfer its mass to the other. Suppose a given star loses some of its mass in this fashion. Use Hydrostatic Equilibrium to explain how the core temperature of that star will change as a result.
3) A black hole is also known as a "singularity" because the entire mass of the object is thought to be concentrated in a single infinitesimal point. Gravitational force can be calculated using the following equation:
4) Astronomers tell us that the absolute luminosity of a star is directly proportional to that staršs mass cubed (i.e. a star twice as massive as the Sun would be eight times more luminous). We also know that the self-gravity of a star is directly proportional to the staršs mass (i.e. a star twice as massive as the Sun would hold itself together with a self-gravity twice as strong).
A careful study of the main sequence in the H-R diagram reveals that the sizes of main sequence stars are proportional to the masses of the stars. In other words, the more massive a main sequence star, the larger we expect it to be. Explain why.
5) For this question, you may wish to refer to the inverse square law, given elsewhere in this exam. The Cepheid Period-Luminosity relationship tells us that the period of a Cepheid is directly proportional to its absolute luminosity. Suppose we observe Cepheids in two different nearby galaxies with no intervening interstellar material interfering with our observations. In both galaxies, the apparent luminosities of the Cepheids are identical. In galaxy A, the period of the Cepheid is much longer than the period of the Cepheid in galaxy B.
6) As a star evolves from the main sequence into the red giant phase of its lifetime, you may assume that angular momentum (mass * size * rotation speed) is conserved. Since the mass of the star remains the same while the size increases by a large factor, what can you conclude happens to the staršs rate of rotation? Explain your answer.
7) We often use the inverse square law to determine the distances to stars:
where the absolute luminosity is defined to be:
However, the effects of the interstellar medium (extinction and reddening) often cause errors in our distance estimates.
8) Suppose as a student project, you decide to determine the sizes, temperatures and masses of all of the stars visible in the sky tonight.
9) At the end of a star's main sequence, after hydrogen fusion ends, there is a brief period of time in the staršs development between the end of hydrogen fusion and (if the star is massive enough) the onset of Helium fusion.
10) Globular clusters are distributed uniformly around the center of our Milky Way Galaxy, and they can be used to deduce the age and size of our galaxy.