Astronomy 10 Spring 2000

Homework #7

Due in one week.

Be careful of units and use appropriate precision. Be sure to explain your reasoning on each problem, so you can get partial credit for your work. Answers without explanations are not acceptable. You are encouraged to work together, but please write this up yourself.

1) If The ``Milky Way" as seen from Astra is a narrow band of light that stretches from horizon to horizon in the middle of summer, but is not seen at all in the winter (it only covers half the celestial sphere). What does this imply about Astra's location in the Galaxy?

2) A supernova occurs in a galaxy 150 million ly distant with the same intrinsic luminosity as Supernova 1987A.

a) how much fainter will it appear than SN 1987A (which was in the Large Magellanic Cloud 150000 ly away)?

b) using a value of the Hubble constant of 25 km/s/million ly, what is the redshift z (z = Dl/l) of the emission lines in the supernova?

3) We can see normal galaxies out to about a third of a billion light years.

a) If quasars are about 1000 times more luminous than normal galaxies, to what distance could you see them?

b) What are the Hubble velocities at each distance, using H = 25 km/s/million ly (the further distance is actually subject to relativistic corrections that we ignore).

c) If a normal galaxy has a luminosity of 10¹¹ solar luminosities, and the power for a quasar comes from accretion into a black hole which is 10% efficient in converting mass into energy, how much mass (in solar masses) does the quasar need to be eating (per second or per year). [Hint: how much mass does the Sun consume to produce one solar luminosity?]

4) The Hubble Law states that as seen from the Milky Way, distant galaxies recede from us with a recession velocity proportional to their distance: V_H = H D.

Students often interpret this to suggest that the Milky Way is at the center of the Universe, but this is not the case. Show this in the following way:

Draw a line with 20 even tics on it or use graph paper. Place galaxies at tic numbers 4,8,10,13, and 17. Now imagine that the line (Universe) has expanded by a factor of 2 during a time interval called a tock, so that each tic has become two tics (you can either redraw the line twice as long, or place a tic between each original tic and imagine the redrawing is half-scale). The velocity of each galaxy as seen from a given one is found by counting how many tics have been added between it and the given one in one tock (v = change in distance /time = # tics added /1 tock ). Show that the Hubble law as seen from the second galaxy is the same as seen from the fourth galaxy by making two tables of the velocity versus distance to all other galaxies as seen from each of the two given galaxies. Use the tables to prove that the velocity is proportional to the distance. What is the Hubble constant in this example (be sure to specify its units)?