Download Final for Astro 322, Prof. Heinke, April 23rd, 2010 Formula sheet

Final for Astro 322, Prof. Heinke, April 23rd, 2010
Formula sheet, sheet of constants, and a calculator are allowed.
Show your work, and write clearly. The 5 questions have equal weight; the
sub-questions may have different weights.
Problem 1: Variable star
a) We use HST to observe a bright star in the nearby galaxy M51 that varies periodically,
with a period of 8.5 days. What kind of star is this likely to be?
b) The star has an average visual magnitude of 25.53. Measurements of its optical spectra
suggest a color excess E(B − V ) = 0.1 due to extinction. What is the distance to M51?
c) What redshift (in km/s) do you expect for this galaxy? Take H0 = 71 km/s/Mpc.
d) If you assume that M51 lies in a group with mass 5 × 1013 M and ap =100 kpc, what is
the size of the peculiar velocity you might expect, on average?
e) Considering c) and d), would you be able to figure out the rate of expansion of the
universe using galaxies like this one in distance and environment? How could you get a
better measurement?
Problem 2: Mystery galaxy
We observe a far-infrared luminosity of 4 × 1038 W (∼100 × the Milky Way’s bolometric
luminosity) from a galaxy.
a) If the peak of the emission is at 50 µm, what is the typical temperature of the emitting
material?
b) What is the emitting material likely to be?
c) What are two possibilities for the original source of the energy we see? (Describe each in
a couple of sentences.) They are not necessarily exclusive.
d) What do you think this galaxy’s recent history has been, and what will happen to it now?
Problem 3: Distorted galaxy, and dark matter
a) We see a galaxy that appears to make a ring (radius 16”) around the center of a cluster
of galaxies. Emission lines in this strange galaxy are shifted from those in the cluster. What
do you think is happening?
b) The cluster is at d = 250 Mpc, the strange galaxy at d = 500 Mpc. What is the amount
of mass enclosed within the ring?
c) Describe one method to show the existence of dark matter in clusters of galaxies.
d) Why is it so hard to directly detect dark matter particles?
e) Describe one of the methods used to try to detect (directly or indirectly) dark matter
particles.
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Problem 4: Ellipticals
a) Why do we expect to find gas in elliptical galaxies, even if all the stars were formed 10
billion years ago?
b) Compute the virial temperature of gas in an elliptical galaxy. The total (three-dimensional)
velocity dispersion of the stars is 433 km/s.
c) Why is gas in elliptical galaxies hotter than gas in spirals?
d) Which of these features in elliptical galaxies indicate a recent merger? Explain for each
feature, why it does or does not.
i) Strong absorption lines of H.
ii) Strong rotation.
iii) “Disky” isophotes.
iv) Spherical shells of stars.
Problem 5: AGN & Clusters
a) A distant quasar is observed to be emitting at L = 3.9 × 1040 W. What can we say about
the mass of the central black hole?
b) Many rich galaxy clusters emit LX ∼ 1011 L in X-rays from their hot gas (assume this
stays constant). Estimate the total energy output from the hot gas in a rich galaxy cluster
over the universe’s lifetime.
c) Assume a massive central AGN (inside the cluster mentioned in part b) has 10% efficiency
(on average) in converting infalling mass to energy, that 10% of this liberated energy is
deposited into cluster gas, and that heating by the central AGN has balanced the cluster’s
gas’s cooling over the history of the universe. What is the minimum mass of the black hole
in this AGN?
d) Explain (roughly) the mechanism by which an AGN deposits energy into hot cluster gas.
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