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Solutions to Homework 4
1. Properties of galaxies.
a. Using the web or some other suitable resource, find a picture of a spiral
galaxy and write down its catalog number (e.g. NGC 224 or M31) and/or
common name (e.g. Andromeda).
A good source is the Hubble Space Telescope archive.1
b. Sketch your galaxy and label the following parts: spiral arms (if visible),
bulge, nucleus, and disk. Feel free to label anything else of interest, such
as dust lanes, etc.
Bonus marks for extra labels.
c. What is the galaxy’s classification on the Hubble sequence (e.g., Sa, SBc,
etc.)? If you can’t find the classification in the literature, make your best
guess from the picture and explain your reasoning.
Bonus mark for discussing whether any classification found in the
literature seems reasonable or not.
d. Can you tell if star formation is actively going on in this galaxy? Explain.
Look for blue stars, especially associated with spiral arms and/or dust.
Since blue stars are massive, they have short lifetimes. Their presence
therefore indicates active star formation.
e. Finally, from the literature, report the size (diameter) of the galaxy in kpc
or lightyears, and its distance from us, if known.
The source for this information should be indicated.
2. Hubble’s law.
a. State Hubble’s law.
Hubble’s law states that the speed of recession of a galaxy is directly
proportional to the galaxy’s distance (the constant of proportionality is
called Hubble’s constant): v = H0d.
1
E.g. http://hubblesite.org/newscenter/newsdesk/archive/releases/category/galaxy/spiral/
b. Suppose we observe a galaxy to be receding from us at a speed of 15,000
km/s. If Hubble’s constant H0 has a value of 65 km/s/Mpc, how far away
is this galaxy?
From Hubble’s law, d = v/H0 = 15000/65 = 230 Mpc.
c. An astronomer observes one end of an edge-on spiral galaxy to have a
recession speed of 1,200 km/s and the other end to have a recession speed
of 800 km/s. How would you interpret this result? If H0 = 65 km/s/Mpc,
how far away is this galaxy?
The difference arises from the galaxy’s rotation, which evidently is (1200
– 800)/2 = 200 km/s towards us at one end and 200 km/s away from us at
the other. To find the distance, use the mean speed (i.e. (1200 + 800)/2 =
1000 km/s) in Hubble’s law to find d = 15.4 Mpc.
3. Dark matter.
a. Explain in your own words why we think galaxies like our own are made
up mostly of “dark matter”.
The best evidence for dark matter in large spiral galaxies comes from
measuring the rotation curves of these galaxies. If the mass of the galaxy
were centrally concentrated, the rotation speed should drop as the square
of the distance from the nucleus. Instead it appears the rotation curves
remain flat out to large distance (beyond the visible edge of the galaxy),
indicating the presence of unseen, or dark, matter.
b. Describe one candidate for dark matter.
Most mundane possibilities except WIMPs (Weakly Interacting Massive
Particles) can be ruled out. WIMPs are non-baryonic matter, i.e. not based
on protons and neutrons, which interact weakly with normal matter but
still exert gravity. WIMPs must be “clumpy”, that is, they must be able to
concentrate in galactic halos, so dynamically they cannot be too “hot”
(neutrinos are weakly interacting particles but are comparatively light and
travel at high speeds, so they cannot account for the dark matter in
galaxies). No WIMPs have yet been found; theoretical possibilities
include super-symmetric particles and gauge bosons.