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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.